diff --git a/go.mod b/go.mod index 3fa382d8..0884a28a 100644 --- a/go.mod +++ b/go.mod @@ -8,7 +8,7 @@ require ( github.com/hashicorp/errwrap v1.1.0 github.com/hashicorp/go-cleanhttp v0.5.2 github.com/hashicorp/terraform-plugin-sdk v1.17.2 - github.com/hashicorp/vault v1.7.10 + github.com/hashicorp/vault v1.13.10 github.com/jen20/awspolicyequivalence v1.1.0 github.com/mitchellh/go-homedir v1.1.0 gopkg.in/yaml.v2 v2.4.0 @@ -23,12 +23,14 @@ require ( github.com/Masterminds/goutils v1.1.1 // indirect github.com/Masterminds/semver/v3 v3.2.1 // indirect github.com/Masterminds/sprig/v3 v3.2.3 // indirect + github.com/ProtonMail/go-crypto v0.0.0-20230626094100-7e9e0395ebec // indirect github.com/agext/levenshtein v1.2.3 // indirect github.com/apparentlymart/go-cidr v1.1.0 // indirect github.com/apparentlymart/go-textseg/v15 v15.0.0 // indirect github.com/armon/go-radix v1.0.0 // indirect github.com/bgentry/go-netrc v0.0.0-20140422174119-9fd32a8b3d3d // indirect github.com/bgentry/speakeasy v0.1.0 // indirect + github.com/cloudflare/circl v1.3.3 // indirect github.com/fatih/color v1.15.0 // indirect github.com/frankban/quicktest v1.14.6 // indirect github.com/golang/groupcache v0.0.0-20210331224755-41bb18bfe9da // indirect diff --git a/go.sum b/go.sum index 227c171e..d187007c 100644 --- a/go.sum +++ b/go.sum @@ -1,8 +1,6 @@ -bazil.org/fuse v0.0.0-20160811212531-371fbbdaa898/go.mod h1:Xbm+BRKSBEpa4q4hTSxohYNQpsxXPbPry4JJWOB3LB8= cloud.google.com/go v0.26.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw= cloud.google.com/go v0.34.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw= cloud.google.com/go v0.38.0/go.mod h1:990N+gfupTy94rShfmMCWGDn0LpTmnzTp2qbd1dvSRU= -cloud.google.com/go v0.39.0/go.mod h1:rVLT6fkc8chs9sfPtFc1SBH6em7n+ZoXaG+87tDISts= cloud.google.com/go v0.44.1/go.mod h1:iSa0KzasP4Uvy3f1mN/7PiObzGgflwredwwASm/v6AU= cloud.google.com/go v0.44.2/go.mod h1:60680Gw3Yr4ikxnPRS/oxxkBccT6SA1yMk63TGekxKY= cloud.google.com/go v0.44.3/go.mod h1:60680Gw3Yr4ikxnPRS/oxxkBccT6SA1yMk63TGekxKY= @@ -56,7 +54,6 @@ cloud.google.com/go/bigquery v1.0.1/go.mod h1:i/xbL2UlR5RvWAURpBYZTtm/cXjCha9lbf cloud.google.com/go/bigquery v1.3.0/go.mod h1:PjpwJnslEMmckchkHFfq+HTD2DmtT67aNFKH1/VBDHE= cloud.google.com/go/bigquery v1.4.0/go.mod h1:S8dzgnTigyfTmLBfrtrhyYhwRxG72rYxvftPBK2Dvzc= cloud.google.com/go/bigquery v1.5.0/go.mod h1:snEHRnqQbz117VIFhE8bmtwIDY80NLUZUMb4Nv6dBIg= -cloud.google.com/go/bigquery v1.6.0/go.mod h1:hyFDG0qSGdHNz8Q6nDN8rYIkld0q/+5uBZaelxiDLfE= cloud.google.com/go/bigquery v1.7.0/go.mod h1://okPTzCYNXSlb24MZs83e2Do+h+VXtc4gLoIoXIAPc= cloud.google.com/go/bigquery v1.8.0/go.mod h1:J5hqkt3O0uAFnINi6JXValWIb1v0goeZM77hZzJN/fQ= cloud.google.com/go/bigquery v1.42.0/go.mod h1:8dRTJxhtG+vwBKzE5OseQn/hiydoQN3EedCaOdYmxRA= @@ -166,7 +163,6 @@ cloud.google.com/go/securitycenter v1.13.0/go.mod h1:cv5qNAqjY84FCN6Y9z28WlkKXyW cloud.google.com/go/securitycenter v1.14.0/go.mod h1:gZLAhtyKv85n52XYWt6RmeBdydyxfPeTrpToDPw4Auc= cloud.google.com/go/servicedirectory v1.4.0/go.mod h1:gH1MUaZCgtP7qQiI+F+A+OpeKF/HQWgtAddhTbhL2bs= cloud.google.com/go/servicedirectory v1.5.0/go.mod h1:QMKFL0NUySbpZJ1UZs3oFAmdvVxhhxB6eJ/Vlp73dfg= -cloud.google.com/go/spanner v1.5.1/go.mod h1:e1+8M6PF3ntV9Xr57X2Gf+UhylXXYF6gI4WRZ1kfu2A= cloud.google.com/go/speech v1.6.0/go.mod h1:79tcr4FHCimOp56lwC01xnt/WPJZc4v3gzyT7FoBkCM= cloud.google.com/go/speech v1.7.0/go.mod h1:KptqL+BAQIhMsj1kOP2la5DSEEerPDuOP/2mmkhHhZQ= cloud.google.com/go/storage v1.0.0/go.mod h1:IhtSnM/ZTZV8YYJWCY8RULGVqBDmpoyjwiyrjsg+URw= @@ -191,68 +187,12 @@ cloud.google.com/go/webrisk v1.4.0/go.mod h1:Hn8X6Zr+ziE2aNd8SliSDWpEnSS1u4R9+xX cloud.google.com/go/webrisk v1.5.0/go.mod h1:iPG6fr52Tv7sGk0H6qUFzmL3HHZev1htXuWDEEsqMTg= cloud.google.com/go/workflows v1.6.0/go.mod h1:6t9F5h/unJz41YqfBmqSASJSXccBLtD1Vwf+KmJENM0= cloud.google.com/go/workflows v1.7.0/go.mod h1:JhSrZuVZWuiDfKEFxU0/F1PQjmpnpcoISEXH2bcHC3M= -code.cloudfoundry.org/gofileutils v0.0.0-20170111115228-4d0c80011a0f/go.mod h1:sk5LnIjB/nIEU7yP5sDQExVm62wu0pBh3yrElngUisI= dmitri.shuralyov.com/gpu/mtl v0.0.0-20190408044501-666a987793e9/go.mod h1:H6x//7gZCb22OMCxBHrMx7a5I7Hp++hsVxbQ4BYO7hU= -git.apache.org/thrift.git v0.12.0/go.mod h1:fPE2ZNJGynbRyZ4dJvy6G277gSllfV2HJqblrnkyeyg= -github.com/Azure/azure-pipeline-go v0.2.3/go.mod h1:x841ezTBIMG6O3lAcl8ATHnsOPVl2bqk7S3ta6S6u4k= -github.com/Azure/azure-sdk-for-go v36.2.0+incompatible/go.mod h1:9XXNKU+eRnpl9moKnB4QOLf1HestfXbmab5FXxiDBjc= -github.com/Azure/azure-sdk-for-go v44.0.0+incompatible/go.mod h1:9XXNKU+eRnpl9moKnB4QOLf1HestfXbmab5FXxiDBjc= -github.com/Azure/azure-sdk-for-go v51.1.0+incompatible/go.mod h1:9XXNKU+eRnpl9moKnB4QOLf1HestfXbmab5FXxiDBjc= -github.com/Azure/azure-storage-blob-go v0.11.0/go.mod h1:A0u4VjtpgZJ7Y7um/+ix2DHBuEKFC6sEIlj0xc13a4Q= -github.com/Azure/go-ansiterm v0.0.0-20170929234023-d6e3b3328b78/go.mod h1:LmzpDX56iTiv29bbRTIsUNlaFfuhWRQBWjQdVyAevI8= -github.com/Azure/go-autorest v14.2.0+incompatible/go.mod h1:r+4oMnoxhatjLLJ6zxSWATqVooLgysK6ZNox3g/xq24= -github.com/Azure/go-autorest/autorest v0.9.0/go.mod h1:xyHB1BMZT0cuDHU7I0+g046+BFDTQ8rEZB0s4Yfa6bI= -github.com/Azure/go-autorest/autorest v0.9.2/go.mod h1:xyHB1BMZT0cuDHU7I0+g046+BFDTQ8rEZB0s4Yfa6bI= -github.com/Azure/go-autorest/autorest v0.9.3/go.mod h1:GsRuLYvwzLjjjRoWEIyMUaYq8GNUx2nRB378IPt/1p0= -github.com/Azure/go-autorest/autorest v0.10.1/go.mod h1:/FALq9T/kS7b5J5qsQ+RSTUdAmGFqi0vUdVNNx8q630= -github.com/Azure/go-autorest/autorest v0.11.0/go.mod h1:JFgpikqFJ/MleTTxwepExTKnFUKKszPS8UavbQYUMuw= -github.com/Azure/go-autorest/autorest v0.11.17/go.mod h1:eipySxLmqSyC5s5k1CLupqet0PSENBEDP93LQ9a8QYw= -github.com/Azure/go-autorest/autorest/adal v0.5.0/go.mod h1:8Z9fGy2MpX0PvDjB1pEgQTmVqjGhiHBW7RJJEciWzS0= -github.com/Azure/go-autorest/autorest/adal v0.6.0/go.mod h1:Z6vX6WXXuyieHAXwMj0S6HY6e6wcHn37qQMBQlvY3lc= -github.com/Azure/go-autorest/autorest/adal v0.7.0/go.mod h1:Z6vX6WXXuyieHAXwMj0S6HY6e6wcHn37qQMBQlvY3lc= -github.com/Azure/go-autorest/autorest/adal v0.8.0/go.mod h1:Z6vX6WXXuyieHAXwMj0S6HY6e6wcHn37qQMBQlvY3lc= -github.com/Azure/go-autorest/autorest/adal v0.8.1/go.mod h1:ZjhuQClTqx435SRJ2iMlOxPYt3d2C/T/7TiQCVZSn3Q= -github.com/Azure/go-autorest/autorest/adal v0.8.2/go.mod h1:ZjhuQClTqx435SRJ2iMlOxPYt3d2C/T/7TiQCVZSn3Q= -github.com/Azure/go-autorest/autorest/adal v0.9.0/go.mod h1:/c022QCutn2P7uY+/oQWWNcK9YU+MH96NgK+jErpbcg= -github.com/Azure/go-autorest/autorest/adal v0.9.2/go.mod h1:/3SMAM86bP6wC9Ev35peQDUeqFZBMH07vvUOmg4z/fE= -github.com/Azure/go-autorest/autorest/adal v0.9.5/go.mod h1:B7KF7jKIeC9Mct5spmyCB/A8CG/sEz1vwIRGv/bbw7A= -github.com/Azure/go-autorest/autorest/adal v0.9.11/go.mod h1:nBKAnTomx8gDtl+3ZCJv2v0KACFHWTB2drffI1B68Pk= -github.com/Azure/go-autorest/autorest/azure/auth v0.4.0/go.mod h1:Oo5cRhLvZteXzI2itUm5ziqsoIxRkzrt3t61FeZaS18= -github.com/Azure/go-autorest/autorest/azure/auth v0.4.2/go.mod h1:90gmfKdlmKgfjUpnCEpOJzsUEjrWDSLwHIG73tSXddM= -github.com/Azure/go-autorest/autorest/azure/auth v0.5.0/go.mod h1:QRTvSZQpxqm8mSErhnbI+tANIBAKP7B+UIE2z4ypUO0= -github.com/Azure/go-autorest/autorest/azure/auth v0.5.7/go.mod h1:AkzUsqkrdmNhfP2i54HqINVQopw0CLDnvHpJ88Zz1eI= -github.com/Azure/go-autorest/autorest/azure/cli v0.3.0/go.mod h1:rNYMNAefZMRowqCV0cVhr/YDW5dD7afFq9nXAXL4ykE= -github.com/Azure/go-autorest/autorest/azure/cli v0.3.1/go.mod h1:ZG5p860J94/0kI9mNJVoIoLgXcirM2gF5i2kWloofxw= -github.com/Azure/go-autorest/autorest/azure/cli v0.4.0/go.mod h1:JljT387FplPzBA31vUcvsetLKF3pec5bdAxjVU4kI2s= -github.com/Azure/go-autorest/autorest/azure/cli v0.4.2/go.mod h1:7qkJkT+j6b+hIpzMOwPChJhTqS8VbsqqgULzMNRugoM= -github.com/Azure/go-autorest/autorest/date v0.1.0/go.mod h1:plvfp3oPSKwf2DNjlBjWF/7vwR+cUD/ELuzDCXwHUVA= -github.com/Azure/go-autorest/autorest/date v0.2.0/go.mod h1:vcORJHLJEh643/Ioh9+vPmf1Ij9AEBM5FuBIXLmIy0g= -github.com/Azure/go-autorest/autorest/date v0.3.0/go.mod h1:BI0uouVdmngYNUzGWeSYnokU+TrmwEsOqdt8Y6sso74= -github.com/Azure/go-autorest/autorest/mocks v0.1.0/go.mod h1:OTyCOPRA2IgIlWxVYxBee2F5Gr4kF2zd2J5cFRaIDN0= -github.com/Azure/go-autorest/autorest/mocks v0.2.0/go.mod h1:OTyCOPRA2IgIlWxVYxBee2F5Gr4kF2zd2J5cFRaIDN0= -github.com/Azure/go-autorest/autorest/mocks v0.3.0/go.mod h1:a8FDP3DYzQ4RYfVAxAN3SVSiiO77gL2j2ronKKP0syM= -github.com/Azure/go-autorest/autorest/mocks v0.4.0/go.mod h1:LTp+uSrOhSkaKrUy935gNZuuIPPVsHlr9DSOxSayd+k= -github.com/Azure/go-autorest/autorest/mocks v0.4.1/go.mod h1:LTp+uSrOhSkaKrUy935gNZuuIPPVsHlr9DSOxSayd+k= -github.com/Azure/go-autorest/autorest/to v0.3.0/go.mod h1:MgwOyqaIuKdG4TL/2ywSsIWKAfJfgHDo8ObuUk3t5sA= -github.com/Azure/go-autorest/autorest/to v0.4.0/go.mod h1:fE8iZBn7LQR7zH/9XU2NcPR4o9jEImooCeWJcYV/zLE= -github.com/Azure/go-autorest/autorest/validation v0.2.0/go.mod h1:3EEqHnBxQGHXRYq3HT1WyXAvT7LLY3tl70hw6tQIbjI= -github.com/Azure/go-autorest/autorest/validation v0.3.0/go.mod h1:yhLgjC0Wda5DYXl6JAsWyUe4KVNffhoDhG0zVzUMo3E= -github.com/Azure/go-autorest/autorest/validation v0.3.1/go.mod h1:yhLgjC0Wda5DYXl6JAsWyUe4KVNffhoDhG0zVzUMo3E= -github.com/Azure/go-autorest/logger v0.1.0/go.mod h1:oExouG+K6PryycPJfVSxi/koC6LSNgds39diKLz7Vrc= -github.com/Azure/go-autorest/logger v0.2.0/go.mod h1:T9E3cAhj2VqvPOtCYAvby9aBXkZmbF5NWuPV8+WeEW8= -github.com/Azure/go-autorest/tracing v0.5.0/go.mod h1:r/s2XiOKccPW3HrqB+W0TQzfbtp2fGCgRFtBroKn4Dk= -github.com/Azure/go-autorest/tracing v0.6.0/go.mod h1:+vhtPC754Xsa23ID7GlGsrdKBpUA79WCAKPPZVC2DeU= -github.com/Azure/go-ntlmssp v0.0.0-20200615164410-66371956d46c/go.mod h1:chxPXzSsl7ZWRAuOIE23GDNzjWuZquvFlgA8xmpunjU= github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03qcyfWMU= github.com/BurntSushi/xgb v0.0.0-20160522181843-27f122750802/go.mod h1:IVnqGOEym/WlBOVXweHU+Q+/VP0lqqI8lqeDx9IjBqo= -github.com/DataDog/datadog-go v2.2.0+incompatible/go.mod h1:LButxg5PwREeZtORoXG3tL4fMGNddJ+vMq1mwgfaqoQ= -github.com/DataDog/datadog-go v3.2.0+incompatible/go.mod h1:LButxg5PwREeZtORoXG3tL4fMGNddJ+vMq1mwgfaqoQ= -github.com/Jeffail/gabs v1.1.1/go.mod h1:6xMvQMK4k33lb7GUUpaAPh6nKMmemQeg5d4gn7/bOXc= -github.com/Knetic/govaluate v3.0.1-0.20171022003610-9aa49832a739+incompatible/go.mod h1:r7JcOSlj0wfOMncg0iLm8Leh48TZaKVeNIfJntJ2wa0= github.com/Masterminds/goutils v1.1.0/go.mod h1:8cTjp+g8YejhMuvIA5y2vz3BpJxksy863GQaJW2MFNU= github.com/Masterminds/goutils v1.1.1 h1:5nUrii3FMTL5diU80unEVvNevw1nH4+ZV4DSLVJLSYI= github.com/Masterminds/goutils v1.1.1/go.mod h1:8cTjp+g8YejhMuvIA5y2vz3BpJxksy863GQaJW2MFNU= -github.com/Masterminds/semver v1.4.2/go.mod h1:MB6lktGJrhw8PrUyiEoblNEGEQ+RzHPF078ddwwvV3Y= github.com/Masterminds/semver v1.5.0/go.mod h1:MB6lktGJrhw8PrUyiEoblNEGEQ+RzHPF078ddwwvV3Y= github.com/Masterminds/semver/v3 v3.1.1/go.mod h1:VPu/7SZ7ePZ3QOrcuXROw5FAcLl4a0cBrbBpGY/8hQs= github.com/Masterminds/semver/v3 v3.2.0/go.mod h1:qvl/7zhW3nngYb5+80sSMF+FG2BjYrf8m9wsX0PNOMQ= @@ -262,49 +202,21 @@ github.com/Masterminds/sprig v2.22.0+incompatible/go.mod h1:y6hNFY5UBTIWBxnzTeuN github.com/Masterminds/sprig/v3 v3.2.1/go.mod h1:UoaO7Yp8KlPnJIYWTFkMaqPUYKTfGFPhxNuwnnxkKlk= github.com/Masterminds/sprig/v3 v3.2.3 h1:eL2fZNezLomi0uOLqjQoN6BfsDD+fyLtgbJMAj9n6YA= github.com/Masterminds/sprig/v3 v3.2.3/go.mod h1:rXcFaZ2zZbLRJv/xSysmlgIM1u11eBaRMhvYXJNkGuM= -github.com/Microsoft/go-winio v0.4.13/go.mod h1:qXqCSQ3Xa7+6tgxaGTIe4Kpcdsi+P8jBhyzoq1bpyYA= github.com/Microsoft/go-winio v0.4.14/go.mod h1:qXqCSQ3Xa7+6tgxaGTIe4Kpcdsi+P8jBhyzoq1bpyYA= -github.com/Microsoft/go-winio v0.4.15-0.20190919025122-fc70bd9a86b5/go.mod h1:tTuCMEN+UleMWgg9dVx4Hu52b1bJo+59jBh3ajtinzw= -github.com/Microsoft/go-winio v0.4.16-0.20201130162521-d1ffc52c7331/go.mod h1:XB6nPKklQyQ7GC9LdcBEcBl8PF76WugXOPRXwdLnMv0= github.com/Microsoft/go-winio v0.4.16/go.mod h1:XB6nPKklQyQ7GC9LdcBEcBl8PF76WugXOPRXwdLnMv0= github.com/Microsoft/go-winio v0.6.1 h1:9/kr64B9VUZrLm5YYwbGtUJnMgqWVOdUAXu6Migciow= -github.com/Microsoft/hcsshim 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v1.3.3/go.mod h1:IbVyRI1SCnLcuJnV2u8VeU0CEYM7e686BmAb1XKL+uU= -go.etcd.io/bbolt v1.3.4/go.mod h1:G5EMThwa9y8QZGBClrRx5EY+Yw9kAhnjy3bSjsnlVTQ= -go.etcd.io/bbolt v1.3.5/go.mod h1:G5EMThwa9y8QZGBClrRx5EY+Yw9kAhnjy3bSjsnlVTQ= -go.etcd.io/etcd v0.0.0-20191023171146-3cf2f69b5738/go.mod h1:dnLIgRNXwCJa5e+c6mIZCrds/GIG4ncV9HhK5PX7jPg= -go.etcd.io/etcd v0.5.0-alpha.5.0.20200425165423-262c93980547/go.mod h1:YoUyTScD3Vcv2RBm3eGVOq7i1ULiz3OuXoQFWOirmAM= -go.mongodb.org/atlas v0.7.1/go.mod h1:CIaBeO8GLHhtYLw7xSSXsw7N90Z4MFY87Oy9qcPyuEs= -go.mongodb.org/mongo-driver v1.4.2/go.mod h1:WcMNYLx/IlOxLe6JRJiv2uXuCz6zBLndR4SoGjYphSc= -go.mongodb.org/mongo-driver v1.4.6/go.mod h1:WcMNYLx/IlOxLe6JRJiv2uXuCz6zBLndR4SoGjYphSc= -go.opencensus.io v0.19.1/go.mod h1:gug0GbSHa8Pafr0d2urOSgoXHZ6x/RUlaiT0d9pqb4A= -go.opencensus.io v0.19.2/go.mod h1:NO/8qkisMZLZ1FCsKNqtJPwc8/TaclWyY0B6wcYNg9M= -go.opencensus.io v0.20.1/go.mod h1:6WKK9ahsWS3RSO+PY9ZHZUfv2irvY6gN279GOPZjmmk= -go.opencensus.io v0.20.2/go.mod h1:6WKK9ahsWS3RSO+PY9ZHZUfv2irvY6gN279GOPZjmmk= go.opencensus.io v0.21.0/go.mod h1:mSImk1erAIZhrmZN+AvHh14ztQfjbGwt4TtuofqLduU= go.opencensus.io v0.22.0/go.mod h1:+kGneAE2xo2IficOXnaByMWTGM9T73dGwxeWcUqIpI8= go.opencensus.io v0.22.2/go.mod h1:yxeiOL68Rb0Xd1ddK5vPZ/oVn4vY4Ynel7k9FzqtOIw= @@ -1407,55 +659,22 @@ go.opencensus.io v0.23.0/go.mod h1:XItmlyltB5F7CS4xOC1DcqMoFqwtC6OG2xF7mCv7P7E= go.opencensus.io v0.24.0 h1:y73uSU6J157QMP2kn2r30vwW1A2W2WFwSCGnAVxeaD0= go.opencensus.io v0.24.0/go.mod h1:vNK8G9p7aAivkbmorf4v+7Hgx+Zs0yY+0fOtgBfjQKo= go.opentelemetry.io/proto/otlp v0.7.0/go.mod h1:PqfVotwruBrMGOCsRd/89rSnXhoiJIqeYNgFYFoEGnI= -go.uber.org/atomic v1.3.2/go.mod h1:gD2HeocX3+yG+ygLZcrzQJaqmWj9AIm7n08wl/qW/PE= -go.uber.org/atomic v1.4.0/go.mod h1:gD2HeocX3+yG+ygLZcrzQJaqmWj9AIm7n08wl/qW/PE= -go.uber.org/atomic v1.5.0/go.mod h1:sABNBOSYdrvTF6hTgEIbc7YasKWGhgEQZyfxyTvoXHQ= -go.uber.org/atomic v1.6.0/go.mod h1:sABNBOSYdrvTF6hTgEIbc7YasKWGhgEQZyfxyTvoXHQ= -go.uber.org/goleak v1.1.10/go.mod 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v0.0.0-20190604053449-0f29369cfe45/go.mod h1:gOpvHmFTYa4IltrdGE7lF6nIHvwfUNPOp7c8zoXwtLw= golang.org/x/oauth2 v0.0.0-20191202225959-858c2ad4c8b6/go.mod h1:gOpvHmFTYa4IltrdGE7lF6nIHvwfUNPOp7c8zoXwtLw= golang.org/x/oauth2 v0.0.0-20200107190931-bf48bf16ab8d/go.mod h1:gOpvHmFTYa4IltrdGE7lF6nIHvwfUNPOp7c8zoXwtLw= @@ -1609,7 +804,6 @@ golang.org/x/sync v0.0.0-20180314180146-1d60e4601c6f/go.mod h1:RxMgew5VJxzue5/jJ golang.org/x/sync v0.0.0-20181108010431-42b317875d0f/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20181221193216-37e7f081c4d4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20190227155943-e225da77a7e6/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= -golang.org/x/sync v0.0.0-20190412183630-56d357773e84/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20190911185100-cd5d95a43a6e/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20200317015054-43a5402ce75a/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= @@ -1620,76 +814,39 @@ golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJ golang.org/x/sync v0.0.0-20220601150217-0de741cfad7f/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20220929204114-8fcdb60fdcc0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= +golang.org/x/sync v0.1.0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.4.0 h1:zxkM55ReGkDlKSM+Fu41A+zmbZuaPVbGMzvvdUPznYQ= golang.org/x/sync v0.4.0/go.mod h1:FU7BRWz2tNW+3quACPkgCx/L+uEAv1htQ0V83Z9Rj+Y= -golang.org/x/sys v0.0.0-20170830134202-bb24a47a89ea/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY= -golang.org/x/sys 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h1:TB2adYChydJhpapKDTa4BR/hXlZSLoq2Wpct/0txZ28= golang.org/x/tools v0.0.0-20200122220014-bf1340f18c4a/go.mod h1:TB2adYChydJhpapKDTa4BR/hXlZSLoq2Wpct/0txZ28= golang.org/x/tools v0.0.0-20200130002326-2f3ba24bd6e7/go.mod h1:TB2adYChydJhpapKDTa4BR/hXlZSLoq2Wpct/0txZ28= @@ -1816,12 +954,9 @@ golang.org/x/tools v0.0.0-20200227222343-706bc42d1f0d/go.mod h1:TB2adYChydJhpapK golang.org/x/tools v0.0.0-20200304193943-95d2e580d8eb/go.mod h1:o4KQGtdN14AW+yjsvvwRTJJuXz8XRtIHtEnmAXLyFUw= golang.org/x/tools v0.0.0-20200312045724-11d5b4c81c7d/go.mod h1:o4KQGtdN14AW+yjsvvwRTJJuXz8XRtIHtEnmAXLyFUw= golang.org/x/tools v0.0.0-20200331025713-a30bf2db82d4/go.mod h1:Sl4aGygMT6LrqrWclx+PTx3U+LnKx/seiNR+3G19Ar8= -golang.org/x/tools v0.0.0-20200409170454-77362c5149f0/go.mod h1:EkVYQZoAsY45+roYkvgYkIh4xh/qjgUK9TdY2XT94GE= -golang.org/x/tools v0.0.0-20200416214402-fc959738d646/go.mod h1:EkVYQZoAsY45+roYkvgYkIh4xh/qjgUK9TdY2XT94GE= golang.org/x/tools v0.0.0-20200501065659-ab2804fb9c9d/go.mod 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h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA= golang.org/x/tools v0.0.0-20201208233053-a543418bbed2/go.mod h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA= -golang.org/x/tools v0.0.0-20210101214203-2dba1e4ea05c/go.mod h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA= golang.org/x/tools v0.0.0-20210105154028-b0ab187a4818/go.mod h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA= golang.org/x/tools v0.0.0-20210108195828-e2f9c7f1fc8e/go.mod h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA= golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0= @@ -1841,7 +975,8 @@ golang.org/x/tools v0.1.3/go.mod h1:o0xws9oXOQQZyjljx8fwUC0k7L1pTE6eaCbjGeHmOkk= golang.org/x/tools v0.1.4/go.mod h1:o0xws9oXOQQZyjljx8fwUC0k7L1pTE6eaCbjGeHmOkk= golang.org/x/tools v0.1.5/go.mod h1:o0xws9oXOQQZyjljx8fwUC0k7L1pTE6eaCbjGeHmOkk= golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc= -golang.org/x/tools v0.7.0 h1:W4OVu8VVOaIO0yzWMNdepAulS7YfoS3Zabrm8DOXXU4= +golang.org/x/tools v0.6.0/go.mod h1:Xwgl3UAJ/d3gWutnCtw505GrjyAbvKui8lOU390QaIU= +golang.org/x/tools v0.10.0 h1:tvDr/iQoUqNdohiYm0LmmKcBk+q86lb9EprIUFhHHGg= golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= @@ -1851,13 +986,7 @@ golang.org/x/xerrors v0.0.0-20220517211312-f3a8303e98df/go.mod h1:K8+ghG5WaK9qNq golang.org/x/xerrors v0.0.0-20220609144429-65e65417b02f/go.mod h1:K8+ghG5WaK9qNqU5K3HdILfMLy1f3aNYFI/wnl100a8= golang.org/x/xerrors v0.0.0-20220907171357-04be3eba64a2 h1:H2TDz8ibqkAF6YGhCdN3jS9O0/s90v0rJh3X/OLHEUk= golang.org/x/xerrors v0.0.0-20220907171357-04be3eba64a2/go.mod h1:K8+ghG5WaK9qNqU5K3HdILfMLy1f3aNYFI/wnl100a8= -google.golang.org/api v0.0.0-20181220000619-583d854617af/go.mod h1:4mhQ8q/RsB7i+udVvVy5NUi08OU8ZlA0gRVgrF7VFY0= -google.golang.org/api v0.2.0/go.mod h1:IfRCZScioGtypHNTlz3gFk67J8uePVW7uDTBzXuIkhU= -google.golang.org/api v0.3.0/go.mod h1:IuvZyQh8jgscv8qWfQ4ABd8m7hEudgBFM/EdhA3BnXw= -google.golang.org/api v0.3.1/go.mod h1:6wY9I6uQWHQ8EM57III9mq/AjF+i8G65rmVagqKMtkk= -google.golang.org/api v0.3.2/go.mod h1:6wY9I6uQWHQ8EM57III9mq/AjF+i8G65rmVagqKMtkk= google.golang.org/api v0.4.0/go.mod h1:8k5glujaEP+g9n7WNsDg8QP6cUVNI86fCNMcbazEtwE= -google.golang.org/api v0.5.0/go.mod h1:8k5glujaEP+g9n7WNsDg8QP6cUVNI86fCNMcbazEtwE= google.golang.org/api v0.7.0/go.mod h1:WtwebWUNSVBH/HAw79HIFXZNqEvBhG+Ra+ax0hx3E3M= google.golang.org/api v0.8.0/go.mod h1:o4eAsZoiT+ibD93RtjEohWalFOjRDx6CVaqeizhEnKg= google.golang.org/api v0.9.0/go.mod h1:o4eAsZoiT+ibD93RtjEohWalFOjRDx6CVaqeizhEnKg= @@ -1868,7 +997,6 @@ google.golang.org/api v0.17.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/ google.golang.org/api v0.18.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/sfE= google.golang.org/api v0.19.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/sfE= google.golang.org/api v0.20.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/sfE= -google.golang.org/api v0.21.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/sfE= google.golang.org/api v0.22.0/go.mod h1:BwFmGc8tA3vsd7r/7kR8DY7iEEGSU04BFxCo5jP/sfE= google.golang.org/api v0.24.0/go.mod h1:lIXQywCXRcnZPGlsd8NbLnOjtAoL6em04bJ9+z0MncE= google.golang.org/api v0.28.0/go.mod h1:lIXQywCXRcnZPGlsd8NbLnOjtAoL6em04bJ9+z0MncE= @@ -1910,11 +1038,8 @@ google.golang.org/api v0.100.0/go.mod h1:ZE3Z2+ZOr87Rx7dqFsdRQkRBk36kDtp/h+QpHbB google.golang.org/api v0.149.0 h1:b2CqT6kG+zqJIVKRQ3ELJVLN1PwHZ6DJ3dW8yl82rgY= google.golang.org/api v0.149.0/go.mod h1:Mwn1B7JTXrzXtnvmzQE2BD6bYZQ8DShKZDZbeN9I7qI= google.golang.org/appengine v1.1.0/go.mod h1:EbEs0AVv82hx2wNQdGPgUI5lhzA/G0D9YwlJXL52JkM= -google.golang.org/appengine v1.2.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4= -google.golang.org/appengine v1.3.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4= google.golang.org/appengine v1.4.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4= google.golang.org/appengine v1.5.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4= -google.golang.org/appengine v1.6.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4= google.golang.org/appengine v1.6.1/go.mod h1:i06prIuMbXzDqacNJfV5OdTW448YApPu5ww/cMBSeb0= google.golang.org/appengine v1.6.5/go.mod h1:8WjMMxjGQR8xUklV/ARdw2HLXBOI7O7uCIDZVag1xfc= google.golang.org/appengine v1.6.6/go.mod h1:8WjMMxjGQR8xUklV/ARdw2HLXBOI7O7uCIDZVag1xfc= @@ -1923,15 +1048,10 @@ google.golang.org/appengine v1.6.8 h1:IhEN5q69dyKagZPYMSdIjS2HqprW324FRQZJcGqPAs google.golang.org/appengine v1.6.8/go.mod h1:1jJ3jBArFh5pcgW8gCtRJnepW8FzD1V44FJffLiz/Ds= google.golang.org/genproto v0.0.0-20170818010345-ee236bd376b0/go.mod h1:JiN7NxoALGmiZfu7CAH4rXhgtRTLTxftemlI0sWmxmc= google.golang.org/genproto v0.0.0-20180817151627-c66870c02cf8/go.mod h1:JiN7NxoALGmiZfu7CAH4rXhgtRTLTxftemlI0sWmxmc= -google.golang.org/genproto v0.0.0-20181219182458-5a97ab628bfb/go.mod h1:7Ep/1NZk928CDR8SjdVbjWNpdIf6nzjE3BTgJDr2Atg= google.golang.org/genproto v0.0.0-20190307195333-5fe7a883aa19/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= -google.golang.org/genproto v0.0.0-20190404172233-64821d5d2107/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= google.golang.org/genproto v0.0.0-20190418145605-e7d98fc518a7/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= google.golang.org/genproto v0.0.0-20190425155659-357c62f0e4bb/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= google.golang.org/genproto v0.0.0-20190502173448-54afdca5d873/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= -google.golang.org/genproto v0.0.0-20190508193815-b515fa19cec8/go.mod h1:VzzqZJRnGkLBvHegQrXjBqPurQTc5/KpmUdxsrq26oE= -google.golang.org/genproto v0.0.0-20190513181449-d00d292a067c/go.mod h1:z3L6/3dTEVtUr6QSP8miRzeRqwQOioJ9I66odjN4I7s= -google.golang.org/genproto v0.0.0-20190530194941-fb225487d101/go.mod h1:z3L6/3dTEVtUr6QSP8miRzeRqwQOioJ9I66odjN4I7s= google.golang.org/genproto v0.0.0-20190801165951-fa694d86fc64/go.mod h1:DMBHOl98Agz4BDEuKkezgsaosCRResVns1a3J2ZsMNc= google.golang.org/genproto v0.0.0-20190819201941-24fa4b261c55/go.mod h1:DMBHOl98Agz4BDEuKkezgsaosCRResVns1a3J2ZsMNc= google.golang.org/genproto v0.0.0-20190911173649-1774047e7e51/go.mod h1:IbNlFCBrqXvoKpeg0TB2l7cyZUmoaFKYIwrEpbDKLA8= @@ -1947,10 +1067,7 @@ google.golang.org/genproto v0.0.0-20200224152610-e50cd9704f63/go.mod h1:55QSHmfG google.golang.org/genproto v0.0.0-20200228133532-8c2c7df3a383/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200305110556-506484158171/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200312145019-da6875a35672/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= -google.golang.org/genproto v0.0.0-20200323114720-3f67cca34472/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200331122359-1ee6d9798940/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= -google.golang.org/genproto v0.0.0-20200409111301-baae70f3302d/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= -google.golang.org/genproto v0.0.0-20200416231807-8751e049a2a0/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200430143042-b979b6f78d84/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200511104702-f5ebc3bea380/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= google.golang.org/genproto v0.0.0-20200513103714-09dca8ec2884/go.mod h1:55QSHmfGQM9UVYDPBsyGGes0y52j32PQ3BqQfXhyH3c= @@ -2040,25 +1157,15 @@ google.golang.org/genproto/googleapis/api v0.0.0-20231016165738-49dd2c1f3d0b/go. google.golang.org/genproto/googleapis/rpc v0.0.0-20231016165738-49dd2c1f3d0b h1:ZlWIi1wSK56/8hn4QcBp/j9M7Gt3U/3hZw3mC7vDICo= google.golang.org/genproto/googleapis/rpc v0.0.0-20231016165738-49dd2c1f3d0b/go.mod h1:swOH3j0KzcDDgGUWr+SNpyTen5YrXjS3eyPzFYKc6lc= google.golang.org/grpc v1.8.0/go.mod h1:yo6s7OP7yaDglbqo1J04qKzAhqBH6lvTonzMVmEdcZw= -google.golang.org/grpc v1.14.0/go.mod h1:yo6s7OP7yaDglbqo1J04qKzAhqBH6lvTonzMVmEdcZw= -google.golang.org/grpc v1.16.0/go.mod h1:0JHn/cJsOMiMfNA9+DeHDlAU7KAAB5GDlYFpa9MZMio= -google.golang.org/grpc v1.17.0/go.mod h1:6QZJwpn2B+Zp71q/5VxRsJ6NXXVCE5NRUHRo+f3cWCs= google.golang.org/grpc v1.19.0/go.mod h1:mqu4LbDTu4XGKhr4mRzUsmM4RtVoemTSY81AxZiDr8c= -google.golang.org/grpc v1.19.1/go.mod h1:mqu4LbDTu4XGKhr4mRzUsmM4RtVoemTSY81AxZiDr8c= -google.golang.org/grpc v1.20.0/go.mod h1:chYK+tFQF0nDUGJgXMSgLCQk3phJEuONr2DCgLDdAQM= google.golang.org/grpc v1.20.1/go.mod h1:10oTOabMzJvdu6/UiuZezV6QK5dSlG84ov/aaiqXj38= -google.golang.org/grpc v1.21.0/go.mod h1:oYelfM1adQP15Ek0mdvEgi9Df8B9CZIaU1084ijfRaM= google.golang.org/grpc v1.21.1/go.mod h1:oYelfM1adQP15Ek0mdvEgi9Df8B9CZIaU1084ijfRaM= -google.golang.org/grpc v1.22.0/go.mod h1:Y5yQAOtifL1yxbo5wqy6BxZv8vAUGQwXBOALyacEbxg= -google.golang.org/grpc v1.22.1/go.mod h1:Y5yQAOtifL1yxbo5wqy6BxZv8vAUGQwXBOALyacEbxg= google.golang.org/grpc v1.23.0/go.mod h1:Y5yQAOtifL1yxbo5wqy6BxZv8vAUGQwXBOALyacEbxg= -google.golang.org/grpc v1.23.1/go.mod h1:Y5yQAOtifL1yxbo5wqy6BxZv8vAUGQwXBOALyacEbxg= google.golang.org/grpc v1.25.1/go.mod h1:c3i+UQWmh7LiEpx4sFZnkU36qjEYZ0imhYfXVyQciAY= google.golang.org/grpc v1.26.0/go.mod h1:qbnxyOmOxrQa7FizSgH+ReBfzJrCY1pSN7KXBS8abTk= google.golang.org/grpc v1.27.0/go.mod h1:qbnxyOmOxrQa7FizSgH+ReBfzJrCY1pSN7KXBS8abTk= google.golang.org/grpc v1.27.1/go.mod h1:qbnxyOmOxrQa7FizSgH+ReBfzJrCY1pSN7KXBS8abTk= google.golang.org/grpc v1.28.0/go.mod h1:rpkK4SK4GF4Ach/+MFLZUBavHOvF2JJB5uozKKal+60= -google.golang.org/grpc v1.28.1/go.mod h1:rpkK4SK4GF4Ach/+MFLZUBavHOvF2JJB5uozKKal+60= google.golang.org/grpc v1.29.1/go.mod h1:itym6AZVZYACWQqET3MqgPpjcuV5QH3BxFS3IjizoKk= google.golang.org/grpc v1.30.0/go.mod h1:N36X2cJ7JwdamYAgDz+s+rVMFjt3numwzf/HckM8pak= google.golang.org/grpc v1.31.0/go.mod h1:N36X2cJ7JwdamYAgDz+s+rVMFjt3numwzf/HckM8pak= @@ -2106,54 +1213,26 @@ google.golang.org/protobuf v1.28.0/go.mod h1:HV8QOd/L58Z+nl8r43ehVNZIU/HEI6OcFqw google.golang.org/protobuf v1.28.1/go.mod h1:HV8QOd/L58Z+nl8r43ehVNZIU/HEI6OcFqwMG9pJV4I= google.golang.org/protobuf v1.31.0 h1:g0LDEJHgrBl9N9r17Ru3sqWhkIx2NB67okBHPwC7hs8= google.golang.org/protobuf v1.31.0/go.mod h1:HV8QOd/L58Z+nl8r43ehVNZIU/HEI6OcFqwMG9pJV4I= -gopkg.in/airbrake/gobrake.v2 v2.0.9/go.mod h1:/h5ZAUhDkGaJfjzjKLSjv6zCL6O0LLBxU4K+aSYdM/U= -gopkg.in/alecthomas/kingpin.v2 v2.2.6/go.mod h1:FMv+mEhP44yOT+4EoQTLFTRgOQ1FBLkstjWtayDeSgw= -gopkg.in/asn1-ber.v1 v1.0.0-20181015200546-f715ec2f112d/go.mod h1:cuepJuh7vyXfUyUwEgHQXw849cJrilpS5NeIjOWESAw= gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0= gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127/go.mod 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h1:fywZKyu//X7iRzaxLgPWsvc0L26IUpVvE/aeIL2JtIQ= rsc.io/binaryregexp v0.2.0/go.mod h1:qTv7/COck+e2FymRvadv62gMdZztPaShugOCi3I+8D8= rsc.io/quote/v3 v3.1.0/go.mod h1:yEA65RcK8LyAZtP9Kv3t0HmxON59tX3rD+tICJqUlj0= rsc.io/sampler v1.3.0/go.mod h1:T1hPZKmBbMNahiBKFy5HrXp6adAjACjK9JXDnKaTXpA= -sigs.k8s.io/structured-merge-diff/v3 v3.0.0-20200116222232-67a7b8c61874/go.mod h1:PlARxl6Hbt/+BC80dRLi1qAmnMqwqDg62YvvVkZjemw= -sigs.k8s.io/structured-merge-diff/v3 v3.0.0/go.mod h1:PlARxl6Hbt/+BC80dRLi1qAmnMqwqDg62YvvVkZjemw= -sigs.k8s.io/yaml v1.1.0/go.mod h1:UJmg0vDUVViEyp3mgSv9WPwZCDxu4rQW1olrI1uml+o= -sigs.k8s.io/yaml v1.2.0/go.mod h1:yfXDCHCao9+ENCvLSE62v9VSji2MKu5jeNfTrofGhJc= -sourcegraph.com/sourcegraph/appdash v0.0.0-20190731080439-ebfcffb1b5c0/go.mod h1:hI742Nqp5OhwiqlzhgfbWU4mW4yO10fP+LoT9WOswdU= diff --git a/vendor/github.com/ProtonMail/go-crypto/AUTHORS b/vendor/github.com/ProtonMail/go-crypto/AUTHORS new file mode 100644 index 00000000..2b00ddba --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/AUTHORS @@ -0,0 +1,3 @@ +# This source code refers to The Go Authors for copyright purposes. +# The master list of authors is in the main Go distribution, +# visible at https://tip.golang.org/AUTHORS. diff --git a/vendor/github.com/ProtonMail/go-crypto/CONTRIBUTORS b/vendor/github.com/ProtonMail/go-crypto/CONTRIBUTORS new file mode 100644 index 00000000..1fbd3e97 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/CONTRIBUTORS @@ -0,0 +1,3 @@ +# This source code was written by the Go contributors. +# The master list of contributors is in the main Go distribution, +# visible at https://tip.golang.org/CONTRIBUTORS. diff --git a/vendor/github.com/ProtonMail/go-crypto/LICENSE b/vendor/github.com/ProtonMail/go-crypto/LICENSE new file mode 100644 index 00000000..6a66aea5 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/LICENSE @@ -0,0 +1,27 @@ +Copyright (c) 2009 The Go Authors. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Google Inc. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/vendor/github.com/ProtonMail/go-crypto/PATENTS b/vendor/github.com/ProtonMail/go-crypto/PATENTS new file mode 100644 index 00000000..73309904 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/PATENTS @@ -0,0 +1,22 @@ +Additional IP Rights Grant (Patents) + +"This implementation" means the copyrightable works distributed by +Google as part of the Go project. + +Google hereby grants to You a perpetual, worldwide, non-exclusive, +no-charge, royalty-free, irrevocable (except as stated in this section) +patent license to make, have made, use, offer to sell, sell, import, +transfer and otherwise run, modify and propagate the contents of this +implementation of Go, where such license applies only to those patent +claims, both currently owned or controlled by Google and acquired in +the future, licensable by Google that are necessarily infringed by this +implementation of Go. This grant does not include claims that would be +infringed only as a consequence of further modification of this +implementation. If you or your agent or exclusive licensee institute or +order or agree to the institution of patent litigation against any +entity (including a cross-claim or counterclaim in a lawsuit) alleging +that this implementation of Go or any code incorporated within this +implementation of Go constitutes direct or contributory patent +infringement, or inducement of patent infringement, then any patent +rights granted to you under this License for this implementation of Go +shall terminate as of the date such litigation is filed. diff --git a/vendor/github.com/ProtonMail/go-crypto/bitcurves/bitcurve.go b/vendor/github.com/ProtonMail/go-crypto/bitcurves/bitcurve.go new file mode 100644 index 00000000..c85e6bef --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/bitcurves/bitcurve.go @@ -0,0 +1,381 @@ +package bitcurves + +// Copyright 2010 The Go Authors. All rights reserved. +// Copyright 2011 ThePiachu. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package bitelliptic implements several Koblitz elliptic curves over prime +// fields. + +// This package operates, internally, on Jacobian coordinates. For a given +// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1) +// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole +// calculation can be performed within the transform (as in ScalarMult and +// ScalarBaseMult). But even for Add and Double, it's faster to apply and +// reverse the transform than to operate in affine coordinates. + +import ( + "crypto/elliptic" + "io" + "math/big" + "sync" +) + +// A BitCurve represents a Koblitz Curve with a=0. +// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html +type BitCurve struct { + Name string + P *big.Int // the order of the underlying field + N *big.Int // the order of the base point + B *big.Int // the constant of the BitCurve equation + Gx, Gy *big.Int // (x,y) of the base point + BitSize int // the size of the underlying field +} + +// Params returns the parameters of the given BitCurve (see BitCurve struct) +func (bitCurve *BitCurve) Params() (cp *elliptic.CurveParams) { + cp = new(elliptic.CurveParams) + cp.Name = bitCurve.Name + cp.P = bitCurve.P + cp.N = bitCurve.N + cp.Gx = bitCurve.Gx + cp.Gy = bitCurve.Gy + cp.BitSize = bitCurve.BitSize + return cp +} + +// IsOnCurve returns true if the given (x,y) lies on the BitCurve. +func (bitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool { + // y² = x³ + b + y2 := new(big.Int).Mul(y, y) //y² + y2.Mod(y2, bitCurve.P) //y²%P + + x3 := new(big.Int).Mul(x, x) //x² + x3.Mul(x3, x) //x³ + + x3.Add(x3, bitCurve.B) //x³+B + x3.Mod(x3, bitCurve.P) //(x³+B)%P + + return x3.Cmp(y2) == 0 +} + +// affineFromJacobian reverses the Jacobian transform. See the comment at the +// top of the file. +func (bitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) { + if z.Cmp(big.NewInt(0)) == 0 { + panic("bitcurve: Can't convert to affine with Jacobian Z = 0") + } + // x = YZ^2 mod P + zinv := new(big.Int).ModInverse(z, bitCurve.P) + zinvsq := new(big.Int).Mul(zinv, zinv) + + xOut = new(big.Int).Mul(x, zinvsq) + xOut.Mod(xOut, bitCurve.P) + // y = YZ^3 mod P + zinvsq.Mul(zinvsq, zinv) + yOut = new(big.Int).Mul(y, zinvsq) + yOut.Mod(yOut, bitCurve.P) + return xOut, yOut +} + +// Add returns the sum of (x1,y1) and (x2,y2) +func (bitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + z := new(big.Int).SetInt64(1) + x, y, z := bitCurve.addJacobian(x1, y1, z, x2, y2, z) + return bitCurve.affineFromJacobian(x, y, z) +} + +// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and +// (x2, y2, z2) and returns their sum, also in Jacobian form. +func (bitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl + z1z1 := new(big.Int).Mul(z1, z1) + z1z1.Mod(z1z1, bitCurve.P) + z2z2 := new(big.Int).Mul(z2, z2) + z2z2.Mod(z2z2, bitCurve.P) + + u1 := new(big.Int).Mul(x1, z2z2) + u1.Mod(u1, bitCurve.P) + u2 := new(big.Int).Mul(x2, z1z1) + u2.Mod(u2, bitCurve.P) + h := new(big.Int).Sub(u2, u1) + if h.Sign() == -1 { + h.Add(h, bitCurve.P) + } + i := new(big.Int).Lsh(h, 1) + i.Mul(i, i) + j := new(big.Int).Mul(h, i) + + s1 := new(big.Int).Mul(y1, z2) + s1.Mul(s1, z2z2) + s1.Mod(s1, bitCurve.P) + s2 := new(big.Int).Mul(y2, z1) + s2.Mul(s2, z1z1) + s2.Mod(s2, bitCurve.P) + r := new(big.Int).Sub(s2, s1) + if r.Sign() == -1 { + r.Add(r, bitCurve.P) + } + r.Lsh(r, 1) + v := new(big.Int).Mul(u1, i) + + x3 := new(big.Int).Set(r) + x3.Mul(x3, x3) + x3.Sub(x3, j) + x3.Sub(x3, v) + x3.Sub(x3, v) + x3.Mod(x3, bitCurve.P) + + y3 := new(big.Int).Set(r) + v.Sub(v, x3) + y3.Mul(y3, v) + s1.Mul(s1, j) + s1.Lsh(s1, 1) + y3.Sub(y3, s1) + y3.Mod(y3, bitCurve.P) + + z3 := new(big.Int).Add(z1, z2) + z3.Mul(z3, z3) + z3.Sub(z3, z1z1) + if z3.Sign() == -1 { + z3.Add(z3, bitCurve.P) + } + z3.Sub(z3, z2z2) + if z3.Sign() == -1 { + z3.Add(z3, bitCurve.P) + } + z3.Mul(z3, h) + z3.Mod(z3, bitCurve.P) + + return x3, y3, z3 +} + +// Double returns 2*(x,y) +func (bitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + z1 := new(big.Int).SetInt64(1) + return bitCurve.affineFromJacobian(bitCurve.doubleJacobian(x1, y1, z1)) +} + +// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and +// returns its double, also in Jacobian form. +func (bitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l + + a := new(big.Int).Mul(x, x) //X1² + b := new(big.Int).Mul(y, y) //Y1² + c := new(big.Int).Mul(b, b) //B² + + d := new(big.Int).Add(x, b) //X1+B + d.Mul(d, d) //(X1+B)² + d.Sub(d, a) //(X1+B)²-A + d.Sub(d, c) //(X1+B)²-A-C + d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C) + + e := new(big.Int).Mul(big.NewInt(3), a) //3*A + f := new(big.Int).Mul(e, e) //E² + + x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D + x3.Sub(f, x3) //F-2*D + x3.Mod(x3, bitCurve.P) + + y3 := new(big.Int).Sub(d, x3) //D-X3 + y3.Mul(e, y3) //E*(D-X3) + y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C + y3.Mod(y3, bitCurve.P) + + z3 := new(big.Int).Mul(y, z) //Y1*Z1 + z3.Mul(big.NewInt(2), z3) //3*Y1*Z1 + z3.Mod(z3, bitCurve.P) + + return x3, y3, z3 +} + +// TODO: double check if it is okay +// ScalarMult returns k*(Bx,By) where k is a number in big-endian form. +func (bitCurve *BitCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) { + // We have a slight problem in that the identity of the group (the + // point at infinity) cannot be represented in (x, y) form on a finite + // machine. Thus the standard add/double algorithm has to be tweaked + // slightly: our initial state is not the identity, but x, and we + // ignore the first true bit in |k|. If we don't find any true bits in + // |k|, then we return nil, nil, because we cannot return the identity + // element. + + Bz := new(big.Int).SetInt64(1) + x := Bx + y := By + z := Bz + + seenFirstTrue := false + for _, byte := range k { + for bitNum := 0; bitNum < 8; bitNum++ { + if seenFirstTrue { + x, y, z = bitCurve.doubleJacobian(x, y, z) + } + if byte&0x80 == 0x80 { + if !seenFirstTrue { + seenFirstTrue = true + } else { + x, y, z = bitCurve.addJacobian(Bx, By, Bz, x, y, z) + } + } + byte <<= 1 + } + } + + if !seenFirstTrue { + return nil, nil + } + + return bitCurve.affineFromJacobian(x, y, z) +} + +// ScalarBaseMult returns k*G, where G is the base point of the group and k is +// an integer in big-endian form. +func (bitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { + return bitCurve.ScalarMult(bitCurve.Gx, bitCurve.Gy, k) +} + +var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f} + +// TODO: double check if it is okay +// GenerateKey returns a public/private key pair. The private key is generated +// using the given reader, which must return random data. +func (bitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) { + byteLen := (bitCurve.BitSize + 7) >> 3 + priv = make([]byte, byteLen) + + for x == nil { + _, err = io.ReadFull(rand, priv) + if err != nil { + return + } + // We have to mask off any excess bits in the case that the size of the + // underlying field is not a whole number of bytes. + priv[0] &= mask[bitCurve.BitSize%8] + // This is because, in tests, rand will return all zeros and we don't + // want to get the point at infinity and loop forever. + priv[1] ^= 0x42 + x, y = bitCurve.ScalarBaseMult(priv) + } + return +} + +// Marshal converts a point into the form specified in section 4.3.6 of ANSI +// X9.62. +func (bitCurve *BitCurve) Marshal(x, y *big.Int) []byte { + byteLen := (bitCurve.BitSize + 7) >> 3 + + ret := make([]byte, 1+2*byteLen) + ret[0] = 4 // uncompressed point + + xBytes := x.Bytes() + copy(ret[1+byteLen-len(xBytes):], xBytes) + yBytes := y.Bytes() + copy(ret[1+2*byteLen-len(yBytes):], yBytes) + return ret +} + +// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On +// error, x = nil. +func (bitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) { + byteLen := (bitCurve.BitSize + 7) >> 3 + if len(data) != 1+2*byteLen { + return + } + if data[0] != 4 { // uncompressed form + return + } + x = new(big.Int).SetBytes(data[1 : 1+byteLen]) + y = new(big.Int).SetBytes(data[1+byteLen:]) + return +} + +//curve parameters taken from: +//http://www.secg.org/collateral/sec2_final.pdf + +var initonce sync.Once +var secp160k1 *BitCurve +var secp192k1 *BitCurve +var secp224k1 *BitCurve +var secp256k1 *BitCurve + +func initAll() { + initS160() + initS192() + initS224() + initS256() +} + +func initS160() { + // See SEC 2 section 2.4.1 + secp160k1 = new(BitCurve) + secp160k1.Name = "secp160k1" + secp160k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", 16) + secp160k1.N, _ = new(big.Int).SetString("0100000000000000000001B8FA16DFAB9ACA16B6B3", 16) + secp160k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000007", 16) + secp160k1.Gx, _ = new(big.Int).SetString("3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", 16) + secp160k1.Gy, _ = new(big.Int).SetString("938CF935318FDCED6BC28286531733C3F03C4FEE", 16) + secp160k1.BitSize = 160 +} + +func initS192() { + // See SEC 2 section 2.5.1 + secp192k1 = new(BitCurve) + secp192k1.Name = "secp192k1" + secp192k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", 16) + secp192k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D", 16) + secp192k1.B, _ = new(big.Int).SetString("000000000000000000000000000000000000000000000003", 16) + secp192k1.Gx, _ = new(big.Int).SetString("DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", 16) + secp192k1.Gy, _ = new(big.Int).SetString("9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D", 16) + secp192k1.BitSize = 192 +} + +func initS224() { + // See SEC 2 section 2.6.1 + secp224k1 = new(BitCurve) + secp224k1.Name = "secp224k1" + secp224k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", 16) + secp224k1.N, _ = new(big.Int).SetString("010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7", 16) + secp224k1.B, _ = new(big.Int).SetString("00000000000000000000000000000000000000000000000000000005", 16) + secp224k1.Gx, _ = new(big.Int).SetString("A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", 16) + secp224k1.Gy, _ = new(big.Int).SetString("7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5", 16) + secp224k1.BitSize = 224 +} + +func initS256() { + // See SEC 2 section 2.7.1 + secp256k1 = new(BitCurve) + secp256k1.Name = "secp256k1" + secp256k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16) + secp256k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16) + secp256k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16) + secp256k1.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16) + secp256k1.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16) + secp256k1.BitSize = 256 +} + +// S160 returns a BitCurve which implements secp160k1 (see SEC 2 section 2.4.1) +func S160() *BitCurve { + initonce.Do(initAll) + return secp160k1 +} + +// S192 returns a BitCurve which implements secp192k1 (see SEC 2 section 2.5.1) +func S192() *BitCurve { + initonce.Do(initAll) + return secp192k1 +} + +// S224 returns a BitCurve which implements secp224k1 (see SEC 2 section 2.6.1) +func S224() *BitCurve { + initonce.Do(initAll) + return secp224k1 +} + +// S256 returns a BitCurve which implements bitcurves (see SEC 2 section 2.7.1) +func S256() *BitCurve { + initonce.Do(initAll) + return secp256k1 +} diff --git a/vendor/github.com/ProtonMail/go-crypto/brainpool/brainpool.go b/vendor/github.com/ProtonMail/go-crypto/brainpool/brainpool.go new file mode 100644 index 00000000..cb6676de --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/brainpool/brainpool.go @@ -0,0 +1,134 @@ +// Package brainpool implements Brainpool elliptic curves. +// Implementation of rcurves is from github.com/ebfe/brainpool +// Note that these curves are implemented with naive, non-constant time operations +// and are likely not suitable for environments where timing attacks are a concern. +package brainpool + +import ( + "crypto/elliptic" + "math/big" + "sync" +) + +var ( + once sync.Once + p256t1, p384t1, p512t1 *elliptic.CurveParams + p256r1, p384r1, p512r1 *rcurve +) + +func initAll() { + initP256t1() + initP384t1() + initP512t1() + initP256r1() + initP384r1() + initP512r1() +} + +func initP256t1() { + p256t1 = &elliptic.CurveParams{Name: "brainpoolP256t1"} + p256t1.P, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", 16) + p256t1.N, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", 16) + p256t1.B, _ = new(big.Int).SetString("662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04", 16) + p256t1.Gx, _ = new(big.Int).SetString("A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4", 16) + p256t1.Gy, _ = new(big.Int).SetString("2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE", 16) + p256t1.BitSize = 256 +} + +func initP256r1() { + twisted := p256t1 + params := &elliptic.CurveParams{ + Name: "brainpoolP256r1", + P: twisted.P, + N: twisted.N, + BitSize: twisted.BitSize, + } + params.Gx, _ = new(big.Int).SetString("8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", 16) + params.Gy, _ = new(big.Int).SetString("547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", 16) + z, _ := new(big.Int).SetString("3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0", 16) + p256r1 = newrcurve(twisted, params, z) +} + +func initP384t1() { + p384t1 = &elliptic.CurveParams{Name: "brainpoolP384t1"} + p384t1.P, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53", 16) + p384t1.N, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565", 16) + p384t1.B, _ = new(big.Int).SetString("7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE1D2074AA263B88805CED70355A33B471EE", 16) + p384t1.Gx, _ = new(big.Int).SetString("18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AABFFC4FF191B946A5F54D8D0AA2F418808CC", 16) + p384t1.Gy, _ = new(big.Int).SetString("25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CCFE469408584DC2B2912675BF5B9E582928", 16) + p384t1.BitSize = 384 +} + +func initP384r1() { + twisted := p384t1 + params := &elliptic.CurveParams{ + Name: "brainpoolP384r1", + P: twisted.P, + N: twisted.N, + BitSize: twisted.BitSize, + } + params.Gx, _ = new(big.Int).SetString("1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E", 16) + params.Gy, _ = new(big.Int).SetString("8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315", 16) + z, _ := new(big.Int).SetString("41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE97D2D63DBC87BCCDDCCC5DA39E8589291C", 16) + p384r1 = newrcurve(twisted, params, z) +} + +func initP512t1() { + p512t1 = &elliptic.CurveParams{Name: "brainpoolP512t1"} + p512t1.P, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3", 16) + p512t1.N, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069", 16) + p512t1.B, _ = new(big.Int).SetString("7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36A62BCDFA2304976540F6450085F2DAE145C22553B465763689180EA2571867423E", 16) + p512t1.Gx, _ = new(big.Int).SetString("640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C0313D82BA51735CDB3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA9035DA", 16) + p512t1.Gy, _ = new(big.Int).SetString("5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CEE9D9932184BEEF216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8B332", 16) + p512t1.BitSize = 512 +} + +func initP512r1() { + twisted := p512t1 + params := &elliptic.CurveParams{ + Name: "brainpoolP512r1", + P: twisted.P, + N: twisted.N, + BitSize: twisted.BitSize, + } + params.Gx, _ = new(big.Int).SetString("81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822", 16) + params.Gy, _ = new(big.Int).SetString("7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892", 16) + z, _ := new(big.Int).SetString("12EE58E6764838B69782136F0F2D3BA06E27695716054092E60A80BEDB212B64E585D90BCE13761F85C3F1D2A64E3BE8FEA2220F01EBA5EEB0F35DBD29D922AB", 16) + p512r1 = newrcurve(twisted, params, z) +} + +// P256t1 returns a Curve which implements Brainpool P256t1 (see RFC 5639, section 3.4) +func P256t1() elliptic.Curve { + once.Do(initAll) + return p256t1 +} + +// P256r1 returns a Curve which implements Brainpool P256r1 (see RFC 5639, section 3.4) +func P256r1() elliptic.Curve { + once.Do(initAll) + return p256r1 +} + +// P384t1 returns a Curve which implements Brainpool P384t1 (see RFC 5639, section 3.6) +func P384t1() elliptic.Curve { + once.Do(initAll) + return p384t1 +} + +// P384r1 returns a Curve which implements Brainpool P384r1 (see RFC 5639, section 3.6) +func P384r1() elliptic.Curve { + once.Do(initAll) + return p384r1 +} + +// P512t1 returns a Curve which implements Brainpool P512t1 (see RFC 5639, section 3.7) +func P512t1() elliptic.Curve { + once.Do(initAll) + return p512t1 +} + +// P512r1 returns a Curve which implements Brainpool P512r1 (see RFC 5639, section 3.7) +func P512r1() elliptic.Curve { + once.Do(initAll) + return p512r1 +} diff --git a/vendor/github.com/ProtonMail/go-crypto/brainpool/rcurve.go b/vendor/github.com/ProtonMail/go-crypto/brainpool/rcurve.go new file mode 100644 index 00000000..7e291d6a --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/brainpool/rcurve.go @@ -0,0 +1,83 @@ +package brainpool + +import ( + "crypto/elliptic" + "math/big" +) + +var _ elliptic.Curve = (*rcurve)(nil) + +type rcurve struct { + twisted elliptic.Curve + params *elliptic.CurveParams + z *big.Int + zinv *big.Int + z2 *big.Int + z3 *big.Int + zinv2 *big.Int + zinv3 *big.Int +} + +var ( + two = big.NewInt(2) + three = big.NewInt(3) +) + +func newrcurve(twisted elliptic.Curve, params *elliptic.CurveParams, z *big.Int) *rcurve { + zinv := new(big.Int).ModInverse(z, params.P) + return &rcurve{ + twisted: twisted, + params: params, + z: z, + zinv: zinv, + z2: new(big.Int).Exp(z, two, params.P), + z3: new(big.Int).Exp(z, three, params.P), + zinv2: new(big.Int).Exp(zinv, two, params.P), + zinv3: new(big.Int).Exp(zinv, three, params.P), + } +} + +func (curve *rcurve) toTwisted(x, y *big.Int) (*big.Int, *big.Int) { + var tx, ty big.Int + tx.Mul(x, curve.z2) + tx.Mod(&tx, curve.params.P) + ty.Mul(y, curve.z3) + ty.Mod(&ty, curve.params.P) + return &tx, &ty +} + +func (curve *rcurve) fromTwisted(tx, ty *big.Int) (*big.Int, *big.Int) { + var x, y big.Int + x.Mul(tx, curve.zinv2) + x.Mod(&x, curve.params.P) + y.Mul(ty, curve.zinv3) + y.Mod(&y, curve.params.P) + return &x, &y +} + +func (curve *rcurve) Params() *elliptic.CurveParams { + return curve.params +} + +func (curve *rcurve) IsOnCurve(x, y *big.Int) bool { + return curve.twisted.IsOnCurve(curve.toTwisted(x, y)) +} + +func (curve *rcurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) { + tx1, ty1 := curve.toTwisted(x1, y1) + tx2, ty2 := curve.toTwisted(x2, y2) + return curve.fromTwisted(curve.twisted.Add(tx1, ty1, tx2, ty2)) +} + +func (curve *rcurve) Double(x1, y1 *big.Int) (x, y *big.Int) { + return curve.fromTwisted(curve.twisted.Double(curve.toTwisted(x1, y1))) +} + +func (curve *rcurve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) { + tx1, ty1 := curve.toTwisted(x1, y1) + return curve.fromTwisted(curve.twisted.ScalarMult(tx1, ty1, scalar)) +} + +func (curve *rcurve) ScalarBaseMult(scalar []byte) (x, y *big.Int) { + return curve.fromTwisted(curve.twisted.ScalarBaseMult(scalar)) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/eax/eax.go b/vendor/github.com/ProtonMail/go-crypto/eax/eax.go new file mode 100644 index 00000000..3ae91d59 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/eax/eax.go @@ -0,0 +1,162 @@ +// Copyright (C) 2019 ProtonTech AG + +// Package eax provides an implementation of the EAX +// (encrypt-authenticate-translate) mode of operation, as described in +// Bellare, Rogaway, and Wagner "THE EAX MODE OF OPERATION: A TWO-PASS +// AUTHENTICATED-ENCRYPTION SCHEME OPTIMIZED FOR SIMPLICITY AND EFFICIENCY." +// In FSE'04, volume 3017 of LNCS, 2004 +package eax + +import ( + "crypto/cipher" + "crypto/subtle" + "errors" + "github.com/ProtonMail/go-crypto/internal/byteutil" +) + +const ( + defaultTagSize = 16 + defaultNonceSize = 16 +) + +type eax struct { + block cipher.Block // Only AES-{128, 192, 256} supported + tagSize int // At least 12 bytes recommended + nonceSize int +} + +func (e *eax) NonceSize() int { + return e.nonceSize +} + +func (e *eax) Overhead() int { + return e.tagSize +} + +// NewEAX returns an EAX instance with AES-{KEYLENGTH} and default nonce and +// tag lengths. Supports {128, 192, 256}- bit key length. +func NewEAX(block cipher.Block) (cipher.AEAD, error) { + return NewEAXWithNonceAndTagSize(block, defaultNonceSize, defaultTagSize) +} + +// NewEAXWithNonceAndTagSize returns an EAX instance with AES-{keyLength} and +// given nonce and tag lengths in bytes. Panics on zero nonceSize and +// exceedingly long tags. +// +// It is recommended to use at least 12 bytes as tag length (see, for instance, +// NIST SP 800-38D). +// +// Only to be used for compatibility with existing cryptosystems with +// non-standard parameters. For all other cases, prefer NewEAX. +func NewEAXWithNonceAndTagSize( + block cipher.Block, nonceSize, tagSize int) (cipher.AEAD, error) { + if nonceSize < 1 { + return nil, eaxError("Cannot initialize EAX with nonceSize = 0") + } + if tagSize > block.BlockSize() { + return nil, eaxError("Custom tag length exceeds blocksize") + } + return &eax{ + block: block, + tagSize: tagSize, + nonceSize: nonceSize, + }, nil +} + +func (e *eax) Seal(dst, nonce, plaintext, adata []byte) []byte { + if len(nonce) > e.nonceSize { + panic("crypto/eax: Nonce too long for this instance") + } + ret, out := byteutil.SliceForAppend(dst, len(plaintext)+e.tagSize) + omacNonce := e.omacT(0, nonce) + omacAdata := e.omacT(1, adata) + + // Encrypt message using CTR mode and omacNonce as IV + ctr := cipher.NewCTR(e.block, omacNonce) + ciphertextData := out[:len(plaintext)] + ctr.XORKeyStream(ciphertextData, plaintext) + + omacCiphertext := e.omacT(2, ciphertextData) + + tag := out[len(plaintext):] + for i := 0; i < e.tagSize; i++ { + tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i] + } + return ret +} + +func (e *eax) Open(dst, nonce, ciphertext, adata []byte) ([]byte, error) { + if len(nonce) > e.nonceSize { + panic("crypto/eax: Nonce too long for this instance") + } + if len(ciphertext) < e.tagSize { + return nil, eaxError("Ciphertext shorter than tag length") + } + sep := len(ciphertext) - e.tagSize + + // Compute tag + omacNonce := e.omacT(0, nonce) + omacAdata := e.omacT(1, adata) + omacCiphertext := e.omacT(2, ciphertext[:sep]) + + tag := make([]byte, e.tagSize) + for i := 0; i < e.tagSize; i++ { + tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i] + } + + // Compare tags + if subtle.ConstantTimeCompare(ciphertext[sep:], tag) != 1 { + return nil, eaxError("Tag authentication failed") + } + + // Decrypt ciphertext + ret, out := byteutil.SliceForAppend(dst, len(ciphertext)) + ctr := cipher.NewCTR(e.block, omacNonce) + ctr.XORKeyStream(out, ciphertext[:sep]) + + return ret[:sep], nil +} + +// Tweakable OMAC - Calls OMAC_K([t]_n || plaintext) +func (e *eax) omacT(t byte, plaintext []byte) []byte { + blockSize := e.block.BlockSize() + byteT := make([]byte, blockSize) + byteT[blockSize-1] = t + concat := append(byteT, plaintext...) + return e.omac(concat) +} + +func (e *eax) omac(plaintext []byte) []byte { + blockSize := e.block.BlockSize() + // L ← E_K(0^n); B ← 2L; P ← 4L + L := make([]byte, blockSize) + e.block.Encrypt(L, L) + B := byteutil.GfnDouble(L) + P := byteutil.GfnDouble(B) + + // CBC with IV = 0 + cbc := cipher.NewCBCEncrypter(e.block, make([]byte, blockSize)) + padded := e.pad(plaintext, B, P) + cbcCiphertext := make([]byte, len(padded)) + cbc.CryptBlocks(cbcCiphertext, padded) + + return cbcCiphertext[len(cbcCiphertext)-blockSize:] +} + +func (e *eax) pad(plaintext, B, P []byte) []byte { + // if |M| in {n, 2n, 3n, ...} + blockSize := e.block.BlockSize() + if len(plaintext) != 0 && len(plaintext)%blockSize == 0 { + return byteutil.RightXor(plaintext, B) + } + + // else return (M || 1 || 0^(n−1−(|M| % n))) xor→ P + ending := make([]byte, blockSize-len(plaintext)%blockSize) + ending[0] = 0x80 + padded := append(plaintext, ending...) + return byteutil.RightXor(padded, P) +} + +func eaxError(err string) error { + return errors.New("crypto/eax: " + err) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/eax/eax_test_vectors.go b/vendor/github.com/ProtonMail/go-crypto/eax/eax_test_vectors.go new file mode 100644 index 00000000..ddb53d07 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/eax/eax_test_vectors.go @@ -0,0 +1,58 @@ +package eax + +// Test vectors from +// https://web.cs.ucdavis.edu/~rogaway/papers/eax.pdf +var testVectors = []struct { + msg, key, nonce, header, ciphertext string +}{ + {"", + "233952DEE4D5ED5F9B9C6D6FF80FF478", + "62EC67F9C3A4A407FCB2A8C49031A8B3", + "6BFB914FD07EAE6B", + "E037830E8389F27B025A2D6527E79D01"}, + {"F7FB", + "91945D3F4DCBEE0BF45EF52255F095A4", + "BECAF043B0A23D843194BA972C66DEBD", + "FA3BFD4806EB53FA", + "19DD5C4C9331049D0BDAB0277408F67967E5"}, + {"1A47CB4933", + "01F74AD64077F2E704C0F60ADA3DD523", + "70C3DB4F0D26368400A10ED05D2BFF5E", + "234A3463C1264AC6", + "D851D5BAE03A59F238A23E39199DC9266626C40F80"}, + {"481C9E39B1", + "D07CF6CBB7F313BDDE66B727AFD3C5E8", + "8408DFFF3C1A2B1292DC199E46B7D617", + "33CCE2EABFF5A79D", + "632A9D131AD4C168A4225D8E1FF755939974A7BEDE"}, + {"40D0C07DA5E4", + "35B6D0580005BBC12B0587124557D2C2", + "FDB6B06676EEDC5C61D74276E1F8E816", + "AEB96EAEBE2970E9", + "071DFE16C675CB0677E536F73AFE6A14B74EE49844DD"}, + {"4DE3B35C3FC039245BD1FB7D", + "BD8E6E11475E60B268784C38C62FEB22", + "6EAC5C93072D8E8513F750935E46DA1B", + "D4482D1CA78DCE0F", + "835BB4F15D743E350E728414ABB8644FD6CCB86947C5E10590210A4F"}, + {"8B0A79306C9CE7ED99DAE4F87F8DD61636", + "7C77D6E813BED5AC98BAA417477A2E7D", + "1A8C98DCD73D38393B2BF1569DEEFC19", + "65D2017990D62528", + "02083E3979DA014812F59F11D52630DA30137327D10649B0AA6E1C181DB617D7F2"}, + {"1BDA122BCE8A8DBAF1877D962B8592DD2D56", + "5FFF20CAFAB119CA2FC73549E20F5B0D", + "DDE59B97D722156D4D9AFF2BC7559826", + "54B9F04E6A09189A", + "2EC47B2C4954A489AFC7BA4897EDCDAE8CC33B60450599BD02C96382902AEF7F832A"}, + {"6CF36720872B8513F6EAB1A8A44438D5EF11", + "A4A4782BCFFD3EC5E7EF6D8C34A56123", + "B781FCF2F75FA5A8DE97A9CA48E522EC", + "899A175897561D7E", + "0DE18FD0FDD91E7AF19F1D8EE8733938B1E8E7F6D2231618102FDB7FE55FF1991700"}, + {"CA40D7446E545FFAED3BD12A740A659FFBBB3CEAB7", + "8395FCF1E95BEBD697BD010BC766AAC3", + "22E7ADD93CFC6393C57EC0B3C17D6B44", + "126735FCC320D25A", + "CB8920F87A6C75CFF39627B56E3ED197C552D295A7CFC46AFC253B4652B1AF3795B124AB6E"}, +} diff --git a/vendor/github.com/ProtonMail/go-crypto/eax/random_vectors.go b/vendor/github.com/ProtonMail/go-crypto/eax/random_vectors.go new file mode 100644 index 00000000..4eb19f28 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/eax/random_vectors.go @@ -0,0 +1,131 @@ +// These vectors include key length in {128, 192, 256}, tag size 128, and +// random nonce, header, and plaintext lengths. + +// This file was automatically generated. + +package eax + +var randomVectors = []struct { + key, nonce, header, plaintext, ciphertext string +}{ + {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}, + {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}, + {"429F514EFC64D98A698A9247274CFF45", + "976AA5EB072F912D126ACEBC954FEC38", + "A71D89DC5B6CEDBB7451A27C3C2CAE09126DB4C421", + "5632FE62AB1DC549D54D3BC3FC868ACCEDEFD9ECF5E9F8", + "848AE4306CA8C7F416F8707625B7F55881C0AB430353A5C967CDA2DA787F581A70E34DBEBB2385"}, + {"398138F309085F47F8457CDF53895A63", + "F8A8A7F2D28E5FFF7BBC2F24353F7A36", + "5D633C21BA7764B8855CAB586F3746E236AD486039C83C6B56EFA9C651D38A41D6B20DAEE3418BFEA44B8BD6", + "A3BBAA91920AF5E10659818B1B3B300AC79BFC129C8329E75251F73A66D3AE0128EB91D5031E0A65C329DB7D1E9C0493E268", + "D078097267606E5FB07CFB7E2B4B718172A82C6A4CEE65D549A4DFB9838003BD2FBF64A7A66988AC1A632FD88F9E9FBB57C5A78AD2E086EACBA3DB68511D81C2970A"}, + {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}, + {"BFB147E1CD5459424F8C0271FC0E0DC5", + "EABCC126442BF373969EA3015988CC45", + "4C0880E1D71AA2C7", + "BE1B5EC78FBF73E7A6682B21BA7E0E5D2D1C7ABE", + "5660D7C1380E2F306895B1402CB2D6C37876504276B414D120F4CF92FDDDBB293A238EA0"}, + {"595DD6F52D18BC2CA8EB4EDAA18D9FA3", + "0F84B5D36CF4BC3B863313AF3B4D2E97", + "30AE6CC5F99580F12A779D98BD379A60948020C0B6FBD5746B30BA3A15C6CD33DAF376C70A9F15B6C0EB410A93161F7958AE23", + "8EF3687A1642B070970B0B91462229D1D76ABC154D18211F7152AA9FF368", + "317C1DDB11417E5A9CC4DDE7FDFF6659A5AC4B31DE025212580A05CDAC6024D3E4AE7C2966E52B9129E9ECDBED86"}, + {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}, + {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}, + {"99C0AD703196D2F60A74E6B378B838B31F82EA861F06FC4E", + "92745C018AA708ECFEB1667E9F3F1B01", + 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"8892E047DA5CFBBDF7F3CFCBD1BD21C6D4C80774B1826999234394BD3E513CC7C222BB40E1E3140A152F19B3802F0D036C24A590512AD0E8", + "D7B15752789DC94ED0F36778A5C7BBB207BEC32BAC66E702B39966F06E381E090C6757653C3D26A81EC6AD6C364D66867A334C91BB0B8A8A4B6EACDF0783D09010AEBA2DD2062308FE99CC1F", + "C071280A732ADC93DF272BF1E613B2BB7D46FC6665EF2DC1671F3E211D6BDE1D6ADDD28DF3AA2E47053FC8BB8AE9271EC8BC8B2CFFA320D225B451685B6D23ACEFDD241FE284F8ADC8DB07F456985B14330BBB66E0FB212213E05B3E"}, +} diff --git a/vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go b/vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go new file mode 100644 index 00000000..affb74a7 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go @@ -0,0 +1,90 @@ +// Copyright (C) 2019 ProtonTech AG +// This file contains necessary tools for the aex and ocb packages. +// +// These functions SHOULD NOT be used elsewhere, since they are optimized for +// specific input nature in the EAX and OCB modes of operation. + +package byteutil + +// GfnDouble computes 2 * input in the field of 2^n elements. +// The irreducible polynomial in the finite field for n=128 is +// x^128 + x^7 + x^2 + x + 1 (equals 0x87) +// Constant-time execution in order to avoid side-channel attacks +func GfnDouble(input []byte) []byte { + if len(input) != 16 { + panic("Doubling in GFn only implemented for n = 128") + } + // If the first bit is zero, return 2L = L << 1 + // Else return (L << 1) xor 0^120 10000111 + shifted := ShiftBytesLeft(input) + shifted[15] ^= ((input[0] >> 7) * 0x87) + return shifted +} + +// ShiftBytesLeft outputs the byte array corresponding to x << 1 in binary. +func ShiftBytesLeft(x []byte) []byte { + l := len(x) + dst := make([]byte, l) + for i := 0; i < l-1; i++ { + dst[i] = (x[i] << 1) | (x[i+1] >> 7) + } + dst[l-1] = x[l-1] << 1 + return dst +} + +// ShiftNBytesLeft puts in dst the byte array corresponding to x << n in binary. +func ShiftNBytesLeft(dst, x []byte, n int) { + // Erase first n / 8 bytes + copy(dst, x[n/8:]) + + // Shift the remaining n % 8 bits + bits := uint(n % 8) + l := len(dst) + for i := 0; i < l-1; i++ { + dst[i] = (dst[i] << bits) | (dst[i+1] >> uint(8-bits)) + } + dst[l-1] = dst[l-1] << bits + + // Append trailing zeroes + dst = append(dst, make([]byte, n/8)...) +} + +// XorBytesMut assumes equal input length, replaces X with X XOR Y +func XorBytesMut(X, Y []byte) { + for i := 0; i < len(X); i++ { + X[i] ^= Y[i] + } +} + +// XorBytes assumes equal input length, puts X XOR Y into Z +func XorBytes(Z, X, Y []byte) { + for i := 0; i < len(X); i++ { + Z[i] = X[i] ^ Y[i] + } +} + +// RightXor XORs smaller input (assumed Y) at the right of the larger input (assumed X) +func RightXor(X, Y []byte) []byte { + offset := len(X) - len(Y) + xored := make([]byte, len(X)) + copy(xored, X) + for i := 0; i < len(Y); i++ { + xored[offset+i] ^= Y[i] + } + return xored +} + +// SliceForAppend takes a slice and a requested number of bytes. It returns a +// slice with the contents of the given slice followed by that many bytes and a +// second slice that aliases into it and contains only the extra bytes. If the +// original slice has sufficient capacity then no allocation is performed. +func SliceForAppend(in []byte, n int) (head, tail []byte) { + if total := len(in) + n; cap(in) >= total { + head = in[:total] + } else { + head = make([]byte, total) + copy(head, in) + } + tail = head[len(in):] + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/ocb/ocb.go b/vendor/github.com/ProtonMail/go-crypto/ocb/ocb.go new file mode 100644 index 00000000..1a6f7350 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/ocb/ocb.go @@ -0,0 +1,317 @@ +// Copyright (C) 2019 ProtonTech AG + +// Package ocb provides an implementation of the OCB (offset codebook) mode of +// operation, as described in RFC-7253 of the IRTF and in Rogaway, Bellare, +// Black and Krovetz - OCB: A BLOCK-CIPHER MODE OF OPERATION FOR EFFICIENT +// AUTHENTICATED ENCRYPTION (2003). +// Security considerations (from RFC-7253): A private key MUST NOT be used to +// encrypt more than 2^48 blocks. Tag length should be at least 12 bytes (a +// brute-force forging adversary succeeds after 2^{tag length} attempts). A +// single key SHOULD NOT be used to decrypt ciphertext with different tag +// lengths. Nonces need not be secret, but MUST NOT be reused. +// This package only supports underlying block ciphers with 128-bit blocks, +// such as AES-{128, 192, 256}, but may be extended to other sizes. +package ocb + +import ( + "bytes" + "crypto/cipher" + "crypto/subtle" + "errors" + "github.com/ProtonMail/go-crypto/internal/byteutil" + "math/bits" +) + +type ocb struct { + block cipher.Block + tagSize int + nonceSize int + mask mask + // Optimized en/decrypt: For each nonce N used to en/decrypt, the 'Ktop' + // internal variable can be reused for en/decrypting with nonces sharing + // all but the last 6 bits with N. The prefix of the first nonce used to + // compute the new Ktop, and the Ktop value itself, are stored in + // reusableKtop. If using incremental nonces, this saves one block cipher + // call every 63 out of 64 OCB encryptions, and stores one nonce and one + // output of the block cipher in memory only. + reusableKtop reusableKtop +} + +type mask struct { + // L_*, L_$, (L_i)_{i ∈ N} + lAst []byte + lDol []byte + L [][]byte +} + +type reusableKtop struct { + noncePrefix []byte + Ktop []byte +} + +const ( + defaultTagSize = 16 + defaultNonceSize = 15 +) + +const ( + enc = iota + dec +) + +func (o *ocb) NonceSize() int { + return o.nonceSize +} + +func (o *ocb) Overhead() int { + return o.tagSize +} + +// NewOCB returns an OCB instance with the given block cipher and default +// tag and nonce sizes. +func NewOCB(block cipher.Block) (cipher.AEAD, error) { + return NewOCBWithNonceAndTagSize(block, defaultNonceSize, defaultTagSize) +} + +// NewOCBWithNonceAndTagSize returns an OCB instance with the given block +// cipher, nonce length, and tag length. Panics on zero nonceSize and +// exceedingly long tag size. +// +// It is recommended to use at least 12 bytes as tag length. +func NewOCBWithNonceAndTagSize( + block cipher.Block, nonceSize, tagSize int) (cipher.AEAD, error) { + if block.BlockSize() != 16 { + return nil, ocbError("Block cipher must have 128-bit blocks") + } + if nonceSize < 1 { + return nil, ocbError("Incorrect nonce length") + } + if nonceSize >= block.BlockSize() { + return nil, ocbError("Nonce length exceeds blocksize - 1") + } + if tagSize > block.BlockSize() { + return nil, ocbError("Custom tag length exceeds blocksize") + } + return &ocb{ + block: block, + tagSize: tagSize, + nonceSize: nonceSize, + mask: initializeMaskTable(block), + reusableKtop: reusableKtop{ + noncePrefix: nil, + Ktop: nil, + }, + }, nil +} + +func (o *ocb) Seal(dst, nonce, plaintext, adata []byte) []byte { + if len(nonce) > o.nonceSize { + panic("crypto/ocb: Incorrect nonce length given to OCB") + } + ret, out := byteutil.SliceForAppend(dst, len(plaintext)+o.tagSize) + o.crypt(enc, out, nonce, adata, plaintext) + return ret +} + +func (o *ocb) Open(dst, nonce, ciphertext, adata []byte) ([]byte, error) { + if len(nonce) > o.nonceSize { + panic("Nonce too long for this instance") + } + if len(ciphertext) < o.tagSize { + return nil, ocbError("Ciphertext shorter than tag length") + } + sep := len(ciphertext) - o.tagSize + ret, out := byteutil.SliceForAppend(dst, len(ciphertext)) + ciphertextData := ciphertext[:sep] + tag := ciphertext[sep:] + o.crypt(dec, out, nonce, adata, ciphertextData) + if subtle.ConstantTimeCompare(ret[sep:], tag) == 1 { + ret = ret[:sep] + return ret, nil + } + for i := range out { + out[i] = 0 + } + return nil, ocbError("Tag authentication failed") +} + +// On instruction enc (resp. dec), crypt is the encrypt (resp. decrypt) +// function. It returns the resulting plain/ciphertext with the tag appended. +func (o *ocb) crypt(instruction int, Y, nonce, adata, X []byte) []byte { + // + // Consider X as a sequence of 128-bit blocks + // + // Note: For encryption (resp. decryption), X is the plaintext (resp., the + // ciphertext without the tag). + blockSize := o.block.BlockSize() + + // + // Nonce-dependent and per-encryption variables + // + // Zero out the last 6 bits of the nonce into truncatedNonce to see if Ktop + // is already computed. + truncatedNonce := make([]byte, len(nonce)) + copy(truncatedNonce, nonce) + truncatedNonce[len(truncatedNonce)-1] &= 192 + Ktop := make([]byte, blockSize) + if bytes.Equal(truncatedNonce, o.reusableKtop.noncePrefix) { + Ktop = o.reusableKtop.Ktop + } else { + // Nonce = num2str(TAGLEN mod 128, 7) || zeros(120 - bitlen(N)) || 1 || N + paddedNonce := append(make([]byte, blockSize-1-len(nonce)), 1) + paddedNonce = append(paddedNonce, truncatedNonce...) + paddedNonce[0] |= byte(((8 * o.tagSize) % (8 * blockSize)) << 1) + // Last 6 bits of paddedNonce are already zero. Encrypt into Ktop + paddedNonce[blockSize-1] &= 192 + Ktop = paddedNonce + o.block.Encrypt(Ktop, Ktop) + o.reusableKtop.noncePrefix = truncatedNonce + o.reusableKtop.Ktop = Ktop + } + + // Stretch = Ktop || ((lower half of Ktop) XOR (lower half of Ktop << 8)) + xorHalves := make([]byte, blockSize/2) + byteutil.XorBytes(xorHalves, Ktop[:blockSize/2], Ktop[1:1+blockSize/2]) + stretch := append(Ktop, xorHalves...) + bottom := int(nonce[len(nonce)-1] & 63) + offset := make([]byte, len(stretch)) + byteutil.ShiftNBytesLeft(offset, stretch, bottom) + offset = offset[:blockSize] + + // + // Process any whole blocks + // + // Note: For encryption Y is ciphertext || tag, for decryption Y is + // plaintext || tag. + checksum := make([]byte, blockSize) + m := len(X) / blockSize + for i := 0; i < m; i++ { + index := bits.TrailingZeros(uint(i + 1)) + if len(o.mask.L)-1 < index { + o.mask.extendTable(index) + } + byteutil.XorBytesMut(offset, o.mask.L[bits.TrailingZeros(uint(i+1))]) + blockX := X[i*blockSize : (i+1)*blockSize] + blockY := Y[i*blockSize : (i+1)*blockSize] + byteutil.XorBytes(blockY, blockX, offset) + switch instruction { + case enc: + o.block.Encrypt(blockY, blockY) + byteutil.XorBytesMut(blockY, offset) + byteutil.XorBytesMut(checksum, blockX) + case dec: + o.block.Decrypt(blockY, blockY) + byteutil.XorBytesMut(blockY, offset) + byteutil.XorBytesMut(checksum, blockY) + } + } + // + // Process any final partial block and compute raw tag + // + tag := make([]byte, blockSize) + if len(X)%blockSize != 0 { + byteutil.XorBytesMut(offset, o.mask.lAst) + pad := make([]byte, blockSize) + o.block.Encrypt(pad, offset) + chunkX := X[blockSize*m:] + chunkY := Y[blockSize*m : len(X)] + byteutil.XorBytes(chunkY, chunkX, pad[:len(chunkX)]) + // P_* || bit(1) || zeroes(127) - len(P_*) + switch instruction { + case enc: + paddedY := append(chunkX, byte(128)) + paddedY = append(paddedY, make([]byte, blockSize-len(chunkX)-1)...) + byteutil.XorBytesMut(checksum, paddedY) + case dec: + paddedX := append(chunkY, byte(128)) + paddedX = append(paddedX, make([]byte, blockSize-len(chunkY)-1)...) + byteutil.XorBytesMut(checksum, paddedX) + } + byteutil.XorBytes(tag, checksum, offset) + byteutil.XorBytesMut(tag, o.mask.lDol) + o.block.Encrypt(tag, tag) + byteutil.XorBytesMut(tag, o.hash(adata)) + copy(Y[blockSize*m+len(chunkY):], tag[:o.tagSize]) + } else { + byteutil.XorBytes(tag, checksum, offset) + byteutil.XorBytesMut(tag, o.mask.lDol) + o.block.Encrypt(tag, tag) + byteutil.XorBytesMut(tag, o.hash(adata)) + copy(Y[blockSize*m:], tag[:o.tagSize]) + } + return Y +} + +// This hash function is used to compute the tag. Per design, on empty input it +// returns a slice of zeros, of the same length as the underlying block cipher +// block size. +func (o *ocb) hash(adata []byte) []byte { + // + // Consider A as a sequence of 128-bit blocks + // + A := make([]byte, len(adata)) + copy(A, adata) + blockSize := o.block.BlockSize() + + // + // Process any whole blocks + // + sum := make([]byte, blockSize) + offset := make([]byte, blockSize) + m := len(A) / blockSize + for i := 0; i < m; i++ { + chunk := A[blockSize*i : blockSize*(i+1)] + index := bits.TrailingZeros(uint(i + 1)) + // If the mask table is too short + if len(o.mask.L)-1 < index { + o.mask.extendTable(index) + } + byteutil.XorBytesMut(offset, o.mask.L[index]) + byteutil.XorBytesMut(chunk, offset) + o.block.Encrypt(chunk, chunk) + byteutil.XorBytesMut(sum, chunk) + } + + // + // Process any final partial block; compute final hash value + // + if len(A)%blockSize != 0 { + byteutil.XorBytesMut(offset, o.mask.lAst) + // Pad block with 1 || 0 ^ 127 - bitlength(a) + ending := make([]byte, blockSize-len(A)%blockSize) + ending[0] = 0x80 + encrypted := append(A[blockSize*m:], ending...) + byteutil.XorBytesMut(encrypted, offset) + o.block.Encrypt(encrypted, encrypted) + byteutil.XorBytesMut(sum, encrypted) + } + return sum +} + +func initializeMaskTable(block cipher.Block) mask { + // + // Key-dependent variables + // + lAst := make([]byte, block.BlockSize()) + block.Encrypt(lAst, lAst) + lDol := byteutil.GfnDouble(lAst) + L := make([][]byte, 1) + L[0] = byteutil.GfnDouble(lDol) + + return mask{ + lAst: lAst, + lDol: lDol, + L: L, + } +} + +// Extends the L array of mask m up to L[limit], with L[i] = GfnDouble(L[i-1]) +func (m *mask) extendTable(limit int) { + for i := len(m.L); i <= limit; i++ { + m.L = append(m.L, byteutil.GfnDouble(m.L[i-1])) + } +} + +func ocbError(err string) error { + return errors.New("crypto/ocb: " + err) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/ocb/random_vectors.go b/vendor/github.com/ProtonMail/go-crypto/ocb/random_vectors.go new file mode 100644 index 00000000..0efaf344 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/ocb/random_vectors.go @@ -0,0 +1,136 @@ +// In the test vectors provided by RFC 7253, the "bottom" +// internal variable, which defines "offset" for the first time, does not +// exceed 15. However, it can attain values up to 63. + +// These vectors include key length in {128, 192, 256}, tag size 128, and +// random nonce, header, and plaintext lengths. + +// This file was automatically generated. + +package ocb + +var randomVectors = []struct { + key, nonce, header, plaintext, ciphertext string +}{ + + {"9438C5D599308EAF13F800D2D31EA7F0", + "C38EE4801BEBFFA1CD8635BE", + "0E507B7DADD8A98CDFE272D3CB6B3E8332B56AE583FB049C0874D4200BED16BD1A044182434E9DA0E841F182DFD5B3016B34641CED0784F1745F63AB3D0DA22D3351C9EF9A658B8081E24498EBF61FCE40DA6D8E184536", + "962D227786FB8913A8BAD5DC3250", + "EEDEF5FFA5986D1E3BF86DDD33EF9ADC79DCA06E215FA772CCBA814F63AD"}, + {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}, + {"2E74B25289F6FD3E578C24866E9C72A5", + "FD912F15025AF8414642BA1D1D", + "FB5FB8C26F365EEDAB5FE260C6E3CCD27806729C8335F146063A7F9EA93290E56CF84576EB446350D22AD730547C267B1F0BBB97EB34E1E2C41A", + "6C092EBF78F76EE8C1C6E592277D9545BA16EDB67BC7D8480B9827702DC2F8A129E2B08A2CE710CA7E1DA45CE162BB6CD4B512E632116E2211D3C90871EFB06B8D4B902681C7FB", + "6AC0A77F26531BF4F354A1737F99E49BE32ECD909A7A71AD69352906F54B08A9CE9B8CA5D724CBFFC5673437F23F630697F3B84117A1431D6FA8CC13A974FB4AD360300522E09511B99E71065D5AC4BBCB1D791E864EF4"}, + {"E7EC507C802528F790AFF5303A017B17", + "4B97A7A568940A9E3CE7A99E93031E", + "28349BDC5A09390C480F9B8AA3EDEA3DDB8B9D64BCA322C570B8225DF0E31190DAB25A4014BA39519E02ABFB12B89AA28BBFD29E486E7FB28734258C817B63CED9912DBAFEBB93E2798AB2890DE3B0ACFCFF906AB15563EF7823CE83D27CDB251195E22BD1337BCBDE65E7C2C427321C463C2777BFE5AEAA", + "9455B3EA706B74", + "7F33BA3EA848D48A96B9530E26888F43EBD4463C9399B6"}, + {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}, + {"ECEA315CA4B3F425B0C9957A17805EA4", + "664CDAE18403F4F9BA13015A44FC", + "642AFB090D6C6DB46783F08B01A3EF2A8FEB5736B531EAC226E7888FCC8505F396818F83105065FACB3267485B9E5E4A0261F621041C08FCCB2A809A49AB5252A91D0971BCC620B9D614BD77E57A0EED2FA5", + "6852C31F8083E20E364CEA21BB7854D67CEE812FE1C9ED2425C0932A90D3780728D1BB", + "2ECEF962A9695A463ADABB275BDA9FF8B2BA57AEC2F52EFFB700CD9271A74D2A011C24AEA946051BD6291776429B7E681BA33E"}, + {"4EE616C4A58AAA380878F71A373461F6", + "91B8C9C176D9C385E9C47E52", + "CDA440B7F9762C572A718AC754EDEECC119E5EE0CCB9FEA4FFB22EEE75087C032EBF3DA9CDD8A28CC010B99ED45143B41A4BA50EA2A005473F89639237838867A57F23B0F0ED3BF22490E4501DAC9C658A9B9F", + "D6E645FA9AE410D15B8123FD757FA356A8DBE9258DDB5BE88832E615910993F497EC", + "B70ED7BF959FB2AAED4F36174A2A99BFB16992C8CDF369C782C4DB9C73DE78C5DB8E0615F647243B97ACDB24503BC9CADC48"}, + {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}, + {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}, + {"53B52B8D4D748BCDF1DDE68857832FA46227FA6E2F32EFA1", + "0B0EF53D4606B28D1398355F", + "F23882436349094AF98BCACA8218E81581A043B19009E28EFBF2DE37883E04864148CC01D240552CA8844EC1456F42034653067DA67E80F87105FD06E14FF771246C9612867BE4D215F6D761", + "F15030679BD4088D42CAC9BF2E9606EAD4798782FA3ED8C57EBE7F84A53236F51B25967C6489D0CD20C9EEA752F9BC", + "67B96E2D67C3729C96DAEAEDF821D61C17E648643A2134C5621FEC621186915AD80864BFD1EB5B238BF526A679385E012A457F583AFA78134242E9D9C1B4E4"}, + {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}, + {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}, + {"B695C691538F8CBD60F039D0E28894E3693CC7C36D92D79D", + "BC099AEB637361BAC536B57618", + "BFFF1A65AE38D1DC142C71637319F5F6508E2CB33C9DCB94202B359ED5A5ED8042E7F4F09231D32A7242976677E6F4C549BF65FADC99E5AF43F7A46FD95E16C2", + "081DF3FD85B415D803F0BE5AC58CFF0023FDDED99788296C3731D8", + "E50C64E3614D94FE69C47092E46ACC9957C6FEA2CCBF96BC62FBABE7424753C75F9C147C42AE26FE171531"}, + {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}, + {"7A832BD2CF5BF4919F353CE2A8C86A5E406DA2D52BE16A72", + "2F2F17CECF7E5A756D10785A3CB9DB", + "61DA05E3788CC2D8405DBA70C7A28E5AF699863C9F72E6C6770126929F5D6FA267F005EBCF49495CB46400958A3AE80D1289D1C671", + "44E91121195A41AF14E8CFDBD39A4B517BE0DF1A72977ED8A3EEF8EEDA1166B2EB6DB2C4AE2E74FA0F0C74537F659BFBD141E5DDEC67E64EDA85AABD3F52C85A785B9FB3CECD70E7DF", + "BEDF596EA21288D2B84901E188F6EE1468B14D5161D3802DBFE00D60203A24E2AB62714BF272A45551489838C3A7FEAADC177B591836E73684867CCF4E12901DCF2064058726BBA554E84ADC5136F507E961188D4AF06943D3"}, + {"1508E8AE9079AA15F1CEC4F776B4D11BCCB061B58AA56C18", + "BCA625674F41D1E3AB47672DC0C3", + "8B12CF84F16360F0EAD2A41BC021530FFCEC7F3579CAE658E10E2D3D81870F65AFCED0C77C6C4C6E6BA424FF23088C796BA6195ABA35094BF1829E089662E7A95FC90750AE16D0C8AFA55DAC789D7735B970B58D4BE7CEC7341DA82A0179A01929C27A59C5063215B859EA43", + "E525422519ECE070E82C", + "B47BC07C3ED1C0A43BA52C43CBACBCDBB29CAF1001E09FDF7107"}, + {"7550C2761644E911FE9ADD119BAC07376BEA442845FEAD876D7E7AC1B713E464", + "36D2EC25ADD33CDEDF495205BBC923", + "7FCFE81A3790DE97FFC3DE160C470847EA7E841177C2F759571CBD837EA004A6CA8C6F4AEBFF2E9FD552D73EB8A30705D58D70C0B67AEEA280CBBF0A477358ACEF1E7508F2735CD9A0E4F9AC92B8C008F575D3B6278F1C18BD01227E3502E5255F3AB1893632AD00C717C588EF652A51A43209E7EE90", + "2B1A62F8FDFAA3C16470A21AD307C9A7D03ADE8EF72C69B06F8D738CDE578D7AEFD0D40BD9C022FB9F580DF5394C998ACCCEFC5471A3996FB8F1045A81FDC6F32D13502EA65A211390C8D882B8E0BEFD8DD8CBEF51D1597B124E9F7F", + "C873E02A22DB89EB0787DB6A60B99F7E4A0A085D5C4232A81ADCE2D60AA36F92DDC33F93DD8640AC0E08416B187FB382B3EC3EE85A64B0E6EE41C1366A5AD2A282F66605E87031CCBA2FA7B2DA201D975994AADE3DD1EE122AE09604AD489B84BF0C1AB7129EE16C6934850E"}, + {"A51300285E554FDBDE7F771A9A9A80955639DD87129FAEF74987C91FB9687C71", + "81691D5D20EC818FCFF24B33DECC", + "C948093218AA9EB2A8E44A87EEA73FC8B6B75A196819A14BD83709EA323E8DF8B491045220E1D88729A38DBCFFB60D3056DAD4564498FD6574F74512945DEB34B69329ACED9FFC05D5D59DFCD5B973E2ACAFE6AD1EF8BBBC49351A2DD12508ED89ED", + "EB861165DAF7625F827C6B574ED703F03215", + "C6CD1CE76D2B3679C1B5AA1CFD67CCB55444B6BFD3E22C81CBC9BB738796B83E54E3"}, + {"8CE0156D26FAEB7E0B9B800BBB2E9D4075B5EAC5C62358B0E7F6FCE610223282", + "D2A7B94DD12CDACA909D3AD7", + "E021A78F374FC271389AB9A3E97077D755", + "7C26000B58929F5095E1CEE154F76C2A299248E299F9B5ADE6C403AA1FD4A67FD4E0232F214CE7B919EE7A1027D2B76C57475715CD078461", + "C556FB38DF069B56F337B5FF5775CE6EAA16824DFA754F20B78819028EA635C3BB7AA731DE8776B2DCB67DCA2D33EEDF3C7E52EA450013722A41755A0752433ED17BDD5991AAE77A"}, + {"1E8000A2CE00A561C9920A30BF0D7B983FEF8A1014C8F04C35CA6970E6BA02BD", + "65ED3D63F79F90BBFD19775E", + "336A8C0B7243582A46B221AA677647FCAE91", + "134A8B34824A290E7B", + "914FBEF80D0E6E17F8BDBB6097EBF5FBB0554952DC2B9E5151"}, + {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}, + {"294362FCC984F440CEA3E9F7D2C06AF20C53AAC1B3738CA2186C914A6E193ABB", + "B15B61C8BB39261A8F55AB178EC3", + "D0729B6B75BB", + "2BD089ADCE9F334BAE3B065996C7D616DD0C27DF4218DCEEA0FBCA0F968837CE26B0876083327E25681FDDD620A32EC0DA12F73FAE826CC94BFF2B90A54D2651", + "AC94B25E4E21DE2437B806966CCD5D9385EF0CD4A51AB9FA6DE675C7B8952D67802E9FEC1FDE9F5D1EAB06057498BC0EEA454804FC9D2068982A3E24182D9AC2E7AB9994DDC899A604264583F63D066B"}, + {"959DBFEB039B1A5B8CE6A44649B602AAA5F98A906DB96143D202CD2024F749D9", + "01D7BDB1133E9C347486C1EFA6", + "F3843955BD741F379DD750585EDC55E2CDA05CCBA8C1F4622AC2FE35214BC3A019B8BD12C4CC42D9213D1E1556941E8D8450830287FFB3B763A13722DD4140ED9846FB5FFF745D7B0B967D810A068222E10B259AF1D392035B0D83DC1498A6830B11B2418A840212599171E0258A1C203B05362978", + "A21811232C950FA8B12237C2EBD6A7CD2C3A155905E9E0C7C120", + "63C1CE397B22F1A03F1FA549B43178BC405B152D3C95E977426D519B3DFCA28498823240592B6EEE7A14"}, + {"096AE499F5294173F34FF2B375F0E5D5AB79D0D03B33B1A74D7D576826345DF4", + "0C52B3D11D636E5910A4DD76D32C", + "229E9ECA3053789E937447BC719467075B6138A142DA528DA8F0CF8DDF022FD9AF8E74779BA3AC306609", + "8B7A00038783E8BAF6EDEAE0C4EAB48FC8FD501A588C7E4A4DB71E3604F2155A97687D3D2FFF8569261375A513CF4398CE0F87CA1658A1050F6EF6C4EA3E25", + "C20B6CF8D3C8241825FD90B2EDAC7593600646E579A8D8DAAE9E2E40C3835FE801B2BE4379131452BC5182C90307B176DFBE2049544222FE7783147B690774F6D9D7CEF52A91E61E298E9AA15464AC"}, +} diff --git a/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go b/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go new file mode 100644 index 00000000..330309ff --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go @@ -0,0 +1,78 @@ +package ocb + +import ( + "encoding/hex" +) + +// Test vectors from https://tools.ietf.org/html/rfc7253. Note that key is +// shared across tests. +var testKey, _ = hex.DecodeString("000102030405060708090A0B0C0D0E0F") + +var rfc7253testVectors = []struct { + nonce, header, plaintext, ciphertext string +}{ + {"BBAA99887766554433221100", + "", + "", + "785407BFFFC8AD9EDCC5520AC9111EE6"}, + {"BBAA99887766554433221101", + "0001020304050607", + "0001020304050607", + "6820B3657B6F615A5725BDA0D3B4EB3A257C9AF1F8F03009"}, + {"BBAA99887766554433221102", + "0001020304050607", + "", + "81017F8203F081277152FADE694A0A00"}, + {"BBAA99887766554433221103", + "", + "0001020304050607", + "45DD69F8F5AAE72414054CD1F35D82760B2CD00D2F99BFA9"}, + {"BBAA99887766554433221104", + "000102030405060708090A0B0C0D0E0F", + "000102030405060708090A0B0C0D0E0F", + "571D535B60B277188BE5147170A9A22C3AD7A4FF3835B8C5701C1CCEC8FC3358"}, + {"BBAA99887766554433221105", + "000102030405060708090A0B0C0D0E0F", + "", + "8CF761B6902EF764462AD86498CA6B97"}, + {"BBAA99887766554433221106", + "", + "000102030405060708090A0B0C0D0E0F", + "5CE88EC2E0692706A915C00AEB8B2396F40E1C743F52436BDF06D8FA1ECA343D"}, + {"BBAA99887766554433221107", + "000102030405060708090A0B0C0D0E0F1011121314151617", + "000102030405060708090A0B0C0D0E0F1011121314151617", + "1CA2207308C87C010756104D8840CE1952F09673A448A122C92C62241051F57356D7F3C90BB0E07F"}, + {"BBAA99887766554433221108", + "000102030405060708090A0B0C0D0E0F1011121314151617", + "", + "6DC225A071FC1B9F7C69F93B0F1E10DE"}, + {"BBAA99887766554433221109", + "", + "000102030405060708090A0B0C0D0E0F1011121314151617", + "221BD0DE7FA6FE993ECCD769460A0AF2D6CDED0C395B1C3CE725F32494B9F914D85C0B1EB38357FF"}, + {"BBAA9988776655443322110A", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", + "BD6F6C496201C69296C11EFD138A467ABD3C707924B964DEAFFC40319AF5A48540FBBA186C5553C68AD9F592A79A4240"}, + {"BBAA9988776655443322110B", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", + "", + "FE80690BEE8A485D11F32965BC9D2A32"}, + {"BBAA9988776655443322110C", + "", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", + "2942BFC773BDA23CABC6ACFD9BFD5835BD300F0973792EF46040C53F1432BCDFB5E1DDE3BC18A5F840B52E653444D5DF"}, + {"BBAA9988776655443322110D", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "D5CA91748410C1751FF8A2F618255B68A0A12E093FF454606E59F9C1D0DDC54B65E8628E568BAD7AED07BA06A4A69483A7035490C5769E60"}, + {"BBAA9988776655443322110E", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "", + "C5CD9D1850C141E358649994EE701B68"}, + {"BBAA9988776655443322110F", + "", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "4412923493C57D5DE0D700F753CCE0D1D2D95060122E9F15A5DDBFC5787E50B5CC55EE507BCB084E479AD363AC366B95A98CA5F3000B1479"}, +} diff --git a/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go b/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go new file mode 100644 index 00000000..14a3c336 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go @@ -0,0 +1,25 @@ +package ocb + +// Second set of test vectors from https://tools.ietf.org/html/rfc7253 +var rfc7253TestVectorTaglen96 = struct { + key, nonce, header, plaintext, ciphertext string +}{"0F0E0D0C0B0A09080706050403020100", + "BBAA9988776655443322110D", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627", + "1792A4E31E0755FB03E31B22116E6C2DDF9EFD6E33D536F1A0124B0A55BAE884ED93481529C76B6AD0C515F4D1CDD4FDAC4F02AA"} + +var rfc7253AlgorithmTest = []struct { + KEYLEN, TAGLEN int + OUTPUT string +}{ + {128, 128, "67E944D23256C5E0B6C61FA22FDF1EA2"}, + {192, 128, "F673F2C3E7174AAE7BAE986CA9F29E17"}, + {256, 128, "D90EB8E9C977C88B79DD793D7FFA161C"}, + {128, 96, "77A3D8E73589158D25D01209"}, + {192, 96, "05D56EAD2752C86BE6932C5E"}, + {256, 96, "5458359AC23B0CBA9E6330DD"}, + {128, 64, "192C9B7BD90BA06A"}, + {192, 64, "0066BC6E0EF34E24"}, + {256, 64, "7D4EA5D445501CBE"}, +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go new file mode 100644 index 00000000..3c6251d1 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go @@ -0,0 +1,153 @@ +// Copyright 2014 Matthew Endsley +// All rights reserved +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted providing that the following conditions +// are met: +// 1. Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// 2. Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR +// IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY +// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING +// IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +// POSSIBILITY OF SUCH DAMAGE. + +// Package keywrap is an implementation of the RFC 3394 AES key wrapping +// algorithm. This is used in OpenPGP with elliptic curve keys. +package keywrap + +import ( + "crypto/aes" + "encoding/binary" + "errors" +) + +var ( + // ErrWrapPlaintext is returned if the plaintext is not a multiple + // of 64 bits. + ErrWrapPlaintext = errors.New("keywrap: plainText must be a multiple of 64 bits") + + // ErrUnwrapCiphertext is returned if the ciphertext is not a + // multiple of 64 bits. + ErrUnwrapCiphertext = errors.New("keywrap: cipherText must by a multiple of 64 bits") + + // ErrUnwrapFailed is returned if unwrapping a key fails. + ErrUnwrapFailed = errors.New("keywrap: failed to unwrap key") + + // NB: the AES NewCipher call only fails if the key is an invalid length. + + // ErrInvalidKey is returned when the AES key is invalid. + ErrInvalidKey = errors.New("keywrap: invalid AES key") +) + +// Wrap a key using the RFC 3394 AES Key Wrap Algorithm. +func Wrap(key, plainText []byte) ([]byte, error) { + if len(plainText)%8 != 0 { + return nil, ErrWrapPlaintext + } + + c, err := aes.NewCipher(key) + if err != nil { + return nil, ErrInvalidKey + } + + nblocks := len(plainText) / 8 + + // 1) Initialize variables. + var block [aes.BlockSize]byte + // - Set A = IV, an initial value (see 2.2.3) + for ii := 0; ii < 8; ii++ { + block[ii] = 0xA6 + } + + // - For i = 1 to n + // - Set R[i] = P[i] + intermediate := make([]byte, len(plainText)) + copy(intermediate, plainText) + + // 2) Calculate intermediate values. + for ii := 0; ii < 6; ii++ { + for jj := 0; jj < nblocks; jj++ { + // - B = AES(K, A | R[i]) + copy(block[8:], intermediate[jj*8:jj*8+8]) + c.Encrypt(block[:], block[:]) + + // - A = MSB(64, B) ^ t where t = (n*j)+1 + t := uint64(ii*nblocks + jj + 1) + val := binary.BigEndian.Uint64(block[:8]) ^ t + binary.BigEndian.PutUint64(block[:8], val) + + // - R[i] = LSB(64, B) + copy(intermediate[jj*8:jj*8+8], block[8:]) + } + } + + // 3) Output results. + // - Set C[0] = A + // - For i = 1 to n + // - C[i] = R[i] + return append(block[:8], intermediate...), nil +} + +// Unwrap a key using the RFC 3394 AES Key Wrap Algorithm. +func Unwrap(key, cipherText []byte) ([]byte, error) { + if len(cipherText)%8 != 0 { + return nil, ErrUnwrapCiphertext + } + + c, err := aes.NewCipher(key) + if err != nil { + return nil, ErrInvalidKey + } + + nblocks := len(cipherText)/8 - 1 + + // 1) Initialize variables. + var block [aes.BlockSize]byte + // - Set A = C[0] + copy(block[:8], cipherText[:8]) + + // - For i = 1 to n + // - Set R[i] = C[i] + intermediate := make([]byte, len(cipherText)-8) + copy(intermediate, cipherText[8:]) + + // 2) Compute intermediate values. + for jj := 5; jj >= 0; jj-- { + for ii := nblocks - 1; ii >= 0; ii-- { + // - B = AES-1(K, (A ^ t) | R[i]) where t = n*j+1 + // - A = MSB(64, B) + t := uint64(jj*nblocks + ii + 1) + val := binary.BigEndian.Uint64(block[:8]) ^ t + binary.BigEndian.PutUint64(block[:8], val) + + copy(block[8:], intermediate[ii*8:ii*8+8]) + c.Decrypt(block[:], block[:]) + + // - R[i] = LSB(B, 64) + copy(intermediate[ii*8:ii*8+8], block[8:]) + } + } + + // 3) Output results. + // - If A is an appropriate initial value (see 2.2.3), + for ii := 0; ii < 8; ii++ { + if block[ii] != 0xA6 { + return nil, ErrUnwrapFailed + } + } + + // - For i = 1 to n + // - P[i] = R[i] + return intermediate, nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/armor.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/armor.go new file mode 100644 index 00000000..d7af9141 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/armor.go @@ -0,0 +1,231 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package armor implements OpenPGP ASCII Armor, see RFC 4880. OpenPGP Armor is +// very similar to PEM except that it has an additional CRC checksum. +package armor // import "github.com/ProtonMail/go-crypto/openpgp/armor" + +import ( + "bufio" + "bytes" + "encoding/base64" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// A Block represents an OpenPGP armored structure. +// +// The encoded form is: +// +// -----BEGIN Type----- +// Headers +// +// base64-encoded Bytes +// '=' base64 encoded checksum +// -----END Type----- +// +// where Headers is a possibly empty sequence of Key: Value lines. +// +// Since the armored data can be very large, this package presents a streaming +// interface. +type Block struct { + Type string // The type, taken from the preamble (i.e. "PGP SIGNATURE"). + Header map[string]string // Optional headers. + Body io.Reader // A Reader from which the contents can be read + lReader lineReader + oReader openpgpReader +} + +var ArmorCorrupt error = errors.StructuralError("armor invalid") + +const crc24Init = 0xb704ce +const crc24Poly = 0x1864cfb +const crc24Mask = 0xffffff + +// crc24 calculates the OpenPGP checksum as specified in RFC 4880, section 6.1 +func crc24(crc uint32, d []byte) uint32 { + for _, b := range d { + crc ^= uint32(b) << 16 + for i := 0; i < 8; i++ { + crc <<= 1 + if crc&0x1000000 != 0 { + crc ^= crc24Poly + } + } + } + return crc +} + +var armorStart = []byte("-----BEGIN ") +var armorEnd = []byte("-----END ") +var armorEndOfLine = []byte("-----") + +// lineReader wraps a line based reader. It watches for the end of an armor +// block and records the expected CRC value. +type lineReader struct { + in *bufio.Reader + buf []byte + eof bool + crc uint32 + crcSet bool +} + +func (l *lineReader) Read(p []byte) (n int, err error) { + if l.eof { + return 0, io.EOF + } + + if len(l.buf) > 0 { + n = copy(p, l.buf) + l.buf = l.buf[n:] + return + } + + line, isPrefix, err := l.in.ReadLine() + if err != nil { + return + } + if isPrefix { + return 0, ArmorCorrupt + } + + if bytes.HasPrefix(line, armorEnd) { + l.eof = true + return 0, io.EOF + } + + if len(line) == 5 && line[0] == '=' { + // This is the checksum line + var expectedBytes [3]byte + var m int + m, err = base64.StdEncoding.Decode(expectedBytes[0:], line[1:]) + if m != 3 || err != nil { + return + } + l.crc = uint32(expectedBytes[0])<<16 | + uint32(expectedBytes[1])<<8 | + uint32(expectedBytes[2]) + + line, _, err = l.in.ReadLine() + if err != nil && err != io.EOF { + return + } + if !bytes.HasPrefix(line, armorEnd) { + return 0, ArmorCorrupt + } + + l.eof = true + l.crcSet = true + return 0, io.EOF + } + + if len(line) > 96 { + return 0, ArmorCorrupt + } + + n = copy(p, line) + bytesToSave := len(line) - n + if bytesToSave > 0 { + if cap(l.buf) < bytesToSave { + l.buf = make([]byte, 0, bytesToSave) + } + l.buf = l.buf[0:bytesToSave] + copy(l.buf, line[n:]) + } + + return +} + +// openpgpReader passes Read calls to the underlying base64 decoder, but keeps +// a running CRC of the resulting data and checks the CRC against the value +// found by the lineReader at EOF. +type openpgpReader struct { + lReader *lineReader + b64Reader io.Reader + currentCRC uint32 +} + +func (r *openpgpReader) Read(p []byte) (n int, err error) { + n, err = r.b64Reader.Read(p) + r.currentCRC = crc24(r.currentCRC, p[:n]) + + if err == io.EOF && r.lReader.crcSet && r.lReader.crc != uint32(r.currentCRC&crc24Mask) { + return 0, ArmorCorrupt + } + + return +} + +// Decode reads a PGP armored block from the given Reader. It will ignore +// leading garbage. If it doesn't find a block, it will return nil, io.EOF. The +// given Reader is not usable after calling this function: an arbitrary amount +// of data may have been read past the end of the block. +func Decode(in io.Reader) (p *Block, err error) { + r := bufio.NewReaderSize(in, 100) + var line []byte + ignoreNext := false + +TryNextBlock: + p = nil + + // Skip leading garbage + for { + ignoreThis := ignoreNext + line, ignoreNext, err = r.ReadLine() + if err != nil { + return + } + if ignoreNext || ignoreThis { + continue + } + line = bytes.TrimSpace(line) + if len(line) > len(armorStart)+len(armorEndOfLine) && bytes.HasPrefix(line, armorStart) { + break + } + } + + p = new(Block) + p.Type = string(line[len(armorStart) : len(line)-len(armorEndOfLine)]) + p.Header = make(map[string]string) + nextIsContinuation := false + var lastKey string + + // Read headers + for { + isContinuation := nextIsContinuation + line, nextIsContinuation, err = r.ReadLine() + if err != nil { + p = nil + return + } + if isContinuation { + p.Header[lastKey] += string(line) + continue + } + line = bytes.TrimSpace(line) + if len(line) == 0 { + break + } + + i := bytes.Index(line, []byte(":")) + if i == -1 { + goto TryNextBlock + } + lastKey = string(line[:i]) + var value string + if len(line) > i+2 { + value = string(line[i+2:]) + } + p.Header[lastKey] = value + } + + p.lReader.in = r + p.oReader.currentCRC = crc24Init + p.oReader.lReader = &p.lReader + p.oReader.b64Reader = base64.NewDecoder(base64.StdEncoding, &p.lReader) + p.Body = &p.oReader + + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/encode.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/encode.go new file mode 100644 index 00000000..5b6e16c1 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/armor/encode.go @@ -0,0 +1,161 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package armor + +import ( + "encoding/base64" + "io" +) + +var armorHeaderSep = []byte(": ") +var blockEnd = []byte("\n=") +var newline = []byte("\n") +var armorEndOfLineOut = []byte("-----\n") + +// writeSlices writes its arguments to the given Writer. +func writeSlices(out io.Writer, slices ...[]byte) (err error) { + for _, s := range slices { + _, err = out.Write(s) + if err != nil { + return err + } + } + return +} + +// lineBreaker breaks data across several lines, all of the same byte length +// (except possibly the last). Lines are broken with a single '\n'. +type lineBreaker struct { + lineLength int + line []byte + used int + out io.Writer + haveWritten bool +} + +func newLineBreaker(out io.Writer, lineLength int) *lineBreaker { + return &lineBreaker{ + lineLength: lineLength, + line: make([]byte, lineLength), + used: 0, + out: out, + } +} + +func (l *lineBreaker) Write(b []byte) (n int, err error) { + n = len(b) + + if n == 0 { + return + } + + if l.used == 0 && l.haveWritten { + _, err = l.out.Write([]byte{'\n'}) + if err != nil { + return + } + } + + if l.used+len(b) < l.lineLength { + l.used += copy(l.line[l.used:], b) + return + } + + l.haveWritten = true + _, err = l.out.Write(l.line[0:l.used]) + if err != nil { + return + } + excess := l.lineLength - l.used + l.used = 0 + + _, err = l.out.Write(b[0:excess]) + if err != nil { + return + } + + _, err = l.Write(b[excess:]) + return +} + +func (l *lineBreaker) Close() (err error) { + if l.used > 0 { + _, err = l.out.Write(l.line[0:l.used]) + if err != nil { + return + } + } + + return +} + +// encoding keeps track of a running CRC24 over the data which has been written +// to it and outputs a OpenPGP checksum when closed, followed by an armor +// trailer. +// +// It's built into a stack of io.Writers: +// +// encoding -> base64 encoder -> lineBreaker -> out +type encoding struct { + out io.Writer + breaker *lineBreaker + b64 io.WriteCloser + crc uint32 + blockType []byte +} + +func (e *encoding) Write(data []byte) (n int, err error) { + e.crc = crc24(e.crc, data) + return e.b64.Write(data) +} + +func (e *encoding) Close() (err error) { + err = e.b64.Close() + if err != nil { + return + } + e.breaker.Close() + + var checksumBytes [3]byte + checksumBytes[0] = byte(e.crc >> 16) + checksumBytes[1] = byte(e.crc >> 8) + checksumBytes[2] = byte(e.crc) + + var b64ChecksumBytes [4]byte + base64.StdEncoding.Encode(b64ChecksumBytes[:], checksumBytes[:]) + + return writeSlices(e.out, blockEnd, b64ChecksumBytes[:], newline, armorEnd, e.blockType, armorEndOfLine) +} + +// Encode returns a WriteCloser which will encode the data written to it in +// OpenPGP armor. +func Encode(out io.Writer, blockType string, headers map[string]string) (w io.WriteCloser, err error) { + bType := []byte(blockType) + err = writeSlices(out, armorStart, bType, armorEndOfLineOut) + if err != nil { + return + } + + for k, v := range headers { + err = writeSlices(out, []byte(k), armorHeaderSep, []byte(v), newline) + if err != nil { + return + } + } + + _, err = out.Write(newline) + if err != nil { + return + } + + e := &encoding{ + out: out, + breaker: newLineBreaker(out, 64), + crc: crc24Init, + blockType: bType, + } + e.b64 = base64.NewEncoder(base64.StdEncoding, e.breaker) + return e, nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/canonical_text.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/canonical_text.go new file mode 100644 index 00000000..a94f6150 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/canonical_text.go @@ -0,0 +1,65 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package openpgp + +import ( + "hash" + "io" +) + +// NewCanonicalTextHash reformats text written to it into the canonical +// form and then applies the hash h. See RFC 4880, section 5.2.1. +func NewCanonicalTextHash(h hash.Hash) hash.Hash { + return &canonicalTextHash{h, 0} +} + +type canonicalTextHash struct { + h hash.Hash + s int +} + +var newline = []byte{'\r', '\n'} + +func writeCanonical(cw io.Writer, buf []byte, s *int) (int, error) { + start := 0 + for i, c := range buf { + switch *s { + case 0: + if c == '\r' { + *s = 1 + } else if c == '\n' { + cw.Write(buf[start:i]) + cw.Write(newline) + start = i + 1 + } + case 1: + *s = 0 + } + } + + cw.Write(buf[start:]) + return len(buf), nil +} + +func (cth *canonicalTextHash) Write(buf []byte) (int, error) { + return writeCanonical(cth.h, buf, &cth.s) +} + +func (cth *canonicalTextHash) Sum(in []byte) []byte { + return cth.h.Sum(in) +} + +func (cth *canonicalTextHash) Reset() { + cth.h.Reset() + cth.s = 0 +} + +func (cth *canonicalTextHash) Size() int { + return cth.h.Size() +} + +func (cth *canonicalTextHash) BlockSize() int { + return cth.h.BlockSize() +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdh/ecdh.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdh/ecdh.go new file mode 100644 index 00000000..c895bad6 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdh/ecdh.go @@ -0,0 +1,210 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package ecdh implements ECDH encryption, suitable for OpenPGP, +// as specified in RFC 6637, section 8. +package ecdh + +import ( + "bytes" + "errors" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/aes/keywrap" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/internal/ecc" +) + +type KDF struct { + Hash algorithm.Hash + Cipher algorithm.Cipher +} + +type PublicKey struct { + curve ecc.ECDHCurve + Point []byte + KDF +} + +type PrivateKey struct { + PublicKey + D []byte +} + +func NewPublicKey(curve ecc.ECDHCurve, kdfHash algorithm.Hash, kdfCipher algorithm.Cipher) *PublicKey { + return &PublicKey{ + curve: curve, + KDF: KDF{ + Hash: kdfHash, + Cipher: kdfCipher, + }, + } +} + +func NewPrivateKey(key PublicKey) *PrivateKey { + return &PrivateKey{ + PublicKey: key, + } +} + +func (pk *PublicKey) GetCurve() ecc.ECDHCurve { + return pk.curve +} + +func (pk *PublicKey) MarshalPoint() []byte { + return pk.curve.MarshalBytePoint(pk.Point) +} + +func (pk *PublicKey) UnmarshalPoint(p []byte) error { + pk.Point = pk.curve.UnmarshalBytePoint(p) + if pk.Point == nil { + return errors.New("ecdh: failed to parse EC point") + } + return nil +} + +func (sk *PrivateKey) MarshalByteSecret() []byte { + return sk.curve.MarshalByteSecret(sk.D) +} + +func (sk *PrivateKey) UnmarshalByteSecret(d []byte) error { + sk.D = sk.curve.UnmarshalByteSecret(d) + + if sk.D == nil { + return errors.New("ecdh: failed to parse scalar") + } + return nil +} + +func GenerateKey(rand io.Reader, c ecc.ECDHCurve, kdf KDF) (priv *PrivateKey, err error) { + priv = new(PrivateKey) + priv.PublicKey.curve = c + priv.PublicKey.KDF = kdf + priv.PublicKey.Point, priv.D, err = c.GenerateECDH(rand) + return +} + +func Encrypt(random io.Reader, pub *PublicKey, msg, curveOID, fingerprint []byte) (vsG, c []byte, err error) { + if len(msg) > 40 { + return nil, nil, errors.New("ecdh: message too long") + } + // the sender MAY use 21, 13, and 5 bytes of padding for AES-128, + // AES-192, and AES-256, respectively, to provide the same number of + // octets, 40 total, as an input to the key wrapping method. + padding := make([]byte, 40-len(msg)) + for i := range padding { + padding[i] = byte(40 - len(msg)) + } + m := append(msg, padding...) + + ephemeral, zb, err := pub.curve.Encaps(random, pub.Point) + if err != nil { + return nil, nil, err + } + + vsG = pub.curve.MarshalBytePoint(ephemeral) + + z, err := buildKey(pub, zb, curveOID, fingerprint, false, false) + if err != nil { + return nil, nil, err + } + + if c, err = keywrap.Wrap(z, m); err != nil { + return nil, nil, err + } + + return vsG, c, nil + +} + +func Decrypt(priv *PrivateKey, vsG, c, curveOID, fingerprint []byte) (msg []byte, err error) { + var m []byte + zb, err := priv.PublicKey.curve.Decaps(priv.curve.UnmarshalBytePoint(vsG), priv.D) + + // Try buildKey three times to workaround an old bug, see comments in buildKey. + for i := 0; i < 3; i++ { + var z []byte + // RFC6637 §8: "Compute Z = KDF( S, Z_len, Param );" + z, err = buildKey(&priv.PublicKey, zb, curveOID, fingerprint, i == 1, i == 2) + if err != nil { + return nil, err + } + + // RFC6637 §8: "Compute C = AESKeyWrap( Z, c ) as per [RFC3394]" + m, err = keywrap.Unwrap(z, c) + if err == nil { + break + } + } + + // Only return an error after we've tried all (required) variants of buildKey. + if err != nil { + return nil, err + } + + // RFC6637 §8: "m = symm_alg_ID || session key || checksum || pkcs5_padding" + // The last byte should be the length of the padding, as per PKCS5; strip it off. + return m[:len(m)-int(m[len(m)-1])], nil +} + +func buildKey(pub *PublicKey, zb []byte, curveOID, fingerprint []byte, stripLeading, stripTrailing bool) ([]byte, error) { + // Param = curve_OID_len || curve_OID || public_key_alg_ID || 03 + // || 01 || KDF_hash_ID || KEK_alg_ID for AESKeyWrap + // || "Anonymous Sender " || recipient_fingerprint; + param := new(bytes.Buffer) + if _, err := param.Write(curveOID); err != nil { + return nil, err + } + algKDF := []byte{18, 3, 1, pub.KDF.Hash.Id(), pub.KDF.Cipher.Id()} + if _, err := param.Write(algKDF); err != nil { + return nil, err + } + if _, err := param.Write([]byte("Anonymous Sender ")); err != nil { + return nil, err + } + // For v5 keys, the 20 leftmost octets of the fingerprint are used. + if _, err := param.Write(fingerprint[:20]); err != nil { + return nil, err + } + if param.Len()-len(curveOID) != 45 { + return nil, errors.New("ecdh: malformed KDF Param") + } + + // MB = Hash ( 00 || 00 || 00 || 01 || ZB || Param ); + h := pub.KDF.Hash.New() + if _, err := h.Write([]byte{0x0, 0x0, 0x0, 0x1}); err != nil { + return nil, err + } + zbLen := len(zb) + i := 0 + j := zbLen - 1 + if stripLeading { + // Work around old go crypto bug where the leading zeros are missing. + for i < zbLen && zb[i] == 0 { + i++ + } + } + if stripTrailing { + // Work around old OpenPGP.js bug where insignificant trailing zeros in + // this little-endian number are missing. + // (See https://github.com/openpgpjs/openpgpjs/pull/853.) + for j >= 0 && zb[j] == 0 { + j-- + } + } + if _, err := h.Write(zb[i : j+1]); err != nil { + return nil, err + } + if _, err := h.Write(param.Bytes()); err != nil { + return nil, err + } + mb := h.Sum(nil) + + return mb[:pub.KDF.Cipher.KeySize()], nil // return oBits leftmost bits of MB. + +} + +func Validate(priv *PrivateKey) error { + return priv.curve.ValidateECDH(priv.Point, priv.D) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdsa/ecdsa.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdsa/ecdsa.go new file mode 100644 index 00000000..f94ae1b2 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/ecdsa/ecdsa.go @@ -0,0 +1,80 @@ +// Package ecdsa implements ECDSA signature, suitable for OpenPGP, +// as specified in RFC 6637, section 5. +package ecdsa + +import ( + "errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/ecc" + "io" + "math/big" +) + +type PublicKey struct { + X, Y *big.Int + curve ecc.ECDSACurve +} + +type PrivateKey struct { + PublicKey + D *big.Int +} + +func NewPublicKey(curve ecc.ECDSACurve) *PublicKey { + return &PublicKey{ + curve: curve, + } +} + +func NewPrivateKey(key PublicKey) *PrivateKey { + return &PrivateKey{ + PublicKey: key, + } +} + +func (pk *PublicKey) GetCurve() ecc.ECDSACurve { + return pk.curve +} + +func (pk *PublicKey) MarshalPoint() []byte { + return pk.curve.MarshalIntegerPoint(pk.X, pk.Y) +} + +func (pk *PublicKey) UnmarshalPoint(p []byte) error { + pk.X, pk.Y = pk.curve.UnmarshalIntegerPoint(p) + if pk.X == nil { + return errors.New("ecdsa: failed to parse EC point") + } + return nil +} + +func (sk *PrivateKey) MarshalIntegerSecret() []byte { + return sk.curve.MarshalIntegerSecret(sk.D) +} + +func (sk *PrivateKey) UnmarshalIntegerSecret(d []byte) error { + sk.D = sk.curve.UnmarshalIntegerSecret(d) + + if sk.D == nil { + return errors.New("ecdsa: failed to parse scalar") + } + return nil +} + +func GenerateKey(rand io.Reader, c ecc.ECDSACurve) (priv *PrivateKey, err error) { + priv = new(PrivateKey) + priv.PublicKey.curve = c + priv.PublicKey.X, priv.PublicKey.Y, priv.D, err = c.GenerateECDSA(rand) + return +} + +func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) { + return priv.PublicKey.curve.Sign(rand, priv.X, priv.Y, priv.D, hash) +} + +func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool { + return pub.curve.Verify(pub.X, pub.Y, hash, r, s) +} + +func Validate(priv *PrivateKey) error { + return priv.curve.ValidateECDSA(priv.X, priv.Y, priv.D.Bytes()) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/eddsa/eddsa.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/eddsa/eddsa.go new file mode 100644 index 00000000..99ecfc7f --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/eddsa/eddsa.go @@ -0,0 +1,91 @@ +// Package eddsa implements EdDSA signature, suitable for OpenPGP, as specified in +// https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7 +package eddsa + +import ( + "errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/ecc" + "io" +) + +type PublicKey struct { + X []byte + curve ecc.EdDSACurve +} + +type PrivateKey struct { + PublicKey + D []byte +} + +func NewPublicKey(curve ecc.EdDSACurve) *PublicKey { + return &PublicKey{ + curve: curve, + } +} + +func NewPrivateKey(key PublicKey) *PrivateKey { + return &PrivateKey{ + PublicKey: key, + } +} + +func (pk *PublicKey) GetCurve() ecc.EdDSACurve { + return pk.curve +} + +func (pk *PublicKey) MarshalPoint() []byte { + return pk.curve.MarshalBytePoint(pk.X) +} + +func (pk *PublicKey) UnmarshalPoint(x []byte) error { + pk.X = pk.curve.UnmarshalBytePoint(x) + + if pk.X == nil { + return errors.New("eddsa: failed to parse EC point") + } + return nil +} + +func (sk *PrivateKey) MarshalByteSecret() []byte { + return sk.curve.MarshalByteSecret(sk.D) +} + +func (sk *PrivateKey) UnmarshalByteSecret(d []byte) error { + sk.D = sk.curve.UnmarshalByteSecret(d) + + if sk.D == nil { + return errors.New("eddsa: failed to parse scalar") + } + return nil +} + +func GenerateKey(rand io.Reader, c ecc.EdDSACurve) (priv *PrivateKey, err error) { + priv = new(PrivateKey) + priv.PublicKey.curve = c + priv.PublicKey.X, priv.D, err = c.GenerateEdDSA(rand) + return +} + +func Sign(priv *PrivateKey, message []byte) (r, s []byte, err error) { + sig, err := priv.PublicKey.curve.Sign(priv.PublicKey.X, priv.D, message) + if err != nil { + return nil, nil, err + } + + r, s = priv.PublicKey.curve.MarshalSignature(sig) + return +} + +func Verify(pub *PublicKey, message, r, s []byte) bool { + sig := pub.curve.UnmarshalSignature(r, s) + if sig == nil { + return false + } + + return pub.curve.Verify(pub.X, message, sig) +} + +func Validate(priv *PrivateKey) error { + return priv.curve.ValidateEdDSA(priv.PublicKey.X, priv.D) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/elgamal/elgamal.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/elgamal/elgamal.go new file mode 100644 index 00000000..bad27743 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/elgamal/elgamal.go @@ -0,0 +1,124 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package elgamal implements ElGamal encryption, suitable for OpenPGP, +// as specified in "A Public-Key Cryptosystem and a Signature Scheme Based on +// Discrete Logarithms," IEEE Transactions on Information Theory, v. IT-31, +// n. 4, 1985, pp. 469-472. +// +// This form of ElGamal embeds PKCS#1 v1.5 padding, which may make it +// unsuitable for other protocols. RSA should be used in preference in any +// case. +package elgamal // import "github.com/ProtonMail/go-crypto/openpgp/elgamal" + +import ( + "crypto/rand" + "crypto/subtle" + "errors" + "io" + "math/big" +) + +// PublicKey represents an ElGamal public key. +type PublicKey struct { + G, P, Y *big.Int +} + +// PrivateKey represents an ElGamal private key. +type PrivateKey struct { + PublicKey + X *big.Int +} + +// Encrypt encrypts the given message to the given public key. The result is a +// pair of integers. Errors can result from reading random, or because msg is +// too large to be encrypted to the public key. +func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err error) { + pLen := (pub.P.BitLen() + 7) / 8 + if len(msg) > pLen-11 { + err = errors.New("elgamal: message too long") + return + } + + // EM = 0x02 || PS || 0x00 || M + em := make([]byte, pLen-1) + em[0] = 2 + ps, mm := em[1:len(em)-len(msg)-1], em[len(em)-len(msg):] + err = nonZeroRandomBytes(ps, random) + if err != nil { + return + } + em[len(em)-len(msg)-1] = 0 + copy(mm, msg) + + m := new(big.Int).SetBytes(em) + + k, err := rand.Int(random, pub.P) + if err != nil { + return + } + + c1 = new(big.Int).Exp(pub.G, k, pub.P) + s := new(big.Int).Exp(pub.Y, k, pub.P) + c2 = s.Mul(s, m) + c2.Mod(c2, pub.P) + + return +} + +// Decrypt takes two integers, resulting from an ElGamal encryption, and +// returns the plaintext of the message. An error can result only if the +// ciphertext is invalid. Users should keep in mind that this is a padding +// oracle and thus, if exposed to an adaptive chosen ciphertext attack, can +// be used to break the cryptosystem. See “Chosen Ciphertext Attacks +// Against Protocols Based on the RSA Encryption Standard PKCS #1”, Daniel +// Bleichenbacher, Advances in Cryptology (Crypto '98), +func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) { + s := new(big.Int).Exp(c1, priv.X, priv.P) + if s.ModInverse(s, priv.P) == nil { + return nil, errors.New("elgamal: invalid private key") + } + s.Mul(s, c2) + s.Mod(s, priv.P) + em := s.Bytes() + + firstByteIsTwo := subtle.ConstantTimeByteEq(em[0], 2) + + // The remainder of the plaintext must be a string of non-zero random + // octets, followed by a 0, followed by the message. + // lookingForIndex: 1 iff we are still looking for the zero. + // index: the offset of the first zero byte. + var lookingForIndex, index int + lookingForIndex = 1 + + for i := 1; i < len(em); i++ { + equals0 := subtle.ConstantTimeByteEq(em[i], 0) + index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index) + lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex) + } + + if firstByteIsTwo != 1 || lookingForIndex != 0 || index < 9 { + return nil, errors.New("elgamal: decryption error") + } + return em[index+1:], nil +} + +// nonZeroRandomBytes fills the given slice with non-zero random octets. +func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) { + _, err = io.ReadFull(rand, s) + if err != nil { + return + } + + for i := 0; i < len(s); i++ { + for s[i] == 0 { + _, err = io.ReadFull(rand, s[i:i+1]) + if err != nil { + return + } + } + } + + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/errors/errors.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/errors/errors.go new file mode 100644 index 00000000..17e2bcfe --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/errors/errors.go @@ -0,0 +1,116 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package errors contains common error types for the OpenPGP packages. +package errors // import "github.com/ProtonMail/go-crypto/openpgp/errors" + +import ( + "strconv" +) + +// A StructuralError is returned when OpenPGP data is found to be syntactically +// invalid. +type StructuralError string + +func (s StructuralError) Error() string { + return "openpgp: invalid data: " + string(s) +} + +// UnsupportedError indicates that, although the OpenPGP data is valid, it +// makes use of currently unimplemented features. +type UnsupportedError string + +func (s UnsupportedError) Error() string { + return "openpgp: unsupported feature: " + string(s) +} + +// InvalidArgumentError indicates that the caller is in error and passed an +// incorrect value. +type InvalidArgumentError string + +func (i InvalidArgumentError) Error() string { + return "openpgp: invalid argument: " + string(i) +} + +// SignatureError indicates that a syntactically valid signature failed to +// validate. +type SignatureError string + +func (b SignatureError) Error() string { + return "openpgp: invalid signature: " + string(b) +} + +var ErrMDCHashMismatch error = SignatureError("MDC hash mismatch") +var ErrMDCMissing error = SignatureError("MDC packet not found") + +type signatureExpiredError int + +func (se signatureExpiredError) Error() string { + return "openpgp: signature expired" +} + +var ErrSignatureExpired error = signatureExpiredError(0) + +type keyExpiredError int + +func (ke keyExpiredError) Error() string { + return "openpgp: key expired" +} + +var ErrKeyExpired error = keyExpiredError(0) + +type keyIncorrectError int + +func (ki keyIncorrectError) Error() string { + return "openpgp: incorrect key" +} + +var ErrKeyIncorrect error = keyIncorrectError(0) + +// KeyInvalidError indicates that the public key parameters are invalid +// as they do not match the private ones +type KeyInvalidError string + +func (e KeyInvalidError) Error() string { + return "openpgp: invalid key: " + string(e) +} + +type unknownIssuerError int + +func (unknownIssuerError) Error() string { + return "openpgp: signature made by unknown entity" +} + +var ErrUnknownIssuer error = unknownIssuerError(0) + +type keyRevokedError int + +func (keyRevokedError) Error() string { + return "openpgp: signature made by revoked key" +} + +var ErrKeyRevoked error = keyRevokedError(0) + +type UnknownPacketTypeError uint8 + +func (upte UnknownPacketTypeError) Error() string { + return "openpgp: unknown packet type: " + strconv.Itoa(int(upte)) +} + +// AEADError indicates that there is a problem when initializing or using a +// AEAD instance, configuration struct, nonces or index values. +type AEADError string + +func (ae AEADError) Error() string { + return "openpgp: aead error: " + string(ae) +} + +// ErrDummyPrivateKey results when operations are attempted on a private key +// that is just a dummy key. See +// https://git.gnupg.org/cgi-bin/gitweb.cgi?p=gnupg.git;a=blob;f=doc/DETAILS;h=fe55ae16ab4e26d8356dc574c9e8bc935e71aef1;hb=23191d7851eae2217ecdac6484349849a24fd94a#l1109 +type ErrDummyPrivateKey string + +func (dke ErrDummyPrivateKey) Error() string { + return "openpgp: s2k GNU dummy key: " + string(dke) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/hash.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/hash.go new file mode 100644 index 00000000..526bd777 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/hash.go @@ -0,0 +1,24 @@ +package openpgp + +import ( + "crypto" + + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" +) + +// HashIdToHash returns a crypto.Hash which corresponds to the given OpenPGP +// hash id. +func HashIdToHash(id byte) (h crypto.Hash, ok bool) { + return algorithm.HashIdToHash(id) +} + +// HashIdToString returns the name of the hash function corresponding to the +// given OpenPGP hash id. +func HashIdToString(id byte) (name string, ok bool) { + return algorithm.HashIdToString(id) +} + +// HashToHashId returns an OpenPGP hash id which corresponds the given Hash. +func HashToHashId(h crypto.Hash) (id byte, ok bool) { + return algorithm.HashToHashId(h) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go new file mode 100644 index 00000000..d0670651 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go @@ -0,0 +1,65 @@ +// Copyright (C) 2019 ProtonTech AG + +package algorithm + +import ( + "crypto/cipher" + "github.com/ProtonMail/go-crypto/eax" + "github.com/ProtonMail/go-crypto/ocb" +) + +// AEADMode defines the Authenticated Encryption with Associated Data mode of +// operation. +type AEADMode uint8 + +// Supported modes of operation (see RFC4880bis [EAX] and RFC7253) +const ( + AEADModeEAX = AEADMode(1) + AEADModeOCB = AEADMode(2) + AEADModeGCM = AEADMode(3) +) + +// TagLength returns the length in bytes of authentication tags. +func (mode AEADMode) TagLength() int { + switch mode { + case AEADModeEAX: + return 16 + case AEADModeOCB: + return 16 + case AEADModeGCM: + return 16 + default: + return 0 + } +} + +// NonceLength returns the length in bytes of nonces. +func (mode AEADMode) NonceLength() int { + switch mode { + case AEADModeEAX: + return 16 + case AEADModeOCB: + return 15 + case AEADModeGCM: + return 12 + default: + return 0 + } +} + +// New returns a fresh instance of the given mode +func (mode AEADMode) New(block cipher.Block) (alg cipher.AEAD) { + var err error + switch mode { + case AEADModeEAX: + alg, err = eax.NewEAX(block) + case AEADModeOCB: + alg, err = ocb.NewOCB(block) + case AEADModeGCM: + alg, err = cipher.NewGCM(block) + } + if err != nil { + panic(err.Error()) + } + return alg +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go new file mode 100644 index 00000000..5760cff8 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go @@ -0,0 +1,107 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package algorithm + +import ( + "crypto/aes" + "crypto/cipher" + "crypto/des" + + "golang.org/x/crypto/cast5" +) + +// Cipher is an official symmetric key cipher algorithm. See RFC 4880, +// section 9.2. +type Cipher interface { + // Id returns the algorithm ID, as a byte, of the cipher. + Id() uint8 + // KeySize returns the key size, in bytes, of the cipher. + KeySize() int + // BlockSize returns the block size, in bytes, of the cipher. + BlockSize() int + // New returns a fresh instance of the given cipher. + New(key []byte) cipher.Block +} + +// The following constants mirror the OpenPGP standard (RFC 4880). +const ( + TripleDES = CipherFunction(2) + CAST5 = CipherFunction(3) + AES128 = CipherFunction(7) + AES192 = CipherFunction(8) + AES256 = CipherFunction(9) +) + +// CipherById represents the different block ciphers specified for OpenPGP. See +// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-13 +var CipherById = map[uint8]Cipher{ + TripleDES.Id(): TripleDES, + CAST5.Id(): CAST5, + AES128.Id(): AES128, + AES192.Id(): AES192, + AES256.Id(): AES256, +} + +type CipherFunction uint8 + +// ID returns the algorithm Id, as a byte, of cipher. +func (sk CipherFunction) Id() uint8 { + return uint8(sk) +} + +var keySizeByID = map[uint8]int{ + TripleDES.Id(): 24, + CAST5.Id(): cast5.KeySize, + AES128.Id(): 16, + AES192.Id(): 24, + AES256.Id(): 32, +} + +// KeySize returns the key size, in bytes, of cipher. +func (cipher CipherFunction) KeySize() int { + switch cipher { + case TripleDES: + return 24 + case CAST5: + return cast5.KeySize + case AES128: + return 16 + case AES192: + return 24 + case AES256: + return 32 + } + return 0 +} + +// BlockSize returns the block size, in bytes, of cipher. +func (cipher CipherFunction) BlockSize() int { + switch cipher { + case TripleDES: + return des.BlockSize + case CAST5: + return 8 + case AES128, AES192, AES256: + return 16 + } + return 0 +} + +// New returns a fresh instance of the given cipher. +func (cipher CipherFunction) New(key []byte) (block cipher.Block) { + var err error + switch cipher { + case TripleDES: + block, err = des.NewTripleDESCipher(key) + case CAST5: + block, err = cast5.NewCipher(key) + case AES128, AES192, AES256: + block, err = aes.NewCipher(key) + } + if err != nil { + panic(err.Error()) + } + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go new file mode 100644 index 00000000..d1a00fc7 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go @@ -0,0 +1,143 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package algorithm + +import ( + "crypto" + "fmt" + "hash" +) + +// Hash is an official hash function algorithm. See RFC 4880, section 9.4. +type Hash interface { + // Id returns the algorithm ID, as a byte, of Hash. + Id() uint8 + // Available reports whether the given hash function is linked into the binary. + Available() bool + // HashFunc simply returns the value of h so that Hash implements SignerOpts. + HashFunc() crypto.Hash + // New returns a new hash.Hash calculating the given hash function. New + // panics if the hash function is not linked into the binary. + New() hash.Hash + // Size returns the length, in bytes, of a digest resulting from the given + // hash function. It doesn't require that the hash function in question be + // linked into the program. + Size() int + // String is the name of the hash function corresponding to the given + // OpenPGP hash id. + String() string +} + +// The following vars mirror the crypto/Hash supported hash functions. +var ( + SHA1 Hash = cryptoHash{2, crypto.SHA1} + SHA256 Hash = cryptoHash{8, crypto.SHA256} + SHA384 Hash = cryptoHash{9, crypto.SHA384} + SHA512 Hash = cryptoHash{10, crypto.SHA512} + SHA224 Hash = cryptoHash{11, crypto.SHA224} + SHA3_256 Hash = cryptoHash{12, crypto.SHA3_256} + SHA3_512 Hash = cryptoHash{14, crypto.SHA3_512} +) + +// HashById represents the different hash functions specified for OpenPGP. See +// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-14 +var ( + HashById = map[uint8]Hash{ + SHA256.Id(): SHA256, + SHA384.Id(): SHA384, + SHA512.Id(): SHA512, + SHA224.Id(): SHA224, + SHA3_256.Id(): SHA3_256, + SHA3_512.Id(): SHA3_512, + } +) + +// cryptoHash contains pairs relating OpenPGP's hash identifier with +// Go's crypto.Hash type. See RFC 4880, section 9.4. +type cryptoHash struct { + id uint8 + crypto.Hash +} + +// Id returns the algorithm ID, as a byte, of cryptoHash. +func (h cryptoHash) Id() uint8 { + return h.id +} + +var hashNames = map[uint8]string{ + SHA256.Id(): "SHA256", + SHA384.Id(): "SHA384", + SHA512.Id(): "SHA512", + SHA224.Id(): "SHA224", + SHA3_256.Id(): "SHA3-256", + SHA3_512.Id(): "SHA3-512", +} + +func (h cryptoHash) String() string { + s, ok := hashNames[h.id] + if !ok { + panic(fmt.Sprintf("Unsupported hash function %d", h.id)) + } + return s +} + +// HashIdToHash returns a crypto.Hash which corresponds to the given OpenPGP +// hash id. +func HashIdToHash(id byte) (h crypto.Hash, ok bool) { + if hash, ok := HashById[id]; ok { + return hash.HashFunc(), true + } + return 0, false +} + +// HashIdToHashWithSha1 returns a crypto.Hash which corresponds to the given OpenPGP +// hash id, allowing sha1. +func HashIdToHashWithSha1(id byte) (h crypto.Hash, ok bool) { + if hash, ok := HashById[id]; ok { + return hash.HashFunc(), true + } + + if id == SHA1.Id() { + return SHA1.HashFunc(), true + } + + return 0, false +} + +// HashIdToString returns the name of the hash function corresponding to the +// given OpenPGP hash id. +func HashIdToString(id byte) (name string, ok bool) { + if hash, ok := HashById[id]; ok { + return hash.String(), true + } + return "", false +} + +// HashToHashId returns an OpenPGP hash id which corresponds the given Hash. +func HashToHashId(h crypto.Hash) (id byte, ok bool) { + for id, hash := range HashById { + if hash.HashFunc() == h { + return id, true + } + } + + return 0, false +} + +// HashToHashIdWithSha1 returns an OpenPGP hash id which corresponds the given Hash, +// allowing instances of SHA1 +func HashToHashIdWithSha1(h crypto.Hash) (id byte, ok bool) { + for id, hash := range HashById { + if hash.HashFunc() == h { + return id, true + } + } + + if h == SHA1.HashFunc() { + return SHA1.Id(), true + } + + return 0, false +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go new file mode 100644 index 00000000..888767c4 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go @@ -0,0 +1,171 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "crypto/subtle" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + x25519lib "github.com/cloudflare/circl/dh/x25519" +) + +type curve25519 struct{} + +func NewCurve25519() *curve25519 { + return &curve25519{} +} + +func (c *curve25519) GetCurveName() string { + return "curve25519" +} + +// MarshalBytePoint encodes the public point from native format, adding the prefix. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6 +func (c *curve25519) MarshalBytePoint(point []byte) []byte { + return append([]byte{0x40}, point...) +} + +// UnmarshalBytePoint decodes the public point to native format, removing the prefix. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6 +func (c *curve25519) UnmarshalBytePoint(point []byte) []byte { + if len(point) != x25519lib.Size+1 { + return nil + } + + // Remove prefix + return point[1:] +} + +// MarshalByteSecret encodes the secret scalar from native format. +// Note that the EC secret scalar differs from the definition of public keys in +// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is +// more uniform with how big integers are represented in OpenPGP, and (2) the +// leading zeros are truncated. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1 +// Note that leading zero bytes are stripped later when encoding as an MPI. +func (c *curve25519) MarshalByteSecret(secret []byte) []byte { + d := make([]byte, x25519lib.Size) + copyReversed(d, secret) + + // The following ensures that the private key is a number of the form + // 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of + // the curve. + // + // This masking is done internally in the underlying lib and so is unnecessary + // for security, but OpenPGP implementations require that private keys be + // pre-masked. + d[0] &= 127 + d[0] |= 64 + d[31] &= 248 + + return d +} + +// UnmarshalByteSecret decodes the secret scalar from native format. +// Note that the EC secret scalar differs from the definition of public keys in +// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is +// more uniform with how big integers are represented in OpenPGP, and (2) the +// leading zeros are truncated. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1 +func (c *curve25519) UnmarshalByteSecret(d []byte) []byte { + if len(d) > x25519lib.Size { + return nil + } + + // Ensure truncated leading bytes are re-added + secret := make([]byte, x25519lib.Size) + copyReversed(secret, d) + + return secret +} + +// generateKeyPairBytes Generates a private-public key-pair. +// 'priv' is a private key; a little-endian scalar belonging to the set +// 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of the +// curve. 'pub' is simply 'priv' * G where G is the base point. +// See https://cr.yp.to/ecdh.html and RFC7748, sec 5. +func (c *curve25519) generateKeyPairBytes(rand io.Reader) (priv, pub x25519lib.Key, err error) { + _, err = io.ReadFull(rand, priv[:]) + if err != nil { + return + } + + x25519lib.KeyGen(&pub, &priv) + return +} + +func (c *curve25519) GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) { + priv, pub, err := c.generateKeyPairBytes(rand) + if err != nil { + return + } + + return pub[:], priv[:], nil +} + +func (c *genericCurve) MaskSecret(secret []byte) []byte { + return secret +} + +func (c *curve25519) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) { + // RFC6637 §8: "Generate an ephemeral key pair {v, V=vG}" + // ephemeralPrivate corresponds to `v`. + // ephemeralPublic corresponds to `V`. + ephemeralPrivate, ephemeralPublic, err := c.generateKeyPairBytes(rand) + if err != nil { + return nil, nil, err + } + + // RFC6637 §8: "Obtain the authenticated recipient public key R" + // pubKey corresponds to `R`. + var pubKey x25519lib.Key + copy(pubKey[:], point) + + // RFC6637 §8: "Compute the shared point S = vR" + // "VB = convert point V to the octet string" + // sharedPoint corresponds to `VB`. + var sharedPoint x25519lib.Key + x25519lib.Shared(&sharedPoint, &ephemeralPrivate, &pubKey) + + return ephemeralPublic[:], sharedPoint[:], nil +} + +func (c *curve25519) Decaps(vsG, secret []byte) (sharedSecret []byte, err error) { + var ephemeralPublic, decodedPrivate, sharedPoint x25519lib.Key + // RFC6637 §8: "The decryption is the inverse of the method given." + // All quoted descriptions in comments below describe encryption, and + // the reverse is performed. + // vsG corresponds to `VB` in RFC6637 §8 . + + // RFC6637 §8: "VB = convert point V to the octet string" + copy(ephemeralPublic[:], vsG) + + // decodedPrivate corresponds to `r` in RFC6637 §8 . + copy(decodedPrivate[:], secret) + + // RFC6637 §8: "Note that the recipient obtains the shared secret by calculating + // S = rV = rvG, where (r,R) is the recipient's key pair." + // sharedPoint corresponds to `S`. + x25519lib.Shared(&sharedPoint, &decodedPrivate, &ephemeralPublic) + + return sharedPoint[:], nil +} + +func (c *curve25519) ValidateECDH(point []byte, secret []byte) (err error) { + var pk, sk x25519lib.Key + copy(sk[:], secret) + x25519lib.KeyGen(&pk, &sk) + + if subtle.ConstantTimeCompare(point, pk[:]) == 0 { + return errors.KeyInvalidError("ecc: invalid curve25519 public point") + } + + return nil +} + +func copyReversed(out []byte, in []byte) { + l := len(in) + for i := 0; i < l; i++ { + out[i] = in[l-i-1] + } +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go new file mode 100644 index 00000000..35751034 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go @@ -0,0 +1,140 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "bytes" + "crypto/elliptic" + "github.com/ProtonMail/go-crypto/bitcurves" + "github.com/ProtonMail/go-crypto/brainpool" + "github.com/ProtonMail/go-crypto/openpgp/internal/encoding" +) + +type CurveInfo struct { + GenName string + Oid *encoding.OID + Curve Curve +} + +var Curves = []CurveInfo{ + { + // NIST P-256 + GenName: "P256", + Oid: encoding.NewOID([]byte{0x2A, 0x86, 0x48, 0xCE, 0x3D, 0x03, 0x01, 0x07}), + Curve: NewGenericCurve(elliptic.P256()), + }, + { + // NIST P-384 + GenName: "P384", + Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x22}), + Curve: NewGenericCurve(elliptic.P384()), + }, + { + // NIST P-521 + GenName: "P521", + Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x23}), + Curve: NewGenericCurve(elliptic.P521()), + }, + { + // SecP256k1 + GenName: "SecP256k1", + Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x0A}), + Curve: NewGenericCurve(bitcurves.S256()), + }, + { + // Curve25519 + GenName: "Curve25519", + Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0x97, 0x55, 0x01, 0x05, 0x01}), + Curve: NewCurve25519(), + }, + { + // X448 + GenName: "Curve448", + Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x6F}), + Curve: NewX448(), + }, + { + // Ed25519 + GenName: "Curve25519", + Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0xDA, 0x47, 0x0F, 0x01}), + Curve: NewEd25519(), + }, + { + // Ed448 + GenName: "Curve448", + Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x71}), + Curve: NewEd448(), + }, + { + // BrainpoolP256r1 + GenName: "BrainpoolP256", + Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x07}), + Curve: NewGenericCurve(brainpool.P256r1()), + }, + { + // BrainpoolP384r1 + GenName: "BrainpoolP384", + Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0B}), + Curve: NewGenericCurve(brainpool.P384r1()), + }, + { + // BrainpoolP512r1 + GenName: "BrainpoolP512", + Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0D}), + Curve: NewGenericCurve(brainpool.P512r1()), + }, +} + +func FindByCurve(curve Curve) *CurveInfo { + for _, curveInfo := range Curves { + if curveInfo.Curve.GetCurveName() == curve.GetCurveName() { + return &curveInfo + } + } + return nil +} + +func FindByOid(oid encoding.Field) *CurveInfo { + var rawBytes = oid.Bytes() + for _, curveInfo := range Curves { + if bytes.Equal(curveInfo.Oid.Bytes(), rawBytes) { + return &curveInfo + } + } + return nil +} + +func FindEdDSAByGenName(curveGenName string) EdDSACurve { + for _, curveInfo := range Curves { + if curveInfo.GenName == curveGenName { + curve, ok := curveInfo.Curve.(EdDSACurve) + if ok { + return curve + } + } + } + return nil +} + +func FindECDSAByGenName(curveGenName string) ECDSACurve { + for _, curveInfo := range Curves { + if curveInfo.GenName == curveGenName { + curve, ok := curveInfo.Curve.(ECDSACurve) + if ok { + return curve + } + } + } + return nil +} + +func FindECDHByGenName(curveGenName string) ECDHCurve { + for _, curveInfo := range Curves { + if curveInfo.GenName == curveGenName { + curve, ok := curveInfo.Curve.(ECDHCurve) + if ok { + return curve + } + } + } + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go new file mode 100644 index 00000000..5ed9c93b --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go @@ -0,0 +1,48 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "io" + "math/big" +) + +type Curve interface { + GetCurveName() string +} + +type ECDSACurve interface { + Curve + MarshalIntegerPoint(x, y *big.Int) []byte + UnmarshalIntegerPoint([]byte) (x, y *big.Int) + MarshalIntegerSecret(d *big.Int) []byte + UnmarshalIntegerSecret(d []byte) *big.Int + GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error) + Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error) + Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool + ValidateECDSA(x, y *big.Int, secret []byte) error +} + +type EdDSACurve interface { + Curve + MarshalBytePoint(x []byte) []byte + UnmarshalBytePoint([]byte) (x []byte) + MarshalByteSecret(d []byte) []byte + UnmarshalByteSecret(d []byte) []byte + MarshalSignature(sig []byte) (r, s []byte) + UnmarshalSignature(r, s []byte) (sig []byte) + GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) + Sign(publicKey, privateKey, message []byte) (sig []byte, err error) + Verify(publicKey, message, sig []byte) bool + ValidateEdDSA(publicKey, privateKey []byte) (err error) +} +type ECDHCurve interface { + Curve + MarshalBytePoint([]byte) (encoded []byte) + UnmarshalBytePoint(encoded []byte) []byte + MarshalByteSecret(d []byte) []byte + UnmarshalByteSecret(d []byte) []byte + GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) + Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) + Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) + ValidateECDH(public []byte, secret []byte) error +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go new file mode 100644 index 00000000..54a08a8a --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go @@ -0,0 +1,112 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "crypto/subtle" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + ed25519lib "github.com/cloudflare/circl/sign/ed25519" +) + +const ed25519Size = 32 + +type ed25519 struct{} + +func NewEd25519() *ed25519 { + return &ed25519{} +} + +func (c *ed25519) GetCurveName() string { + return "ed25519" +} + +// MarshalBytePoint encodes the public point from native format, adding the prefix. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed25519) MarshalBytePoint(x []byte) []byte { + return append([]byte{0x40}, x...) +} + +// UnmarshalBytePoint decodes a point from prefixed format to native. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed25519) UnmarshalBytePoint(point []byte) (x []byte) { + if len(point) != ed25519lib.PublicKeySize+1 { + return nil + } + + // Return unprefixed + return point[1:] +} + +// MarshalByteSecret encodes a scalar in native format. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed25519) MarshalByteSecret(d []byte) []byte { + return d +} + +// UnmarshalByteSecret decodes a scalar in native format and re-adds the stripped leading zeroes +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed25519) UnmarshalByteSecret(s []byte) (d []byte) { + if len(s) > ed25519lib.SeedSize { + return nil + } + + // Handle stripped leading zeroes + d = make([]byte, ed25519lib.SeedSize) + copy(d[ed25519lib.SeedSize-len(s):], s) + return +} + +// MarshalSignature splits a signature in R and S. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1 +func (c *ed25519) MarshalSignature(sig []byte) (r, s []byte) { + return sig[:ed25519Size], sig[ed25519Size:] +} + +// UnmarshalSignature decodes R and S in the native format, re-adding the stripped leading zeroes +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1 +func (c *ed25519) UnmarshalSignature(r, s []byte) (sig []byte) { + // Check size + if len(r) > 32 || len(s) > 32 { + return nil + } + + sig = make([]byte, ed25519lib.SignatureSize) + + // Handle stripped leading zeroes + copy(sig[ed25519Size-len(r):ed25519Size], r) + copy(sig[ed25519lib.SignatureSize-len(s):], s) + return sig +} + +func (c *ed25519) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) { + pk, sk, err := ed25519lib.GenerateKey(rand) + + if err != nil { + return nil, nil, err + } + + return pk, sk[:ed25519lib.SeedSize], nil +} + +func getEd25519Sk(publicKey, privateKey []byte) ed25519lib.PrivateKey { + return append(privateKey, publicKey...) +} + +func (c *ed25519) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) { + sig = ed25519lib.Sign(getEd25519Sk(publicKey, privateKey), message) + return sig, nil +} + +func (c *ed25519) Verify(publicKey, message, sig []byte) bool { + return ed25519lib.Verify(publicKey, message, sig) +} + +func (c *ed25519) ValidateEdDSA(publicKey, privateKey []byte) (err error) { + priv := getEd25519Sk(publicKey, privateKey) + expectedPriv := ed25519lib.NewKeyFromSeed(priv.Seed()) + if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 { + return errors.KeyInvalidError("ecc: invalid ed25519 secret") + } + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go new file mode 100644 index 00000000..18cd8043 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go @@ -0,0 +1,111 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "crypto/subtle" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + ed448lib "github.com/cloudflare/circl/sign/ed448" +) + +type ed448 struct{} + +func NewEd448() *ed448 { + return &ed448{} +} + +func (c *ed448) GetCurveName() string { + return "ed448" +} + +// MarshalBytePoint encodes the public point from native format, adding the prefix. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed448) MarshalBytePoint(x []byte) []byte { + // Return prefixed + return append([]byte{0x40}, x...) +} + +// UnmarshalBytePoint decodes a point from prefixed format to native. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed448) UnmarshalBytePoint(point []byte) (x []byte) { + if len(point) != ed448lib.PublicKeySize+1 { + return nil + } + + // Strip prefix + return point[1:] +} + +// MarshalByteSecret encoded a scalar from native format to prefixed. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed448) MarshalByteSecret(d []byte) []byte { + // Return prefixed + return append([]byte{0x40}, d...) +} + +// UnmarshalByteSecret decodes a scalar from prefixed format to native. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5 +func (c *ed448) UnmarshalByteSecret(s []byte) (d []byte) { + // Check prefixed size + if len(s) != ed448lib.SeedSize+1 { + return nil + } + + // Strip prefix + return s[1:] +} + +// MarshalSignature splits a signature in R and S, where R is in prefixed native format and +// S is an MPI with value zero. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2 +func (c *ed448) MarshalSignature(sig []byte) (r, s []byte) { + return append([]byte{0x40}, sig...), []byte{} +} + +// UnmarshalSignature decodes R and S in the native format. Only R is used, in prefixed native format. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2 +func (c *ed448) UnmarshalSignature(r, s []byte) (sig []byte) { + if len(r) != ed448lib.SignatureSize+1 { + return nil + } + + return r[1:] +} + +func (c *ed448) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) { + pk, sk, err := ed448lib.GenerateKey(rand) + + if err != nil { + return nil, nil, err + } + + return pk, sk[:ed448lib.SeedSize], nil +} + +func getEd448Sk(publicKey, privateKey []byte) ed448lib.PrivateKey { + return append(privateKey, publicKey...) +} + +func (c *ed448) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) { + // Ed448 is used with the empty string as a context string. + // See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7 + sig = ed448lib.Sign(getEd448Sk(publicKey, privateKey), message, "") + + return sig, nil +} + +func (c *ed448) Verify(publicKey, message, sig []byte) bool { + // Ed448 is used with the empty string as a context string. + // See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7 + return ed448lib.Verify(publicKey, message, sig, "") +} + +func (c *ed448) ValidateEdDSA(publicKey, privateKey []byte) (err error) { + priv := getEd448Sk(publicKey, privateKey) + expectedPriv := ed448lib.NewKeyFromSeed(priv.Seed()) + if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 { + return errors.KeyInvalidError("ecc: invalid ed448 secret") + } + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go new file mode 100644 index 00000000..e28d7c71 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go @@ -0,0 +1,149 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "crypto/ecdsa" + "crypto/elliptic" + "fmt" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "io" + "math/big" +) + +type genericCurve struct { + Curve elliptic.Curve +} + +func NewGenericCurve(c elliptic.Curve) *genericCurve { + return &genericCurve{ + Curve: c, + } +} + +func (c *genericCurve) GetCurveName() string { + return c.Curve.Params().Name +} + +func (c *genericCurve) MarshalBytePoint(point []byte) []byte { + return point +} + +func (c *genericCurve) UnmarshalBytePoint(point []byte) []byte { + return point +} + +func (c *genericCurve) MarshalIntegerPoint(x, y *big.Int) []byte { + return elliptic.Marshal(c.Curve, x, y) +} + +func (c *genericCurve) UnmarshalIntegerPoint(point []byte) (x, y *big.Int) { + return elliptic.Unmarshal(c.Curve, point) +} + +func (c *genericCurve) MarshalByteSecret(d []byte) []byte { + return d +} + +func (c *genericCurve) UnmarshalByteSecret(d []byte) []byte { + return d +} + +func (c *genericCurve) MarshalIntegerSecret(d *big.Int) []byte { + return d.Bytes() +} + +func (c *genericCurve) UnmarshalIntegerSecret(d []byte) *big.Int { + return new(big.Int).SetBytes(d) +} + +func (c *genericCurve) GenerateECDH(rand io.Reader) (point, secret []byte, err error) { + secret, x, y, err := elliptic.GenerateKey(c.Curve, rand) + if err != nil { + return nil, nil, err + } + + point = elliptic.Marshal(c.Curve, x, y) + return point, secret, nil +} + +func (c *genericCurve) GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error) { + priv, err := ecdsa.GenerateKey(c.Curve, rand) + if err != nil { + return + } + + return priv.X, priv.Y, priv.D, nil +} + +func (c *genericCurve) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) { + xP, yP := elliptic.Unmarshal(c.Curve, point) + if xP == nil { + panic("invalid point") + } + + d, x, y, err := elliptic.GenerateKey(c.Curve, rand) + if err != nil { + return nil, nil, err + } + + vsG := elliptic.Marshal(c.Curve, x, y) + zbBig, _ := c.Curve.ScalarMult(xP, yP, d) + + byteLen := (c.Curve.Params().BitSize + 7) >> 3 + zb := make([]byte, byteLen) + zbBytes := zbBig.Bytes() + copy(zb[byteLen-len(zbBytes):], zbBytes) + + return vsG, zb, nil +} + +func (c *genericCurve) Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) { + x, y := elliptic.Unmarshal(c.Curve, ephemeral) + zbBig, _ := c.Curve.ScalarMult(x, y, secret) + byteLen := (c.Curve.Params().BitSize + 7) >> 3 + zb := make([]byte, byteLen) + zbBytes := zbBig.Bytes() + copy(zb[byteLen-len(zbBytes):], zbBytes) + + return zb, nil +} + +func (c *genericCurve) Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error) { + priv := &ecdsa.PrivateKey{D: d, PublicKey: ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve}} + return ecdsa.Sign(rand, priv, hash) +} + +func (c *genericCurve) Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool { + pub := &ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve} + return ecdsa.Verify(pub, hash, r, s) +} + +func (c *genericCurve) validate(xP, yP *big.Int, secret []byte) error { + // the public point should not be at infinity (0,0) + zero := new(big.Int) + if xP.Cmp(zero) == 0 && yP.Cmp(zero) == 0 { + return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): infinity point", c.Curve.Params().Name)) + } + + // re-derive the public point Q' = (X,Y) = dG + // to compare to declared Q in public key + expectedX, expectedY := c.Curve.ScalarBaseMult(secret) + if xP.Cmp(expectedX) != 0 || yP.Cmp(expectedY) != 0 { + return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name)) + } + + return nil +} + +func (c *genericCurve) ValidateECDSA(xP, yP *big.Int, secret []byte) error { + return c.validate(xP, yP, secret) +} + +func (c *genericCurve) ValidateECDH(point []byte, secret []byte) error { + xP, yP := elliptic.Unmarshal(c.Curve, point) + if xP == nil { + return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name)) + } + + return c.validate(xP, yP, secret) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go new file mode 100644 index 00000000..ffdd5151 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go @@ -0,0 +1,105 @@ +// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA. +package ecc + +import ( + "crypto/subtle" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + x448lib "github.com/cloudflare/circl/dh/x448" +) + +type x448 struct{} + +func NewX448() *x448 { + return &x448{} +} + +func (c *x448) GetCurveName() string { + return "x448" +} + +// MarshalBytePoint encodes the public point from native format, adding the prefix. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6 +func (c *x448) MarshalBytePoint(point []byte) []byte { + return append([]byte{0x40}, point...) +} + +// UnmarshalBytePoint decodes a point from prefixed format to native. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6 +func (c *x448) UnmarshalBytePoint(point []byte) []byte { + if len(point) != x448lib.Size+1 { + return nil + } + + return point[1:] +} + +// MarshalByteSecret encoded a scalar from native format to prefixed. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.2 +func (c *x448) MarshalByteSecret(d []byte) []byte { + return append([]byte{0x40}, d...) +} + +// UnmarshalByteSecret decodes a scalar from prefixed format to native. +// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.2 +func (c *x448) UnmarshalByteSecret(d []byte) []byte { + if len(d) != x448lib.Size+1 { + return nil + } + + // Store without prefix + return d[1:] +} + +func (c *x448) generateKeyPairBytes(rand io.Reader) (sk, pk x448lib.Key, err error) { + if _, err = rand.Read(sk[:]); err != nil { + return + } + + x448lib.KeyGen(&pk, &sk) + return +} + +func (c *x448) GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) { + priv, pub, err := c.generateKeyPairBytes(rand) + if err != nil { + return + } + + return pub[:], priv[:], nil +} + +func (c *x448) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) { + var pk, ss x448lib.Key + seed, e, err := c.generateKeyPairBytes(rand) + + copy(pk[:], point) + x448lib.Shared(&ss, &seed, &pk) + + return e[:], ss[:], nil +} + +func (c *x448) Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) { + var ss, sk, e x448lib.Key + + copy(sk[:], secret) + copy(e[:], ephemeral) + x448lib.Shared(&ss, &sk, &e) + + return ss[:], nil +} + +func (c *x448) ValidateECDH(point []byte, secret []byte) error { + var sk, pk, expectedPk x448lib.Key + + copy(pk[:], point) + copy(sk[:], secret) + x448lib.KeyGen(&expectedPk, &sk) + + if subtle.ConstantTimeCompare(expectedPk[:], pk[:]) == 0 { + return errors.KeyInvalidError("ecc: invalid curve25519 public point") + } + + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go new file mode 100644 index 00000000..6c921481 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go @@ -0,0 +1,27 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package encoding implements openpgp packet field encodings as specified in +// RFC 4880 and 6637. +package encoding + +import "io" + +// Field is an encoded field of an openpgp packet. +type Field interface { + // Bytes returns the decoded data. + Bytes() []byte + + // BitLength is the size in bits of the decoded data. + BitLength() uint16 + + // EncodedBytes returns the encoded data. + EncodedBytes() []byte + + // EncodedLength is the size in bytes of the encoded data. + EncodedLength() uint16 + + // ReadFrom reads the next Field from r. + ReadFrom(r io.Reader) (int64, error) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go new file mode 100644 index 00000000..02e5e695 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go @@ -0,0 +1,91 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package encoding + +import ( + "io" + "math/big" + "math/bits" +) + +// An MPI is used to store the contents of a big integer, along with the bit +// length that was specified in the original input. This allows the MPI to be +// reserialized exactly. +type MPI struct { + bytes []byte + bitLength uint16 +} + +// NewMPI returns a MPI initialized with bytes. +func NewMPI(bytes []byte) *MPI { + for len(bytes) != 0 && bytes[0] == 0 { + bytes = bytes[1:] + } + if len(bytes) == 0 { + bitLength := uint16(0) + return &MPI{bytes, bitLength} + } + bitLength := 8*uint16(len(bytes)-1) + uint16(bits.Len8(bytes[0])) + return &MPI{bytes, bitLength} +} + +// Bytes returns the decoded data. +func (m *MPI) Bytes() []byte { + return m.bytes +} + +// BitLength is the size in bits of the decoded data. +func (m *MPI) BitLength() uint16 { + return m.bitLength +} + +// EncodedBytes returns the encoded data. +func (m *MPI) EncodedBytes() []byte { + return append([]byte{byte(m.bitLength >> 8), byte(m.bitLength)}, m.bytes...) +} + +// EncodedLength is the size in bytes of the encoded data. +func (m *MPI) EncodedLength() uint16 { + return uint16(2 + len(m.bytes)) +} + +// ReadFrom reads into m the next MPI from r. +func (m *MPI) ReadFrom(r io.Reader) (int64, error) { + var buf [2]byte + n, err := io.ReadFull(r, buf[0:]) + if err != nil { + if err == io.EOF { + err = io.ErrUnexpectedEOF + } + return int64(n), err + } + + m.bitLength = uint16(buf[0])<<8 | uint16(buf[1]) + m.bytes = make([]byte, (int(m.bitLength)+7)/8) + + nn, err := io.ReadFull(r, m.bytes) + if err == io.EOF { + err = io.ErrUnexpectedEOF + } + + // remove leading zero bytes from malformed GnuPG encoded MPIs: + // https://bugs.gnupg.org/gnupg/issue1853 + // for _, b := range m.bytes { + // if b != 0 { + // break + // } + // m.bytes = m.bytes[1:] + // m.bitLength -= 8 + // } + + return int64(n) + int64(nn), err +} + +// SetBig initializes m with the bits from n. +func (m *MPI) SetBig(n *big.Int) *MPI { + m.bytes = n.Bytes() + m.bitLength = uint16(n.BitLen()) + return m +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go new file mode 100644 index 00000000..c9df9fe2 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go @@ -0,0 +1,88 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package encoding + +import ( + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// OID is used to store a variable-length field with a one-octet size +// prefix. See https://tools.ietf.org/html/rfc6637#section-9. +type OID struct { + bytes []byte +} + +const ( + // maxOID is the maximum number of bytes in a OID. + maxOID = 254 + // reservedOIDLength1 and reservedOIDLength2 are OID lengths that the RFC + // specifies are reserved. + reservedOIDLength1 = 0 + reservedOIDLength2 = 0xff +) + +// NewOID returns a OID initialized with bytes. +func NewOID(bytes []byte) *OID { + switch len(bytes) { + case reservedOIDLength1, reservedOIDLength2: + panic("encoding: NewOID argument length is reserved") + default: + if len(bytes) > maxOID { + panic("encoding: NewOID argument too large") + } + } + + return &OID{ + bytes: bytes, + } +} + +// Bytes returns the decoded data. +func (o *OID) Bytes() []byte { + return o.bytes +} + +// BitLength is the size in bits of the decoded data. +func (o *OID) BitLength() uint16 { + return uint16(len(o.bytes) * 8) +} + +// EncodedBytes returns the encoded data. +func (o *OID) EncodedBytes() []byte { + return append([]byte{byte(len(o.bytes))}, o.bytes...) +} + +// EncodedLength is the size in bytes of the encoded data. +func (o *OID) EncodedLength() uint16 { + return uint16(1 + len(o.bytes)) +} + +// ReadFrom reads into b the next OID from r. +func (o *OID) ReadFrom(r io.Reader) (int64, error) { + var buf [1]byte + n, err := io.ReadFull(r, buf[:]) + if err != nil { + if err == io.EOF { + err = io.ErrUnexpectedEOF + } + return int64(n), err + } + + switch buf[0] { + case reservedOIDLength1, reservedOIDLength2: + return int64(n), errors.UnsupportedError("reserved for future extensions") + } + + o.bytes = make([]byte, buf[0]) + + nn, err := io.ReadFull(r, o.bytes) + if err == io.EOF { + err = io.ErrUnexpectedEOF + } + + return int64(n) + int64(nn), err +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/key_generation.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/key_generation.go new file mode 100644 index 00000000..0e71934c --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/key_generation.go @@ -0,0 +1,389 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package openpgp + +import ( + "crypto" + "crypto/rand" + "crypto/rsa" + goerrors "errors" + "io" + "math/big" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/ecdh" + "github.com/ProtonMail/go-crypto/openpgp/ecdsa" + "github.com/ProtonMail/go-crypto/openpgp/eddsa" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/internal/ecc" + "github.com/ProtonMail/go-crypto/openpgp/packet" +) + +// NewEntity returns an Entity that contains a fresh RSA/RSA keypair with a +// single identity composed of the given full name, comment and email, any of +// which may be empty but must not contain any of "()<>\x00". +// If config is nil, sensible defaults will be used. +func NewEntity(name, comment, email string, config *packet.Config) (*Entity, error) { + creationTime := config.Now() + keyLifetimeSecs := config.KeyLifetime() + + // Generate a primary signing key + primaryPrivRaw, err := newSigner(config) + if err != nil { + return nil, err + } + primary := packet.NewSignerPrivateKey(creationTime, primaryPrivRaw) + if config != nil && config.V5Keys { + primary.UpgradeToV5() + } + + e := &Entity{ + PrimaryKey: &primary.PublicKey, + PrivateKey: primary, + Identities: make(map[string]*Identity), + Subkeys: []Subkey{}, + } + + err = e.addUserId(name, comment, email, config, creationTime, keyLifetimeSecs) + if err != nil { + return nil, err + } + + // NOTE: No key expiry here, but we will not return this subkey in EncryptionKey() + // if the primary/master key has expired. + err = e.addEncryptionSubkey(config, creationTime, 0) + if err != nil { + return nil, err + } + + return e, nil +} + +func (t *Entity) AddUserId(name, comment, email string, config *packet.Config) error { + creationTime := config.Now() + keyLifetimeSecs := config.KeyLifetime() + return t.addUserId(name, comment, email, config, creationTime, keyLifetimeSecs) +} + +func (t *Entity) addUserId(name, comment, email string, config *packet.Config, creationTime time.Time, keyLifetimeSecs uint32) error { + uid := packet.NewUserId(name, comment, email) + if uid == nil { + return errors.InvalidArgumentError("user id field contained invalid characters") + } + + if _, ok := t.Identities[uid.Id]; ok { + return errors.InvalidArgumentError("user id exist") + } + + primary := t.PrivateKey + + isPrimaryId := len(t.Identities) == 0 + + selfSignature := createSignaturePacket(&primary.PublicKey, packet.SigTypePositiveCert, config) + selfSignature.CreationTime = creationTime + selfSignature.KeyLifetimeSecs = &keyLifetimeSecs + selfSignature.IsPrimaryId = &isPrimaryId + selfSignature.FlagsValid = true + selfSignature.FlagSign = true + selfSignature.FlagCertify = true + selfSignature.SEIPDv1 = true // true by default, see 5.8 vs. 5.14 + selfSignature.SEIPDv2 = config.AEAD() != nil + + // Set the PreferredHash for the SelfSignature from the packet.Config. + // If it is not the must-implement algorithm from rfc4880bis, append that. + hash, ok := algorithm.HashToHashId(config.Hash()) + if !ok { + return errors.UnsupportedError("unsupported preferred hash function") + } + + selfSignature.PreferredHash = []uint8{hash} + if config.Hash() != crypto.SHA256 { + selfSignature.PreferredHash = append(selfSignature.PreferredHash, hashToHashId(crypto.SHA256)) + } + + // Likewise for DefaultCipher. + selfSignature.PreferredSymmetric = []uint8{uint8(config.Cipher())} + if config.Cipher() != packet.CipherAES128 { + selfSignature.PreferredSymmetric = append(selfSignature.PreferredSymmetric, uint8(packet.CipherAES128)) + } + + // We set CompressionNone as the preferred compression algorithm because + // of compression side channel attacks, then append the configured + // DefaultCompressionAlgo if any is set (to signal support for cases + // where the application knows that using compression is safe). + selfSignature.PreferredCompression = []uint8{uint8(packet.CompressionNone)} + if config.Compression() != packet.CompressionNone { + selfSignature.PreferredCompression = append(selfSignature.PreferredCompression, uint8(config.Compression())) + } + + // And for DefaultMode. + modes := []uint8{uint8(config.AEAD().Mode())} + if config.AEAD().Mode() != packet.AEADModeOCB { + modes = append(modes, uint8(packet.AEADModeOCB)) + } + + // For preferred (AES256, GCM), we'll generate (AES256, GCM), (AES256, OCB), (AES128, GCM), (AES128, OCB) + for _, cipher := range selfSignature.PreferredSymmetric { + for _, mode := range modes { + selfSignature.PreferredCipherSuites = append(selfSignature.PreferredCipherSuites, [2]uint8{cipher, mode}) + } + } + + // User ID binding signature + err := selfSignature.SignUserId(uid.Id, &primary.PublicKey, primary, config) + if err != nil { + return err + } + t.Identities[uid.Id] = &Identity{ + Name: uid.Id, + UserId: uid, + SelfSignature: selfSignature, + Signatures: []*packet.Signature{selfSignature}, + } + return nil +} + +// AddSigningSubkey adds a signing keypair as a subkey to the Entity. +// If config is nil, sensible defaults will be used. +func (e *Entity) AddSigningSubkey(config *packet.Config) error { + creationTime := config.Now() + keyLifetimeSecs := config.KeyLifetime() + + subPrivRaw, err := newSigner(config) + if err != nil { + return err + } + sub := packet.NewSignerPrivateKey(creationTime, subPrivRaw) + sub.IsSubkey = true + if config != nil && config.V5Keys { + sub.UpgradeToV5() + } + + subkey := Subkey{ + PublicKey: &sub.PublicKey, + PrivateKey: sub, + } + subkey.Sig = createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyBinding, config) + subkey.Sig.CreationTime = creationTime + subkey.Sig.KeyLifetimeSecs = &keyLifetimeSecs + subkey.Sig.FlagsValid = true + subkey.Sig.FlagSign = true + subkey.Sig.EmbeddedSignature = createSignaturePacket(subkey.PublicKey, packet.SigTypePrimaryKeyBinding, config) + subkey.Sig.EmbeddedSignature.CreationTime = creationTime + + err = subkey.Sig.EmbeddedSignature.CrossSignKey(subkey.PublicKey, e.PrimaryKey, subkey.PrivateKey, config) + if err != nil { + return err + } + + err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config) + if err != nil { + return err + } + + e.Subkeys = append(e.Subkeys, subkey) + return nil +} + +// AddEncryptionSubkey adds an encryption keypair as a subkey to the Entity. +// If config is nil, sensible defaults will be used. +func (e *Entity) AddEncryptionSubkey(config *packet.Config) error { + creationTime := config.Now() + keyLifetimeSecs := config.KeyLifetime() + return e.addEncryptionSubkey(config, creationTime, keyLifetimeSecs) +} + +func (e *Entity) addEncryptionSubkey(config *packet.Config, creationTime time.Time, keyLifetimeSecs uint32) error { + subPrivRaw, err := newDecrypter(config) + if err != nil { + return err + } + sub := packet.NewDecrypterPrivateKey(creationTime, subPrivRaw) + sub.IsSubkey = true + if config != nil && config.V5Keys { + sub.UpgradeToV5() + } + + subkey := Subkey{ + PublicKey: &sub.PublicKey, + PrivateKey: sub, + } + subkey.Sig = createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyBinding, config) + subkey.Sig.CreationTime = creationTime + subkey.Sig.KeyLifetimeSecs = &keyLifetimeSecs + subkey.Sig.FlagsValid = true + subkey.Sig.FlagEncryptStorage = true + subkey.Sig.FlagEncryptCommunications = true + + err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config) + if err != nil { + return err + } + + e.Subkeys = append(e.Subkeys, subkey) + return nil +} + +// Generates a signing key +func newSigner(config *packet.Config) (signer interface{}, err error) { + switch config.PublicKeyAlgorithm() { + case packet.PubKeyAlgoRSA: + bits := config.RSAModulusBits() + if bits < 1024 { + return nil, errors.InvalidArgumentError("bits must be >= 1024") + } + if config != nil && len(config.RSAPrimes) >= 2 { + primes := config.RSAPrimes[0:2] + config.RSAPrimes = config.RSAPrimes[2:] + return generateRSAKeyWithPrimes(config.Random(), 2, bits, primes) + } + return rsa.GenerateKey(config.Random(), bits) + case packet.PubKeyAlgoEdDSA: + curve := ecc.FindEdDSAByGenName(string(config.CurveName())) + if curve == nil { + return nil, errors.InvalidArgumentError("unsupported curve") + } + + priv, err := eddsa.GenerateKey(config.Random(), curve) + if err != nil { + return nil, err + } + return priv, nil + case packet.PubKeyAlgoECDSA: + curve := ecc.FindECDSAByGenName(string(config.CurveName())) + if curve == nil { + return nil, errors.InvalidArgumentError("unsupported curve") + } + + priv, err := ecdsa.GenerateKey(config.Random(), curve) + if err != nil { + return nil, err + } + return priv, nil + default: + return nil, errors.InvalidArgumentError("unsupported public key algorithm") + } +} + +// Generates an encryption/decryption key +func newDecrypter(config *packet.Config) (decrypter interface{}, err error) { + switch config.PublicKeyAlgorithm() { + case packet.PubKeyAlgoRSA: + bits := config.RSAModulusBits() + if bits < 1024 { + return nil, errors.InvalidArgumentError("bits must be >= 1024") + } + if config != nil && len(config.RSAPrimes) >= 2 { + primes := config.RSAPrimes[0:2] + config.RSAPrimes = config.RSAPrimes[2:] + return generateRSAKeyWithPrimes(config.Random(), 2, bits, primes) + } + return rsa.GenerateKey(config.Random(), bits) + case packet.PubKeyAlgoEdDSA, packet.PubKeyAlgoECDSA: + fallthrough // When passing EdDSA or ECDSA, we generate an ECDH subkey + case packet.PubKeyAlgoECDH: + var kdf = ecdh.KDF{ + Hash: algorithm.SHA512, + Cipher: algorithm.AES256, + } + curve := ecc.FindECDHByGenName(string(config.CurveName())) + if curve == nil { + return nil, errors.InvalidArgumentError("unsupported curve") + } + return ecdh.GenerateKey(config.Random(), curve, kdf) + default: + return nil, errors.InvalidArgumentError("unsupported public key algorithm") + } +} + +var bigOne = big.NewInt(1) + +// generateRSAKeyWithPrimes generates a multi-prime RSA keypair of the +// given bit size, using the given random source and prepopulated primes. +func generateRSAKeyWithPrimes(random io.Reader, nprimes int, bits int, prepopulatedPrimes []*big.Int) (*rsa.PrivateKey, error) { + priv := new(rsa.PrivateKey) + priv.E = 65537 + + if nprimes < 2 { + return nil, goerrors.New("generateRSAKeyWithPrimes: nprimes must be >= 2") + } + + if bits < 1024 { + return nil, goerrors.New("generateRSAKeyWithPrimes: bits must be >= 1024") + } + + primes := make([]*big.Int, nprimes) + +NextSetOfPrimes: + for { + todo := bits + // crypto/rand should set the top two bits in each prime. + // Thus each prime has the form + // p_i = 2^bitlen(p_i) × 0.11... (in base 2). + // And the product is: + // P = 2^todo × α + // where α is the product of nprimes numbers of the form 0.11... + // + // If α < 1/2 (which can happen for nprimes > 2), we need to + // shift todo to compensate for lost bits: the mean value of 0.11... + // is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2 + // will give good results. + if nprimes >= 7 { + todo += (nprimes - 2) / 5 + } + for i := 0; i < nprimes; i++ { + var err error + if len(prepopulatedPrimes) == 0 { + primes[i], err = rand.Prime(random, todo/(nprimes-i)) + if err != nil { + return nil, err + } + } else { + primes[i] = prepopulatedPrimes[0] + prepopulatedPrimes = prepopulatedPrimes[1:] + } + + todo -= primes[i].BitLen() + } + + // Make sure that primes is pairwise unequal. + for i, prime := range primes { + for j := 0; j < i; j++ { + if prime.Cmp(primes[j]) == 0 { + continue NextSetOfPrimes + } + } + } + + n := new(big.Int).Set(bigOne) + totient := new(big.Int).Set(bigOne) + pminus1 := new(big.Int) + for _, prime := range primes { + n.Mul(n, prime) + pminus1.Sub(prime, bigOne) + totient.Mul(totient, pminus1) + } + if n.BitLen() != bits { + // This should never happen for nprimes == 2 because + // crypto/rand should set the top two bits in each prime. + // For nprimes > 2 we hope it does not happen often. + continue NextSetOfPrimes + } + + priv.D = new(big.Int) + e := big.NewInt(int64(priv.E)) + ok := priv.D.ModInverse(e, totient) + + if ok != nil { + priv.Primes = primes + priv.N = n + break + } + } + + priv.Precompute() + return priv, nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/keys.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/keys.go new file mode 100644 index 00000000..2d7b0cf3 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/keys.go @@ -0,0 +1,842 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package openpgp + +import ( + goerrors "errors" + "io" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/armor" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/packet" +) + +// PublicKeyType is the armor type for a PGP public key. +var PublicKeyType = "PGP PUBLIC KEY BLOCK" + +// PrivateKeyType is the armor type for a PGP private key. +var PrivateKeyType = "PGP PRIVATE KEY BLOCK" + +// An Entity represents the components of an OpenPGP key: a primary public key +// (which must be a signing key), one or more identities claimed by that key, +// and zero or more subkeys, which may be encryption keys. +type Entity struct { + PrimaryKey *packet.PublicKey + PrivateKey *packet.PrivateKey + Identities map[string]*Identity // indexed by Identity.Name + Revocations []*packet.Signature + Subkeys []Subkey +} + +// An Identity represents an identity claimed by an Entity and zero or more +// assertions by other entities about that claim. +type Identity struct { + Name string // by convention, has the form "Full Name (comment) " + UserId *packet.UserId + SelfSignature *packet.Signature + Revocations []*packet.Signature + Signatures []*packet.Signature // all (potentially unverified) self-signatures, revocations, and third-party signatures +} + +// A Subkey is an additional public key in an Entity. Subkeys can be used for +// encryption. +type Subkey struct { + PublicKey *packet.PublicKey + PrivateKey *packet.PrivateKey + Sig *packet.Signature + Revocations []*packet.Signature +} + +// A Key identifies a specific public key in an Entity. This is either the +// Entity's primary key or a subkey. +type Key struct { + Entity *Entity + PublicKey *packet.PublicKey + PrivateKey *packet.PrivateKey + SelfSignature *packet.Signature + Revocations []*packet.Signature +} + +// A KeyRing provides access to public and private keys. +type KeyRing interface { + // KeysById returns the set of keys that have the given key id. + KeysById(id uint64) []Key + // KeysByIdAndUsage returns the set of keys with the given id + // that also meet the key usage given by requiredUsage. + // The requiredUsage is expressed as the bitwise-OR of + // packet.KeyFlag* values. + KeysByIdUsage(id uint64, requiredUsage byte) []Key + // DecryptionKeys returns all private keys that are valid for + // decryption. + DecryptionKeys() []Key +} + +// PrimaryIdentity returns an Identity, preferring non-revoked identities, +// identities marked as primary, or the latest-created identity, in that order. +func (e *Entity) PrimaryIdentity() *Identity { + var primaryIdentity *Identity + for _, ident := range e.Identities { + if shouldPreferIdentity(primaryIdentity, ident) { + primaryIdentity = ident + } + } + return primaryIdentity +} + +func shouldPreferIdentity(existingId, potentialNewId *Identity) bool { + if existingId == nil { + return true + } + + if len(existingId.Revocations) > len(potentialNewId.Revocations) { + return true + } + + if len(existingId.Revocations) < len(potentialNewId.Revocations) { + return false + } + + if existingId.SelfSignature == nil { + return true + } + + if existingId.SelfSignature.IsPrimaryId != nil && *existingId.SelfSignature.IsPrimaryId && + !(potentialNewId.SelfSignature.IsPrimaryId != nil && *potentialNewId.SelfSignature.IsPrimaryId) { + return false + } + + if !(existingId.SelfSignature.IsPrimaryId != nil && *existingId.SelfSignature.IsPrimaryId) && + potentialNewId.SelfSignature.IsPrimaryId != nil && *potentialNewId.SelfSignature.IsPrimaryId { + return true + } + + return potentialNewId.SelfSignature.CreationTime.After(existingId.SelfSignature.CreationTime) +} + +// EncryptionKey returns the best candidate Key for encrypting a message to the +// given Entity. +func (e *Entity) EncryptionKey(now time.Time) (Key, bool) { + // Fail to find any encryption key if the... + i := e.PrimaryIdentity() + if e.PrimaryKey.KeyExpired(i.SelfSignature, now) || // primary key has expired + i.SelfSignature == nil || // user ID has no self-signature + i.SelfSignature.SigExpired(now) || // user ID self-signature has expired + e.Revoked(now) || // primary key has been revoked + i.Revoked(now) { // user ID has been revoked + return Key{}, false + } + + // Iterate the keys to find the newest, unexpired one + candidateSubkey := -1 + var maxTime time.Time + for i, subkey := range e.Subkeys { + if subkey.Sig.FlagsValid && + subkey.Sig.FlagEncryptCommunications && + subkey.PublicKey.PubKeyAlgo.CanEncrypt() && + !subkey.PublicKey.KeyExpired(subkey.Sig, now) && + !subkey.Sig.SigExpired(now) && + !subkey.Revoked(now) && + (maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) { + candidateSubkey = i + maxTime = subkey.Sig.CreationTime + } + } + + if candidateSubkey != -1 { + subkey := e.Subkeys[candidateSubkey] + return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Revocations}, true + } + + // If we don't have any subkeys for encryption and the primary key + // is marked as OK to encrypt with, then we can use it. + if i.SelfSignature.FlagsValid && i.SelfSignature.FlagEncryptCommunications && + e.PrimaryKey.PubKeyAlgo.CanEncrypt() { + return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, e.Revocations}, true + } + + return Key{}, false +} + +// CertificationKey return the best candidate Key for certifying a key with this +// Entity. +func (e *Entity) CertificationKey(now time.Time) (Key, bool) { + return e.CertificationKeyById(now, 0) +} + +// CertificationKeyById return the Key for key certification with this +// Entity and keyID. +func (e *Entity) CertificationKeyById(now time.Time, id uint64) (Key, bool) { + return e.signingKeyByIdUsage(now, id, packet.KeyFlagCertify) +} + +// SigningKey return the best candidate Key for signing a message with this +// Entity. +func (e *Entity) SigningKey(now time.Time) (Key, bool) { + return e.SigningKeyById(now, 0) +} + +// SigningKeyById return the Key for signing a message with this +// Entity and keyID. +func (e *Entity) SigningKeyById(now time.Time, id uint64) (Key, bool) { + return e.signingKeyByIdUsage(now, id, packet.KeyFlagSign) +} + +func (e *Entity) signingKeyByIdUsage(now time.Time, id uint64, flags int) (Key, bool) { + // Fail to find any signing key if the... + i := e.PrimaryIdentity() + if e.PrimaryKey.KeyExpired(i.SelfSignature, now) || // primary key has expired + i.SelfSignature == nil || // user ID has no self-signature + i.SelfSignature.SigExpired(now) || // user ID self-signature has expired + e.Revoked(now) || // primary key has been revoked + i.Revoked(now) { // user ID has been revoked + return Key{}, false + } + + // Iterate the keys to find the newest, unexpired one + candidateSubkey := -1 + var maxTime time.Time + for idx, subkey := range e.Subkeys { + if subkey.Sig.FlagsValid && + (flags&packet.KeyFlagCertify == 0 || subkey.Sig.FlagCertify) && + (flags&packet.KeyFlagSign == 0 || subkey.Sig.FlagSign) && + subkey.PublicKey.PubKeyAlgo.CanSign() && + !subkey.PublicKey.KeyExpired(subkey.Sig, now) && + !subkey.Sig.SigExpired(now) && + !subkey.Revoked(now) && + (maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) && + (id == 0 || subkey.PublicKey.KeyId == id) { + candidateSubkey = idx + maxTime = subkey.Sig.CreationTime + } + } + + if candidateSubkey != -1 { + subkey := e.Subkeys[candidateSubkey] + return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Revocations}, true + } + + // If we don't have any subkeys for signing and the primary key + // is marked as OK to sign with, then we can use it. + if i.SelfSignature.FlagsValid && + (flags&packet.KeyFlagCertify == 0 || i.SelfSignature.FlagCertify) && + (flags&packet.KeyFlagSign == 0 || i.SelfSignature.FlagSign) && + e.PrimaryKey.PubKeyAlgo.CanSign() && + (id == 0 || e.PrimaryKey.KeyId == id) { + return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, e.Revocations}, true + } + + // No keys with a valid Signing Flag or no keys matched the id passed in + return Key{}, false +} + +func revoked(revocations []*packet.Signature, now time.Time) bool { + for _, revocation := range revocations { + if revocation.RevocationReason != nil && *revocation.RevocationReason == packet.KeyCompromised { + // If the key is compromised, the key is considered revoked even before the revocation date. + return true + } + if !revocation.SigExpired(now) { + return true + } + } + return false +} + +// Revoked returns whether the entity has any direct key revocation signatures. +// Note that third-party revocation signatures are not supported. +// Note also that Identity and Subkey revocation should be checked separately. +func (e *Entity) Revoked(now time.Time) bool { + return revoked(e.Revocations, now) +} + +// EncryptPrivateKeys encrypts all non-encrypted keys in the entity with the same key +// derived from the provided passphrase. Public keys and dummy keys are ignored, +// and don't cause an error to be returned. +func (e *Entity) EncryptPrivateKeys(passphrase []byte, config *packet.Config) error { + var keysToEncrypt []*packet.PrivateKey + // Add entity private key to encrypt. + if e.PrivateKey != nil && !e.PrivateKey.Dummy() && !e.PrivateKey.Encrypted { + keysToEncrypt = append(keysToEncrypt, e.PrivateKey) + } + + // Add subkeys to encrypt. + for _, sub := range e.Subkeys { + if sub.PrivateKey != nil && !sub.PrivateKey.Dummy() && !sub.PrivateKey.Encrypted { + keysToEncrypt = append(keysToEncrypt, sub.PrivateKey) + } + } + return packet.EncryptPrivateKeys(keysToEncrypt, passphrase, config) +} + +// DecryptPrivateKeys decrypts all encrypted keys in the entitiy with the given passphrase. +// Avoids recomputation of similar s2k key derivations. Public keys and dummy keys are ignored, +// and don't cause an error to be returned. +func (e *Entity) DecryptPrivateKeys(passphrase []byte) error { + var keysToDecrypt []*packet.PrivateKey + // Add entity private key to decrypt. + if e.PrivateKey != nil && !e.PrivateKey.Dummy() && e.PrivateKey.Encrypted { + keysToDecrypt = append(keysToDecrypt, e.PrivateKey) + } + + // Add subkeys to decrypt. + for _, sub := range e.Subkeys { + if sub.PrivateKey != nil && !sub.PrivateKey.Dummy() && sub.PrivateKey.Encrypted { + keysToDecrypt = append(keysToDecrypt, sub.PrivateKey) + } + } + return packet.DecryptPrivateKeys(keysToDecrypt, passphrase) +} + +// Revoked returns whether the identity has been revoked by a self-signature. +// Note that third-party revocation signatures are not supported. +func (i *Identity) Revoked(now time.Time) bool { + return revoked(i.Revocations, now) +} + +// Revoked returns whether the subkey has been revoked by a self-signature. +// Note that third-party revocation signatures are not supported. +func (s *Subkey) Revoked(now time.Time) bool { + return revoked(s.Revocations, now) +} + +// Revoked returns whether the key or subkey has been revoked by a self-signature. +// Note that third-party revocation signatures are not supported. +// Note also that Identity revocation should be checked separately. +// Normally, it's not necessary to call this function, except on keys returned by +// KeysById or KeysByIdUsage. +func (key *Key) Revoked(now time.Time) bool { + return revoked(key.Revocations, now) +} + +// An EntityList contains one or more Entities. +type EntityList []*Entity + +// KeysById returns the set of keys that have the given key id. +func (el EntityList) KeysById(id uint64) (keys []Key) { + for _, e := range el { + if e.PrimaryKey.KeyId == id { + ident := e.PrimaryIdentity() + selfSig := ident.SelfSignature + keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig, e.Revocations}) + } + + for _, subKey := range e.Subkeys { + if subKey.PublicKey.KeyId == id { + keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig, subKey.Revocations}) + } + } + } + return +} + +// KeysByIdAndUsage returns the set of keys with the given id that also meet +// the key usage given by requiredUsage. The requiredUsage is expressed as +// the bitwise-OR of packet.KeyFlag* values. +func (el EntityList) KeysByIdUsage(id uint64, requiredUsage byte) (keys []Key) { + for _, key := range el.KeysById(id) { + if requiredUsage != 0 { + if key.SelfSignature == nil || !key.SelfSignature.FlagsValid { + continue + } + + var usage byte + if key.SelfSignature.FlagCertify { + usage |= packet.KeyFlagCertify + } + if key.SelfSignature.FlagSign { + usage |= packet.KeyFlagSign + } + if key.SelfSignature.FlagEncryptCommunications { + usage |= packet.KeyFlagEncryptCommunications + } + if key.SelfSignature.FlagEncryptStorage { + usage |= packet.KeyFlagEncryptStorage + } + if usage&requiredUsage != requiredUsage { + continue + } + } + + keys = append(keys, key) + } + return +} + +// DecryptionKeys returns all private keys that are valid for decryption. +func (el EntityList) DecryptionKeys() (keys []Key) { + for _, e := range el { + for _, subKey := range e.Subkeys { + if subKey.PrivateKey != nil && subKey.Sig.FlagsValid && (subKey.Sig.FlagEncryptStorage || subKey.Sig.FlagEncryptCommunications) { + keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig, subKey.Revocations}) + } + } + } + return +} + +// ReadArmoredKeyRing reads one or more public/private keys from an armor keyring file. +func ReadArmoredKeyRing(r io.Reader) (EntityList, error) { + block, err := armor.Decode(r) + if err == io.EOF { + return nil, errors.InvalidArgumentError("no armored data found") + } + if err != nil { + return nil, err + } + if block.Type != PublicKeyType && block.Type != PrivateKeyType { + return nil, errors.InvalidArgumentError("expected public or private key block, got: " + block.Type) + } + + return ReadKeyRing(block.Body) +} + +// ReadKeyRing reads one or more public/private keys. Unsupported keys are +// ignored as long as at least a single valid key is found. +func ReadKeyRing(r io.Reader) (el EntityList, err error) { + packets := packet.NewReader(r) + var lastUnsupportedError error + + for { + var e *Entity + e, err = ReadEntity(packets) + if err != nil { + // TODO: warn about skipped unsupported/unreadable keys + if _, ok := err.(errors.UnsupportedError); ok { + lastUnsupportedError = err + err = readToNextPublicKey(packets) + } else if _, ok := err.(errors.StructuralError); ok { + // Skip unreadable, badly-formatted keys + lastUnsupportedError = err + err = readToNextPublicKey(packets) + } + if err == io.EOF { + err = nil + break + } + if err != nil { + el = nil + break + } + } else { + el = append(el, e) + } + } + + if len(el) == 0 && err == nil { + err = lastUnsupportedError + } + return +} + +// readToNextPublicKey reads packets until the start of the entity and leaves +// the first packet of the new entity in the Reader. +func readToNextPublicKey(packets *packet.Reader) (err error) { + var p packet.Packet + for { + p, err = packets.Next() + if err == io.EOF { + return + } else if err != nil { + if _, ok := err.(errors.UnsupportedError); ok { + err = nil + continue + } + return + } + + if pk, ok := p.(*packet.PublicKey); ok && !pk.IsSubkey { + packets.Unread(p) + return + } + } +} + +// ReadEntity reads an entity (public key, identities, subkeys etc) from the +// given Reader. +func ReadEntity(packets *packet.Reader) (*Entity, error) { + e := new(Entity) + e.Identities = make(map[string]*Identity) + + p, err := packets.Next() + if err != nil { + return nil, err + } + + var ok bool + if e.PrimaryKey, ok = p.(*packet.PublicKey); !ok { + if e.PrivateKey, ok = p.(*packet.PrivateKey); !ok { + packets.Unread(p) + return nil, errors.StructuralError("first packet was not a public/private key") + } + e.PrimaryKey = &e.PrivateKey.PublicKey + } + + if !e.PrimaryKey.PubKeyAlgo.CanSign() { + return nil, errors.StructuralError("primary key cannot be used for signatures") + } + + var revocations []*packet.Signature +EachPacket: + for { + p, err := packets.Next() + if err == io.EOF { + break + } else if err != nil { + return nil, err + } + + switch pkt := p.(type) { + case *packet.UserId: + if err := addUserID(e, packets, pkt); err != nil { + return nil, err + } + case *packet.Signature: + if pkt.SigType == packet.SigTypeKeyRevocation { + revocations = append(revocations, pkt) + } else if pkt.SigType == packet.SigTypeDirectSignature { + // TODO: RFC4880 5.2.1 permits signatures + // directly on keys (eg. to bind additional + // revocation keys). + } + // Else, ignoring the signature as it does not follow anything + // we would know to attach it to. + case *packet.PrivateKey: + if !pkt.IsSubkey { + packets.Unread(p) + break EachPacket + } + err = addSubkey(e, packets, &pkt.PublicKey, pkt) + if err != nil { + return nil, err + } + case *packet.PublicKey: + if !pkt.IsSubkey { + packets.Unread(p) + break EachPacket + } + err = addSubkey(e, packets, pkt, nil) + if err != nil { + return nil, err + } + default: + // we ignore unknown packets + } + } + + if len(e.Identities) == 0 { + return nil, errors.StructuralError("entity without any identities") + } + + for _, revocation := range revocations { + err = e.PrimaryKey.VerifyRevocationSignature(revocation) + if err == nil { + e.Revocations = append(e.Revocations, revocation) + } else { + // TODO: RFC 4880 5.2.3.15 defines revocation keys. + return nil, errors.StructuralError("revocation signature signed by alternate key") + } + } + + return e, nil +} + +func addUserID(e *Entity, packets *packet.Reader, pkt *packet.UserId) error { + // Make a new Identity object, that we might wind up throwing away. + // We'll only add it if we get a valid self-signature over this + // userID. + identity := new(Identity) + identity.Name = pkt.Id + identity.UserId = pkt + + for { + p, err := packets.Next() + if err == io.EOF { + break + } else if err != nil { + return err + } + + sig, ok := p.(*packet.Signature) + if !ok { + packets.Unread(p) + break + } + + if sig.SigType != packet.SigTypeGenericCert && + sig.SigType != packet.SigTypePersonaCert && + sig.SigType != packet.SigTypeCasualCert && + sig.SigType != packet.SigTypePositiveCert && + sig.SigType != packet.SigTypeCertificationRevocation { + return errors.StructuralError("user ID signature with wrong type") + } + + if sig.CheckKeyIdOrFingerprint(e.PrimaryKey) { + if err = e.PrimaryKey.VerifyUserIdSignature(pkt.Id, e.PrimaryKey, sig); err != nil { + return errors.StructuralError("user ID self-signature invalid: " + err.Error()) + } + if sig.SigType == packet.SigTypeCertificationRevocation { + identity.Revocations = append(identity.Revocations, sig) + } else if identity.SelfSignature == nil || sig.CreationTime.After(identity.SelfSignature.CreationTime) { + identity.SelfSignature = sig + } + identity.Signatures = append(identity.Signatures, sig) + e.Identities[pkt.Id] = identity + } else { + identity.Signatures = append(identity.Signatures, sig) + } + } + + return nil +} + +func addSubkey(e *Entity, packets *packet.Reader, pub *packet.PublicKey, priv *packet.PrivateKey) error { + var subKey Subkey + subKey.PublicKey = pub + subKey.PrivateKey = priv + + for { + p, err := packets.Next() + if err == io.EOF { + break + } else if err != nil { + return errors.StructuralError("subkey signature invalid: " + err.Error()) + } + + sig, ok := p.(*packet.Signature) + if !ok { + packets.Unread(p) + break + } + + if sig.SigType != packet.SigTypeSubkeyBinding && sig.SigType != packet.SigTypeSubkeyRevocation { + return errors.StructuralError("subkey signature with wrong type") + } + + if err := e.PrimaryKey.VerifyKeySignature(subKey.PublicKey, sig); err != nil { + return errors.StructuralError("subkey signature invalid: " + err.Error()) + } + + switch sig.SigType { + case packet.SigTypeSubkeyRevocation: + subKey.Revocations = append(subKey.Revocations, sig) + case packet.SigTypeSubkeyBinding: + if subKey.Sig == nil || sig.CreationTime.After(subKey.Sig.CreationTime) { + subKey.Sig = sig + } + } + } + + if subKey.Sig == nil { + return errors.StructuralError("subkey packet not followed by signature") + } + + e.Subkeys = append(e.Subkeys, subKey) + + return nil +} + +// SerializePrivate serializes an Entity, including private key material, but +// excluding signatures from other entities, to the given Writer. +// Identities and subkeys are re-signed in case they changed since NewEntry. +// If config is nil, sensible defaults will be used. +func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error) { + if e.PrivateKey.Dummy() { + return errors.ErrDummyPrivateKey("dummy private key cannot re-sign identities") + } + return e.serializePrivate(w, config, true) +} + +// SerializePrivateWithoutSigning serializes an Entity, including private key +// material, but excluding signatures from other entities, to the given Writer. +// Self-signatures of identities and subkeys are not re-signed. This is useful +// when serializing GNU dummy keys, among other things. +// If config is nil, sensible defaults will be used. +func (e *Entity) SerializePrivateWithoutSigning(w io.Writer, config *packet.Config) (err error) { + return e.serializePrivate(w, config, false) +} + +func (e *Entity) serializePrivate(w io.Writer, config *packet.Config, reSign bool) (err error) { + if e.PrivateKey == nil { + return goerrors.New("openpgp: private key is missing") + } + err = e.PrivateKey.Serialize(w) + if err != nil { + return + } + for _, revocation := range e.Revocations { + err := revocation.Serialize(w) + if err != nil { + return err + } + } + for _, ident := range e.Identities { + err = ident.UserId.Serialize(w) + if err != nil { + return + } + if reSign { + if ident.SelfSignature == nil { + return goerrors.New("openpgp: can't re-sign identity without valid self-signature") + } + err = ident.SelfSignature.SignUserId(ident.UserId.Id, e.PrimaryKey, e.PrivateKey, config) + if err != nil { + return + } + } + for _, sig := range ident.Signatures { + err = sig.Serialize(w) + if err != nil { + return err + } + } + } + for _, subkey := range e.Subkeys { + err = subkey.PrivateKey.Serialize(w) + if err != nil { + return + } + if reSign { + err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config) + if err != nil { + return + } + if subkey.Sig.EmbeddedSignature != nil { + err = subkey.Sig.EmbeddedSignature.CrossSignKey(subkey.PublicKey, e.PrimaryKey, + subkey.PrivateKey, config) + if err != nil { + return + } + } + } + for _, revocation := range subkey.Revocations { + err := revocation.Serialize(w) + if err != nil { + return err + } + } + err = subkey.Sig.Serialize(w) + if err != nil { + return + } + } + return nil +} + +// Serialize writes the public part of the given Entity to w, including +// signatures from other entities. No private key material will be output. +func (e *Entity) Serialize(w io.Writer) error { + err := e.PrimaryKey.Serialize(w) + if err != nil { + return err + } + for _, revocation := range e.Revocations { + err := revocation.Serialize(w) + if err != nil { + return err + } + } + for _, ident := range e.Identities { + err = ident.UserId.Serialize(w) + if err != nil { + return err + } + for _, sig := range ident.Signatures { + err = sig.Serialize(w) + if err != nil { + return err + } + } + } + for _, subkey := range e.Subkeys { + err = subkey.PublicKey.Serialize(w) + if err != nil { + return err + } + for _, revocation := range subkey.Revocations { + err := revocation.Serialize(w) + if err != nil { + return err + } + } + err = subkey.Sig.Serialize(w) + if err != nil { + return err + } + } + return nil +} + +// SignIdentity adds a signature to e, from signer, attesting that identity is +// associated with e. The provided identity must already be an element of +// e.Identities and the private key of signer must have been decrypted if +// necessary. +// If config is nil, sensible defaults will be used. +func (e *Entity) SignIdentity(identity string, signer *Entity, config *packet.Config) error { + certificationKey, ok := signer.CertificationKey(config.Now()) + if !ok { + return errors.InvalidArgumentError("no valid certification key found") + } + + if certificationKey.PrivateKey.Encrypted { + return errors.InvalidArgumentError("signing Entity's private key must be decrypted") + } + + ident, ok := e.Identities[identity] + if !ok { + return errors.InvalidArgumentError("given identity string not found in Entity") + } + + sig := createSignaturePacket(certificationKey.PublicKey, packet.SigTypeGenericCert, config) + + signingUserID := config.SigningUserId() + if signingUserID != "" { + if _, ok := signer.Identities[signingUserID]; !ok { + return errors.InvalidArgumentError("signer identity string not found in signer Entity") + } + sig.SignerUserId = &signingUserID + } + + if err := sig.SignUserId(identity, e.PrimaryKey, certificationKey.PrivateKey, config); err != nil { + return err + } + ident.Signatures = append(ident.Signatures, sig) + return nil +} + +// RevokeKey generates a key revocation signature (packet.SigTypeKeyRevocation) with the +// specified reason code and text (RFC4880 section-5.2.3.23). +// If config is nil, sensible defaults will be used. +func (e *Entity) RevokeKey(reason packet.ReasonForRevocation, reasonText string, config *packet.Config) error { + revSig := createSignaturePacket(e.PrimaryKey, packet.SigTypeKeyRevocation, config) + revSig.RevocationReason = &reason + revSig.RevocationReasonText = reasonText + + if err := revSig.RevokeKey(e.PrimaryKey, e.PrivateKey, config); err != nil { + return err + } + e.Revocations = append(e.Revocations, revSig) + return nil +} + +// RevokeSubkey generates a subkey revocation signature (packet.SigTypeSubkeyRevocation) for +// a subkey with the specified reason code and text (RFC4880 section-5.2.3.23). +// If config is nil, sensible defaults will be used. +func (e *Entity) RevokeSubkey(sk *Subkey, reason packet.ReasonForRevocation, reasonText string, config *packet.Config) error { + if err := e.PrimaryKey.VerifyKeySignature(sk.PublicKey, sk.Sig); err != nil { + return errors.InvalidArgumentError("given subkey is not associated with this key") + } + + revSig := createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyRevocation, config) + revSig.RevocationReason = &reason + revSig.RevocationReasonText = reasonText + + if err := revSig.RevokeSubkey(sk.PublicKey, e.PrivateKey, config); err != nil { + return err + } + + sk.Revocations = append(sk.Revocations, revSig) + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/keys_test_data.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/keys_test_data.go new file mode 100644 index 00000000..108fd096 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/keys_test_data.go @@ -0,0 +1,538 @@ +package openpgp + +const expiringKeyHex = "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" +const subkeyUsageHex = "988d04533a52bc010400d26af43085558f65b9e7dbc90cb9238015259aed5e954637adcfa2181548b2d0b60c65f1f42ec5081cbf1bc0a8aa4900acfb77070837c58f26012fbce297d70afe96e759ad63531f0037538e70dbf8e384569b9720d99d8eb39d8d0a2947233ed242436cb6ac7dfe74123354b3d0119b5c235d3dd9c9d6c004f8ffaf67ad8583001101000188b7041f010200210502533b8552170c8001ce094aa433f7040bb2ddf0be3893cb843d0fe70c020700000a0910a42704b92866382aa98404009d63d916a27543da4221c60087c33f1c44bec9998c5438018ed370cca4962876c748e94b73eb39c58eb698063f3fd6346d58dd2a11c0247934c4a9d71f24754f7468f96fb24c3e791dd2392b62f626148ad724189498cbf993db2df7c0cdc2d677c35da0f16cb16c9ce7c33b4de65a4a91b1d21a130ae9cc26067718910ef8e2b417556d627261203c756d627261407379642e65642e61753e88b80413010200220502533a52bc021b03060b090807030206150802090a0b0416020301021e01021780000a0910a42704b92866382a47840400c0c2bd04f5fca586de408b395b3c280a278259c93eaaa8b79a53b97003f8ed502a8a00446dd9947fb462677e4fcac0dac2f0701847d15130aadb6cd9e0705ea0cf5f92f129136c7be21a718d46c8e641eb7f044f2adae573e11ae423a0a9ca51324f03a8a2f34b91fa40c3cc764bee4dccadedb54c768ba0469b683ea53f1c29b88d04533a52bc01040099c92a5d6f8b744224da27bc2369127c35269b58bec179de6bbc038f749344222f85a31933224f26b70243c4e4b2d242f0c4777eaef7b5502f9dad6d8bf3aaeb471210674b74de2d7078af497d55f5cdad97c7bedfbc1b41e8065a97c9c3d344b21fc81d27723af8e374bc595da26ea242dccb6ae497be26eea57e563ed517e90011010001889f0418010200090502533a52bc021b0c000a0910a42704b92866382afa1403ff70284c2de8a043ff51d8d29772602fa98009b7861c540535f874f2c230af8caf5638151a636b21f8255003997ccd29747fdd06777bb24f9593bd7d98a3e887689bf902f999915fcc94625ae487e5d13e6616f89090ebc4fdc7eb5cad8943e4056995bb61c6af37f8043016876a958ec7ebf39c43d20d53b7f546cfa83e8d2604b88d04533b8283010400c0b529316dbdf58b4c54461e7e669dc11c09eb7f73819f178ccd4177b9182b91d138605fcf1e463262fabefa73f94a52b5e15d1904635541c7ea540f07050ce0fb51b73e6f88644cec86e91107c957a114f69554548a85295d2b70bd0b203992f76eb5d493d86d9eabcaa7ef3fc7db7e458438db3fcdb0ca1cc97c638439a9170011010001889f0418010200090502533b8283021b0c000a0910a42704b92866382adc6d0400cfff6258485a21675adb7a811c3e19ebca18851533f75a7ba317950b9997fda8d1a4c8c76505c08c04b6c2cc31dc704d33da36a21273f2b388a1a706f7c3378b66d887197a525936ed9a69acb57fe7f718133da85ec742001c5d1864e9c6c8ea1b94f1c3759cebfd93b18606066c063a63be86085b7e37bdbc65f9a915bf084bb901a204533b85cd110400aed3d2c52af2b38b5b67904b0ef73d6dd7aef86adb770e2b153cd22489654dcc91730892087bb9856ae2d9f7ed1eb48f214243fe86bfe87b349ebd7c30e630e49c07b21fdabf78b7a95c8b7f969e97e3d33f2e074c63552ba64a2ded7badc05ce0ea2be6d53485f6900c7860c7aa76560376ce963d7271b9b54638a4028b573f00a0d8854bfcdb04986141568046202192263b9b67350400aaa1049dbc7943141ef590a70dcb028d730371d92ea4863de715f7f0f16d168bd3dc266c2450457d46dcbbf0b071547e5fbee7700a820c3750b236335d8d5848adb3c0da010e998908dfd93d961480084f3aea20b247034f8988eccb5546efaa35a92d0451df3aaf1aee5aa36a4c4d462c760ecd9cebcabfbe1412b1f21450f203fd126687cd486496e971a87fd9e1a8a765fe654baa219a6871ab97768596ab05c26c1aeea8f1a2c72395a58dbc12ef9640d2b95784e974a4d2d5a9b17c25fedacfe551bda52602de8f6d2e48443f5dd1a2a2a8e6a5e70ecdb88cd6e766ad9745c7ee91d78cc55c3d06536b49c3fee6c3d0b6ff0fb2bf13a314f57c953b8f4d93bf88e70418010200090502533b85cd021b0200520910a42704b92866382a47200419110200060502533b85cd000a091042ce2c64bc0ba99214b2009e26b26852c8b13b10c35768e40e78fbbb48bd084100a0c79d9ea0844fa5853dd3c85ff3ecae6f2c9dd6c557aa04008bbbc964cd65b9b8299d4ebf31f41cc7264b8cf33a00e82c5af022331fac79efc9563a822497ba012953cefe2629f1242fcdcb911dbb2315985bab060bfd58261ace3c654bdbbe2e8ed27a46e836490145c86dc7bae15c011f7e1ffc33730109b9338cd9f483e7cef3d2f396aab5bd80efb6646d7e778270ee99d934d187dd98" +const revokedKeyHex = "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" +const revokedSubkeyHex = "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" + +const missingCrossSignatureKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- +Charset: UTF-8 + +mQENBFMYynYBCACVOZ3/e8Bm2b9KH9QyIlHGo/i1bnkpqsgXj8tpJ2MIUOnXMMAY +ztW7kKFLCmgVdLIC0vSoLA4yhaLcMojznh/2CcUglZeb6Ao8Gtelr//Rd5DRfPpG +zqcfUo+m+eO1co2Orabw0tZDfGpg5p3AYl0hmxhUyYSc/xUq93xL1UJzBFgYXY54 +QsM8dgeQgFseSk/YvdP5SMx1ev+eraUyiiUtWzWrWC1TdyRa5p4UZg6Rkoppf+WJ +QrW6BWrhAtqATHc8ozV7uJjeONjUEq24roRc/OFZdmQQGK6yrzKnnbA6MdHhqpdo +9kWDcXYb7pSE63Lc+OBa5X2GUVvXJLS/3nrtABEBAAG0F2ludmFsaWQtc2lnbmlu +Zy1zdWJrZXlziQEoBBMBAgASBQJTnKB5AhsBAgsHAhUIAh4BAAoJEO3UDQUIHpI/ +dN4H/idX4FQ1LIZCnpHS/oxoWQWfpRgdKAEM0qCqjMgiipJeEwSQbqjTCynuh5/R +JlODDz85ABR06aoF4l5ebGLQWFCYifPnJZ/Yf5OYcMGtb7dIbqxWVFL9iLMO/oDL +ioI3dotjPui5e+2hI9pVH1UHB/bZ/GvMGo6Zg0XxLPolKQODMVjpjLAQ0YJ3spew +RAmOGre6tIvbDsMBnm8qREt7a07cBJ6XK7xjxYaZHQBiHVxyEWDa6gyANONx8duW +/fhQ/zDTnyVM/ik6VO0Ty9BhPpcEYLFwh5c1ilFari1ta3e6qKo6ZGa9YMk/REhu +yBHd9nTkI+0CiQUmbckUiVjDKKe5AQ0EUxjKdgEIAJcXQeP+NmuciE99YcJoffxv +2gVLU4ZXBNHEaP0mgaJ1+tmMD089vUQAcyGRvw8jfsNsVZQIOAuRxY94aHQhIRHR +bUzBN28ofo/AJJtfx62C15xt6fDKRV6HXYqAiygrHIpEoRLyiN69iScUsjIJeyFL +C8wa72e8pSL6dkHoaV1N9ZH/xmrJ+k0vsgkQaAh9CzYufncDxcwkoP+aOlGtX1gP +WwWoIbz0JwLEMPHBWvDDXQcQPQTYQyj+LGC9U6f9VZHN25E94subM1MjuT9OhN9Y +MLfWaaIc5WyhLFyQKW2Upofn9wSFi8ubyBnv640Dfd0rVmaWv7LNTZpoZ/GbJAMA +EQEAAYkBHwQYAQIACQUCU5ygeQIbAgAKCRDt1A0FCB6SP0zCB/sEzaVR38vpx+OQ +MMynCBJrakiqDmUZv9xtplY7zsHSQjpd6xGflbU2n+iX99Q+nav0ETQZifNUEd4N +1ljDGQejcTyKD6Pkg6wBL3x9/RJye7Zszazm4+toJXZ8xJ3800+BtaPoI39akYJm ++ijzbskvN0v/j5GOFJwQO0pPRAFtdHqRs9Kf4YanxhedB4dIUblzlIJuKsxFit6N +lgGRblagG3Vv2eBszbxzPbJjHCgVLR3RmrVezKOsZjr/2i7X+xLWIR0uD3IN1qOW +CXQxLBizEEmSNVNxsp7KPGTLnqO3bPtqFirxS9PJLIMPTPLNBY7ZYuPNTMqVIUWF +4artDmrG +=7FfJ +-----END PGP PUBLIC KEY BLOCK-----` + +const invalidCrossSignatureKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mQENBFMYynYBCACVOZ3/e8Bm2b9KH9QyIlHGo/i1bnkpqsgXj8tpJ2MIUOnXMMAY +ztW7kKFLCmgVdLIC0vSoLA4yhaLcMojznh/2CcUglZeb6Ao8Gtelr//Rd5DRfPpG +zqcfUo+m+eO1co2Orabw0tZDfGpg5p3AYl0hmxhUyYSc/xUq93xL1UJzBFgYXY54 +QsM8dgeQgFseSk/YvdP5SMx1ev+eraUyiiUtWzWrWC1TdyRa5p4UZg6Rkoppf+WJ +QrW6BWrhAtqATHc8ozV7uJjeONjUEq24roRc/OFZdmQQGK6yrzKnnbA6MdHhqpdo +9kWDcXYb7pSE63Lc+OBa5X2GUVvXJLS/3nrtABEBAAG0F2ludmFsaWQtc2lnbmlu +Zy1zdWJrZXlziQEoBBMBAgASBQJTnKB5AhsBAgsHAhUIAh4BAAoJEO3UDQUIHpI/ +dN4H/idX4FQ1LIZCnpHS/oxoWQWfpRgdKAEM0qCqjMgiipJeEwSQbqjTCynuh5/R +JlODDz85ABR06aoF4l5ebGLQWFCYifPnJZ/Yf5OYcMGtb7dIbqxWVFL9iLMO/oDL +ioI3dotjPui5e+2hI9pVH1UHB/bZ/GvMGo6Zg0XxLPolKQODMVjpjLAQ0YJ3spew +RAmOGre6tIvbDsMBnm8qREt7a07cBJ6XK7xjxYaZHQBiHVxyEWDa6gyANONx8duW +/fhQ/zDTnyVM/ik6VO0Ty9BhPpcEYLFwh5c1ilFari1ta3e6qKo6ZGa9YMk/REhu +yBHd9nTkI+0CiQUmbckUiVjDKKe5AQ0EUxjKdgEIAIINDqlj7X6jYKc6DjwrOkjQ +UIRWbQQar0LwmNilehmt70g5DCL1SYm9q4LcgJJ2Nhxj0/5qqsYib50OSWMcKeEe +iRXpXzv1ObpcQtI5ithp0gR53YPXBib80t3bUzomQ5UyZqAAHzMp3BKC54/vUrSK +FeRaxDzNLrCeyI00+LHNUtwghAqHvdNcsIf8VRumK8oTm3RmDh0TyjASWYbrt9c8 +R1Um3zuoACOVy+mEIgIzsfHq0u7dwYwJB5+KeM7ZLx+HGIYdUYzHuUE1sLwVoELh ++SHIGHI1HDicOjzqgajShuIjj5hZTyQySVprrsLKiXS6NEwHAP20+XjayJ/R3tEA +EQEAAYkCPgQYAQIBKAUCU5ygeQIbAsBdIAQZAQIABgUCU5ygeQAKCRCpVlnFZmhO +52RJB/9uD1MSa0wjY6tHOIgquZcP3bHBvHmrHNMw9HR2wRCMO91ZkhrpdS3ZHtgb +u3/55etj0FdvDo1tb8P8FGSVtO5Vcwf5APM8sbbqoi8L951Q3i7qt847lfhu6sMl +w0LWFvPTOLHrliZHItPRjOltS1WAWfr2jUYhsU9ytaDAJmvf9DujxEOsN5G1YJep +54JCKVCkM/y585Zcnn+yxk/XwqoNQ0/iJUT9qRrZWvoeasxhl1PQcwihCwss44A+ +YXaAt3hbk+6LEQuZoYS73yR3WHj+42tfm7YxRGeubXfgCEz/brETEWXMh4pe0vCL +bfWrmfSPq2rDegYcAybxRQz0lF8PAAoJEO3UDQUIHpI/exkH/0vQfdHA8g/N4T6E +i6b1CUVBAkvtdJpCATZjWPhXmShOw62gkDw306vHPilL4SCvEEi4KzG72zkp6VsB +DSRcpxCwT4mHue+duiy53/aRMtSJ+vDfiV1Vhq+3sWAck/yUtfDU9/u4eFaiNok1 +8/Gd7reyuZt5CiJnpdPpjCwelK21l2w7sHAnJF55ITXdOxI8oG3BRKufz0z5lyDY +s2tXYmhhQIggdgelN8LbcMhWs/PBbtUr6uZlNJG2lW1yscD4aI529VjwJlCeo745 +U7pO4eF05VViUJ2mmfoivL3tkhoTUWhx8xs8xCUcCg8DoEoSIhxtOmoTPR22Z9BL +6LCg2mg= +=Dhm4 +-----END PGP PUBLIC KEY BLOCK-----` + +const goodCrossSignatureKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- +Version: GnuPG v1 + +mI0EVUqeVwEEAMufHRrMPWK3gyvi0O0tABCs/oON9zV9KDZlr1a1M91ShCSFwCPo +7r80PxdWVWcj0V5h50/CJYtpN3eE/mUIgW2z1uDYQF1OzrQ8ubrksfsJvpAhENom +lTQEppv9mV8qhcM278teb7TX0pgrUHLYF5CfPdp1L957JLLXoQR/lwLVABEBAAG0 +E2dvb2Qtc2lnbmluZy1zdWJrZXmIuAQTAQIAIgUCVUqeVwIbAwYLCQgHAwIGFQgC +CQoLBBYCAwECHgECF4AACgkQNRjL95IRWP69XQQAlH6+eyXJN4DZTLX78KGjHrsw +6FCvxxClEPtPUjcJy/1KCRQmtLAt9PbbA78dvgzjDeZMZqRAwdjyJhjyg/fkU2OH +7wq4ktjUu+dLcOBb+BFMEY+YjKZhf6EJuVfxoTVr5f82XNPbYHfTho9/OABKH6kv +X70PaKZhbwnwij8Nts65AaIEVUqftREEAJ3WxZfqAX0bTDbQPf2CMT2IVMGDfhK7 +GyubOZgDFFjwUJQvHNvsrbeGLZ0xOBumLINyPO1amIfTgJNm1iiWFWfmnHReGcDl +y5mpYG60Mb79Whdcer7CMm3AqYh/dW4g6IB02NwZMKoUHo3PXmFLxMKXnWyJ0clw +R0LI/Qn509yXAKDh1SO20rqrBM+EAP2c5bfI98kyNwQAi3buu94qo3RR1ZbvfxgW +CKXDVm6N99jdZGNK7FbRifXqzJJDLcXZKLnstnC4Sd3uyfyf1uFhmDLIQRryn5m+ +LBYHfDBPN3kdm7bsZDDq9GbTHiFZUfm/tChVKXWxkhpAmHhU/tH6GGzNSMXuIWSO +aOz3Rqq0ED4NXyNKjdF9MiwD/i83S0ZBc0LmJYt4Z10jtH2B6tYdqnAK29uQaadx +yZCX2scE09UIm32/w7pV77CKr1Cp/4OzAXS1tmFzQ+bX7DR+Gl8t4wxr57VeEMvl +BGw4Vjh3X8//m3xynxycQU18Q1zJ6PkiMyPw2owZ/nss3hpSRKFJsxMLhW3fKmKr +Ey2KiOcEGAECAAkFAlVKn7UCGwIAUgkQNRjL95IRWP5HIAQZEQIABgUCVUqftQAK +CRD98VjDN10SqkWrAKDTpEY8D8HC02E/KVC5YUI01B30wgCgurpILm20kXEDCeHp +C5pygfXw1DJrhAP+NyPJ4um/bU1I+rXaHHJYroYJs8YSweiNcwiHDQn0Engh/mVZ +SqLHvbKh2dL/RXymC3+rjPvQf5cup9bPxNMa6WagdYBNAfzWGtkVISeaQW+cTEp/ +MtgVijRGXR/lGLGETPg2X3Afwn9N9bLMBkBprKgbBqU7lpaoPupxT61bL70= +=vtbN +-----END PGP PUBLIC KEY BLOCK-----` + +const revokedUserIDKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mQENBFsgO5EBCADhREPmcjsPkXe1z7ctvyWL0S7oa9JaoGZ9oPDHFDlQxd0qlX2e +DZJZDg0qYvVixmaULIulApq1puEsaJCn3lHUbHlb4PYKwLEywYXM28JN91KtLsz/ +uaEX2KC5WqeP40utmzkNLq+oRX/xnRMgwbO7yUNVG2UlEa6eI+xOXO3YtLdmJMBW +ClQ066ZnOIzEo1JxnIwha1CDBMWLLfOLrg6l8InUqaXbtEBbnaIYO6fXVXELUjkx +nmk7t/QOk0tXCy8muH9UDqJkwDUESY2l79XwBAcx9riX8vY7vwC34pm22fAUVLCJ +x1SJx0J8bkeNp38jKM2Zd9SUQqSbfBopQ4pPABEBAAG0I0dvbGFuZyBHb3BoZXIg +PG5vLXJlcGx5QGdvbGFuZy5jb20+iQFUBBMBCgA+FiEE5Ik5JLcNx6l6rZfw1oFy +9I6cUoMFAlsgO5ECGwMFCQPCZwAFCwkIBwMFFQoJCAsFFgIDAQACHgECF4AACgkQ +1oFy9I6cUoMIkwf8DNPeD23i4jRwd/pylbvxwZintZl1fSwTJW1xcOa1emXaEtX2 +depuqhP04fjlRQGfsYAQh7X9jOJxAHjTmhqFBi5sD7QvKU00cPFYbJ/JTx0B41bl +aXnSbGhRPh63QtEZL7ACAs+shwvvojJqysx7kyVRu0EW2wqjXdHwR/SJO6nhNBa2 +DXzSiOU/SUA42mmG+5kjF8Aabq9wPwT9wjraHShEweNerNMmOqJExBOy3yFeyDpa +XwEZFzBfOKoxFNkIaVf5GSdIUGhFECkGvBMB935khftmgR8APxdU4BE7XrXexFJU +8RCuPXonm4WQOwTWR0vQg64pb2WKAzZ8HhwTGbQiR29sYW5nIEdvcGhlciA8cmV2 +b2tlZEBnb2xhbmcuY29tPokBNgQwAQoAIBYhBOSJOSS3Dcepeq2X8NaBcvSOnFKD +BQJbIDv3Ah0AAAoJENaBcvSOnFKDfWMIAKhI/Tvu3h8fSUxp/gSAcduT6bC1JttG +0lYQ5ilKB/58lBUA5CO3ZrKDKlzW3M8VEcvohVaqeTMKeoQd5rCZq8KxHn/KvN6N +s85REfXfniCKfAbnGgVXX3kDmZ1g63pkxrFu0fDZjVDXC6vy+I0sGyI/Inro0Pzb +tvn0QCsxjapKK15BtmSrpgHgzVqVg0cUp8vqZeKFxarYbYB2idtGRci4b9tObOK0 +BSTVFy26+I/mrFGaPrySYiy2Kz5NMEcRhjmTxJ8jSwEr2O2sUR0yjbgUAXbTxDVE +/jg5fQZ1ACvBRQnB7LvMHcInbzjyeTM3FazkkSYQD6b97+dkWwb1iWG5AQ0EWyA7 +kQEIALkg04REDZo1JgdYV4x8HJKFS4xAYWbIva1ZPqvDNmZRUbQZR2+gpJGEwn7z +VofGvnOYiGW56AS5j31SFf5kro1+1bZQ5iOONBng08OOo58/l1hRseIIVGB5TGSa +PCdChKKHreJI6hS3mShxH6hdfFtiZuB45rwoaArMMsYcjaezLwKeLc396cpUwwcZ +snLUNd1Xu5EWEF2OdFkZ2a1qYdxBvAYdQf4+1Nr+NRIx1u1NS9c8jp3PuMOkrQEi +bNtc1v6v0Jy52mKLG4y7mC/erIkvkQBYJdxPaP7LZVaPYc3/xskcyijrJ/5ufoD8 +K71/ShtsZUXSQn9jlRaYR0EbojMAEQEAAYkBPAQYAQoAJhYhBOSJOSS3Dcepeq2X +8NaBcvSOnFKDBQJbIDuRAhsMBQkDwmcAAAoJENaBcvSOnFKDkFMIAIt64bVZ8x7+ +TitH1bR4pgcNkaKmgKoZz6FXu80+SnbuEt2NnDyf1cLOSimSTILpwLIuv9Uft5Pb +OraQbYt3xi9yrqdKqGLv80bxqK0NuryNkvh9yyx5WoG1iKqMj9/FjGghuPrRaT4l +QinNAghGVkEy1+aXGFrG2DsOC1FFI51CC2WVTzZ5RwR2GpiNRfESsU1rZAUqf/2V +yJl9bD5R4SUNy8oQmhOxi+gbhD4Ao34e4W0ilibslI/uawvCiOwlu5NGd8zv5n+U +heiQvzkApQup5c+BhH5zFDFdKJ2CBByxw9+7QjMFI/wgLixKuE0Ob2kAokXf7RlB +7qTZOahrETw= +=IKnw +-----END PGP PUBLIC KEY BLOCK-----` + +const keyWithFirstUserIDRevoked = `-----BEGIN PGP PUBLIC KEY BLOCK----- +Version: OpenPGP.js v4.10.10 +Comment: https://openpgpjs.org + +xsBNBFsgO5EBCADhREPmcjsPkXe1z7ctvyWL0S7oa9JaoGZ9oPDHFDlQxd0q +lX2eDZJZDg0qYvVixmaULIulApq1puEsaJCn3lHUbHlb4PYKwLEywYXM28JN +91KtLsz/uaEX2KC5WqeP40utmzkNLq+oRX/xnRMgwbO7yUNVG2UlEa6eI+xO +XO3YtLdmJMBWClQ066ZnOIzEo1JxnIwha1CDBMWLLfOLrg6l8InUqaXbtEBb +naIYO6fXVXELUjkxnmk7t/QOk0tXCy8muH9UDqJkwDUESY2l79XwBAcx9riX +8vY7vwC34pm22fAUVLCJx1SJx0J8bkeNp38jKM2Zd9SUQqSbfBopQ4pPABEB +AAHNIkdvbGFuZyBHb3BoZXIgPHJldm9rZWRAZ29sYW5nLmNvbT7CwI0EMAEK +ACAWIQTkiTkktw3HqXqtl/DWgXL0jpxSgwUCWyA79wIdAAAhCRDWgXL0jpxS +gxYhBOSJOSS3Dcepeq2X8NaBcvSOnFKDfWMIAKhI/Tvu3h8fSUxp/gSAcduT +6bC1JttG0lYQ5ilKB/58lBUA5CO3ZrKDKlzW3M8VEcvohVaqeTMKeoQd5rCZ +q8KxHn/KvN6Ns85REfXfniCKfAbnGgVXX3kDmZ1g63pkxrFu0fDZjVDXC6vy ++I0sGyI/Inro0Pzbtvn0QCsxjapKK15BtmSrpgHgzVqVg0cUp8vqZeKFxarY +bYB2idtGRci4b9tObOK0BSTVFy26+I/mrFGaPrySYiy2Kz5NMEcRhjmTxJ8j +SwEr2O2sUR0yjbgUAXbTxDVE/jg5fQZ1ACvBRQnB7LvMHcInbzjyeTM3Fazk +kSYQD6b97+dkWwb1iWHNI0dvbGFuZyBHb3BoZXIgPG5vLXJlcGx5QGdvbGFu +Zy5jb20+wsCrBBMBCgA+FiEE5Ik5JLcNx6l6rZfw1oFy9I6cUoMFAlsgO5EC +GwMFCQPCZwAFCwkIBwMFFQoJCAsFFgIDAQACHgECF4AAIQkQ1oFy9I6cUoMW +IQTkiTkktw3HqXqtl/DWgXL0jpxSgwiTB/wM094PbeLiNHB3+nKVu/HBmKe1 +mXV9LBMlbXFw5rV6ZdoS1fZ16m6qE/Th+OVFAZ+xgBCHtf2M4nEAeNOaGoUG +LmwPtC8pTTRw8Vhsn8lPHQHjVuVpedJsaFE+HrdC0RkvsAICz6yHC++iMmrK +zHuTJVG7QRbbCqNd0fBH9Ik7qeE0FrYNfNKI5T9JQDjaaYb7mSMXwBpur3A/ +BP3COtodKETB416s0yY6okTEE7LfIV7IOlpfARkXMF84qjEU2QhpV/kZJ0hQ +aEUQKQa8EwH3fmSF+2aBHwA/F1TgETtetd7EUlTxEK49eiebhZA7BNZHS9CD +rilvZYoDNnweHBMZzsBNBFsgO5EBCAC5INOERA2aNSYHWFeMfByShUuMQGFm +yL2tWT6rwzZmUVG0GUdvoKSRhMJ+81aHxr5zmIhluegEuY99UhX+ZK6NftW2 +UOYjjjQZ4NPDjqOfP5dYUbHiCFRgeUxkmjwnQoSih63iSOoUt5kocR+oXXxb +YmbgeOa8KGgKzDLGHI2nsy8Cni3N/enKVMMHGbJy1DXdV7uRFhBdjnRZGdmt +amHcQbwGHUH+PtTa/jUSMdbtTUvXPI6dz7jDpK0BImzbXNb+r9CcudpiixuM +u5gv3qyJL5EAWCXcT2j+y2VWj2HN/8bJHMoo6yf+bn6A/Cu9f0obbGVF0kJ/ +Y5UWmEdBG6IzABEBAAHCwJMEGAEKACYWIQTkiTkktw3HqXqtl/DWgXL0jpxS +gwUCWyA7kQIbDAUJA8JnAAAhCRDWgXL0jpxSgxYhBOSJOSS3Dcepeq2X8NaB +cvSOnFKDkFMIAIt64bVZ8x7+TitH1bR4pgcNkaKmgKoZz6FXu80+SnbuEt2N +nDyf1cLOSimSTILpwLIuv9Uft5PbOraQbYt3xi9yrqdKqGLv80bxqK0NuryN +kvh9yyx5WoG1iKqMj9/FjGghuPrRaT4lQinNAghGVkEy1+aXGFrG2DsOC1FF +I51CC2WVTzZ5RwR2GpiNRfESsU1rZAUqf/2VyJl9bD5R4SUNy8oQmhOxi+gb +hD4Ao34e4W0ilibslI/uawvCiOwlu5NGd8zv5n+UheiQvzkApQup5c+BhH5z +FDFdKJ2CBByxw9+7QjMFI/wgLixKuE0Ob2kAokXf7RlB7qTZOahrETw= +=+2T8 +-----END PGP PUBLIC KEY BLOCK----- +` + +const keyWithOnlyUserIDRevoked = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mDMEYYwB7RYJKwYBBAHaRw8BAQdARimqhPPzyGAXmfQJjcqM1QVPzLtURJSzNVll +JV4tEaW0KVJldm9rZWQgUHJpbWFyeSBVc2VyIElEIDxyZXZva2VkQGtleS5jb20+ +iHgEMBYIACAWIQSpyJZAXYqVEFkjyKutFcS0yeB0LQUCYYwCtgIdAAAKCRCtFcS0 +yeB0LbSsAQD8OYMaaBjrdzzpwIkP1stgmPd4/kzN/ZG28Ywl6a5F5QEA5Xg7aq4e +/t6Fsb4F5iqB956kSPe6YJrikobD/tBbMwSIkAQTFggAOBYhBKnIlkBdipUQWSPI +q60VxLTJ4HQtBQJhjAHtAhsDBQsJCAcCBhUKCQgLAgQWAgMBAh4BAheAAAoJEK0V +xLTJ4HQtBaoBAPZL7luTCji+Tqhn7XNfFE/0QIahCt8k9wfO1cGlB3inAQDf8Tzw +ZGR5fNluUcNoVxQT7bUSFStbaGo3k0BaOYPbCLg4BGGMAe0SCisGAQQBl1UBBQEB +B0DLwSpveSrbIO/IVZD13yrs1XuB3FURZUnafGrRq7+jUAMBCAeIeAQYFggAIBYh +BKnIlkBdipUQWSPIq60VxLTJ4HQtBQJhjAHtAhsMAAoJEK0VxLTJ4HQtZ1oA/j9u +8+p3xTNzsmabTL6BkNbMeB/RUKCrlm6woM6AV+vxAQCcXTn3JC2sNoNrLoXuVzaA +mcG3/TwG5GSQUUPkrDsGDA== +=mFWy +-----END PGP PUBLIC KEY BLOCK----- +` + +const keyWithSubKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mI0EWyKwKQEEALwXhKBnyaaNFeK3ljfc/qn9X/QFw+28EUfgZPHjRmHubuXLE2uR +s3ZoSXY2z7Dkv+NyHYMt8p+X8q5fR7JvUjK2XbPyKoiJVnHINll83yl67DaWfKNL +EjNoO0kIfbXfCkZ7EG6DL+iKtuxniGTcnGT47e+HJSqb/STpLMnWwXjBABEBAAG0 +I0dvbGFuZyBHb3BoZXIgPG5vLXJlcGx5QGdvbGFuZy5jb20+iM4EEwEKADgWIQQ/ +lRafP/p9PytHbwxMvYJsOQdOOAUCWyKwKQIbAwULCQgHAwUVCgkICwUWAgMBAAIe +AQIXgAAKCRBMvYJsOQdOOOsFBAC62mXww8XuqvYLcVOvHkWLT6mhxrQOJXnlfpn7 +2uBV9CMhoG/Ycd43NONsJrB95Apr9TDIqWnVszNbqPCuBhZQSGLdbiDKjxnCWBk0 +69qv4RNtkpOhYB7jK4s8F5oQZqId6JasT/PmJTH92mhBYhhTQr0GYFuPX2UJdkw9 +Sn9C67iNBFsisDUBBAC3A+Yo9lgCnxi/pfskyLrweYif6kIXWLAtLTsM6g/6jt7b +wTrknuCPyTv0QKGXsAEe/cK/Xq3HvX9WfXPGIHc/X56ZIsHQ+RLowbZV/Lhok1IW +FAuQm8axr/by80cRwFnzhfPc/ukkAq2Qyj4hLsGblu6mxeAhzcp8aqmWOO2H9QAR +AQABiLYEKAEKACAWIQQ/lRafP/p9PytHbwxMvYJsOQdOOAUCWyK16gIdAAAKCRBM +vYJsOQdOOB1vA/4u4uLONsE+2GVOyBsHyy7uTdkuxaR9b54A/cz6jT/tzUbeIzgx +22neWhgvIEghnUZd0vEyK9k1wy5vbDlEo6nKzHso32N1QExGr5upRERAxweDxGOj +7luDwNypI7QcifE64lS/JmlnunwRCdRWMKc0Fp+7jtRc5mpwyHN/Suf5RokBagQY +AQoAIBYhBD+VFp8/+n0/K0dvDEy9gmw5B044BQJbIrA1AhsCAL8JEEy9gmw5B044 +tCAEGQEKAB0WIQSNdnkaWY6t62iX336UXbGvYdhXJwUCWyKwNQAKCRCUXbGvYdhX +JxJSA/9fCPHP6sUtGF1o3G1a3yvOUDGr1JWcct9U+QpbCt1mZoNopCNDDQAJvDWl +mvDgHfuogmgNJRjOMznvahbF+wpTXmB7LS0SK412gJzl1fFIpK4bgnhu0TwxNsO1 +8UkCZWqxRMgcNUn9z6XWONK8dgt5JNvHSHrwF4CxxwjL23AAtK+FA/UUoi3U4kbC +0XnSr1Sl+mrzQi1+H7xyMe7zjqe+gGANtskqexHzwWPUJCPZ5qpIa2l8ghiUim6b +4ymJ+N8/T8Yva1FaPEqfMzzqJr8McYFm0URioXJPvOAlRxdHPteZ0qUopt/Jawxl +Xt6B9h1YpeLoJwjwsvbi98UTRs0jXwoY +=3fWu +-----END PGP PUBLIC KEY BLOCK-----` + +const keyWithSubKeyAndBadSelfSigOrder = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mI0EWyLLDQEEAOqIOpJ/ha1OYAGduu9tS3rBz5vyjbNgJO4sFveEM0mgsHQ0X9/L +plonW+d0gRoO1dhJ8QICjDAc6+cna1DE3tEb5m6JtQ30teLZuqrR398Cf6w7NNVz +r3lrlmnH9JaKRuXl7tZciwyovneBfZVCdtsRZjaLI1uMQCz/BToiYe3DABEBAAG0 +I0dvbGFuZyBHb3BoZXIgPG5vLXJlcGx5QGdvbGFuZy5jb20+iM4EEwEKADgWIQRZ +sixZOfQcZdW0wUqmgmdsv1O9xgUCWyLLDQIbAwULCQgHAwUVCgkICwUWAgMBAAIe +AQIXgAAKCRCmgmdsv1O9xql2A/4pix98NxjhdsXtazA9agpAKeADf9tG4Za27Gj+ +3DCww/E4iP2X35jZimSm/30QRB6j08uGCqd9vXkkJxtOt63y/IpVOtWX6vMWSTUm +k8xKkaYMP0/IzKNJ1qC/qYEUYpwERBKg9Z+k99E2Ql4kRHdxXUHq6OzY79H18Y+s +GdeM/riNBFsiyxsBBAC54Pxg/8ZWaZX1phGdwfe5mek27SOYpC0AxIDCSOdMeQ6G +HPk38pywl1d+S+KmF/F4Tdi+kWro62O4eG2uc/T8JQuRDUhSjX0Qa51gPzJrUOVT +CFyUkiZ/3ZDhtXkgfuso8ua2ChBgR9Ngr4v43tSqa9y6AK7v0qjxD1x+xMrjXQAR +AQABiQFxBBgBCgAmAhsCFiEEWbIsWTn0HGXVtMFKpoJnbL9TvcYFAlsizTIFCQAN +MRcAv7QgBBkBCgAdFiEEJcoVUVJIk5RWj1c/o62jUpRPICQFAlsiyxsACgkQo62j +UpRPICQq5gQApoWIigZxXFoM0uw4uJBS5JFZtirTANvirZV5RhndwHeMN6JttaBS +YnjyA4+n1D+zB2VqliD2QrsX12KJN6rGOehCtEIClQ1Hodo9nC6kMzzAwW1O8bZs +nRJmXV+bsvD4sidLZLjdwOVa3Cxh6pvq4Uur6a7/UYx121hEY0Qx0s8JEKaCZ2y/ +U73GGi0D/i20VW8AWYAPACm2zMlzExKTOAV01YTQH/3vW0WLrOse53WcIVZga6es +HuO4So0SOEAvxKMe5HpRIu2dJxTvd99Bo9xk9xJU0AoFrO0vNCRnL+5y68xMlODK +lEw5/kl0jeaTBp6xX0HDQOEVOpPGUwWV4Ij2EnvfNDXaE1vK1kffiQFrBBgBCgAg +AhsCFiEEWbIsWTn0HGXVtMFKpoJnbL9TvcYFAlsi0AYAv7QgBBkBCgAdFiEEJcoV +UVJIk5RWj1c/o62jUpRPICQFAlsiyxsACgkQo62jUpRPICQq5gQApoWIigZxXFoM +0uw4uJBS5JFZtirTANvirZV5RhndwHeMN6JttaBSYnjyA4+n1D+zB2VqliD2QrsX +12KJN6rGOehCtEIClQ1Hodo9nC6kMzzAwW1O8bZsnRJmXV+bsvD4sidLZLjdwOVa +3Cxh6pvq4Uur6a7/UYx121hEY0Qx0s8JEKaCZ2y/U73GRl0EAJokkXmy4zKDHWWi +wvK9gi2gQgRkVnu2AiONxJb5vjeLhM/07BRmH6K1o+w3fOeEQp4FjXj1eQ5fPSM6 +Hhwx2CTl9SDnPSBMiKXsEFRkmwQ2AAsQZLmQZvKBkLZYeBiwf+IY621eYDhZfo+G +1dh1WoUCyREZsJQg2YoIpWIcvw+a +=bNRo +-----END PGP PUBLIC KEY BLOCK----- +` + +const onlySubkeyNoPrivateKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- +Version: GnuPG v1 + +lQCVBFggvocBBAC7vBsHn7MKmS6IiiZNTXdciplVgS9cqVd+RTdIAoyNTcsiV1H0 +GQ3QtodOPeDlQDNoqinqaobd7R9g3m3hS53Nor7yBZkCWQ5x9v9JxRtoAq0sklh1 +I1X2zEqZk2l6YrfBF/64zWrhjnW3j23szkrAIVu0faQXbQ4z56tmZrw11wARAQAB +/gdlAkdOVQG0CUdOVSBEdW1teYi4BBMBAgAiBQJYIL6HAhsDBgsJCAcDAgYVCAIJ +CgsEFgIDAQIeAQIXgAAKCRCd1xxWp1CYAnjGA/9synn6ZXJUKAXQzySgmCZvCIbl +rqBfEpxwLG4Q/lONhm5vthAE0z49I8hj5Gc5e2tLYUtq0o0OCRdCrYHa/efOYWpJ +6RsK99bePOisVzmOABLIgZkcr022kHoMCmkPgv9CUGKP1yqbGl+zzAwQfUjRUmvD +ZIcWLHi2ge4GzPMPi50B2ARYIL6cAQQAxWHnicKejAFcFcF1/3gUSgSH7eiwuBPX +M7vDdgGzlve1o1jbV4tzrjN9jsCl6r0nJPDMfBSzgLr1auNTRG6HpJ4abcOx86ED +Ad+avDcQPZb7z3dPhH/gb2lQejZsHh7bbeOS8WMSzHV3RqCLd8J/xwWPNR5zKn1f +yp4IGfopidMAEQEAAQAD+wQOelnR82+dxyM2IFmZdOB9wSXQeCVOvxSaNMh6Y3lk +UOOkO8Nlic4x0ungQRvjoRs4wBmCuwFK/MII6jKui0B7dn/NDf51i7rGdNGuJXDH +e676By1sEY/NGkc74jr74T+5GWNU64W0vkpfgVmjSAzsUtpmhJMXsc7beBhJdnVl +AgDKCb8hZqj1alcdmLoNvb7ibA3K/V8J462CPD7bMySPBa/uayoFhNxibpoXml2r +oOtHa5izF3b0/9JY97F6rqkdAgD6GdTJ+xmlCoz1Sewoif1I6krq6xoa7gOYpIXo +UL1Afr+LiJeyAnF/M34j/kjIVmPanZJjry0kkjHE5ILjH3uvAf4/6n9np+Th8ujS +YDCIzKwR7639+H+qccOaddCep8Y6KGUMVdD/vTKEx1rMtK+hK/CDkkkxnFslifMJ +kqoqv3WUqCWJAT0EGAECAAkFAlggvpwCGwIAqAkQndccVqdQmAKdIAQZAQIABgUC +WCC+nAAKCRDmGUholQPwvQk+A/9latnSsR5s5/1A9TFki11GzSEnfLbx46FYOdkW +n3YBxZoPQGxNA1vIn8GmouxZInw9CF4jdOJxEdzLlYQJ9YLTLtN5tQEMl/19/bR8 +/qLacAZ9IOezYRWxxZsyn6//jfl7A0Y+FV59d4YajKkEfItcIIlgVBSW6T+TNQT3 +R+EH5HJ/A/4/AN0CmBhhE2vGzTnVU0VPrE4V64pjn1rufFdclgpixNZCuuqpKpoE +VVHn6mnBf4njKjZrAGPs5kfQ+H4NsM7v3Zz4yV6deu9FZc4O6E+V1WJ38rO8eBix +7G2jko106CC6vtxsCPVIzY7aaG3H5pjRtomw+pX7SzrQ7FUg2PGumg== +=F/T0 +-----END PGP PRIVATE KEY BLOCK-----` + +const ecdsaPrivateKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- + +xaUEX1KsSRMIKoZIzj0DAQcCAwTpYqJsnJiFhKKh+8TulWD+lVmerBFNS+Ii +B+nlG3T0xQQ4Sy5eIjJ0CExIQQzi3EElF/Z2l4F3WC5taFA11NgA/gkDCHSS +PThf1M2K4LN8F1MRcvR+sb7i0nH55ojkwuVB1DE6jqIT9m9i+mX1tzjSAS+6 +lPQiweCJvG7xTC7Hs3AzRapf/r1At4TB+v+5G2/CKynNFEJpbGwgPGJpbGxA +aG9tZS5jb20+wncEEBMIAB8FAl9SrEkGCwkHCAMCBBUICgIDFgIBAhkBAhsD +Ah4BAAoJEMpwT3+q3+xqw5UBAMebZN9isEZ1ML+R/jWAAWMwa/knMugrEZ1v +Bl9+ZwM0AQCZdf80/wYY4Nve01qSRFv8OmKswLli3TvDv6FKc4cLz8epBF9S +rEkSCCqGSM49AwEHAgMEAjKnT9b5wY2bf9TpAV3d7OUfPOxKj9c4VzeVzSrH +AtQgo/MuI1cdYVURicV4i76DNjFhQHQFTk7BrC+C2u1yqQMBCAf+CQMIHImA +iYfzQtjgQWSFZYUkCFpbbwhNF0ch+3HNaZkaHCnZRIsWsRnc6FCb6lRQyK9+ +Dq59kHlduE5QgY40894jfmP2JdJHU6nBdYrivbEdbMJhBBgTCAAJBQJfUqxJ +AhsMAAoJEMpwT3+q3+xqUI0BAMykhV08kQ4Ip9Qlbss6Jdufv7YrU0Vd5hou +b5TmiPd0APoDBh3qIic+aLLUcAuG3+Gt1P1AbUlmqV61ozn1WfHxfw== +=KLN8 +-----END PGP PRIVATE KEY BLOCK-----` + +const dsaPrivateKeyWithElGamalSubkey = `-----BEGIN PGP PRIVATE KEY BLOCK----- + +lQOBBF9/MLsRCACeaF6BI0jTgDAs86t8/kXPfwlPvR2MCYzB0BCqAdcq1hV/GTYd +oNmJRna/ZJfsI/vf+d8Nv+EYOQkPheFS1MJVBitkAXjQPgm8i1tQWen1FCWZxqGk +/vwZYF4yo8GhZ+Wxi3w09W9Cp9QM/CTmyE1Xe7wpPBGe+oD+me8Zxjyt8JBS4Qx+ +gvWbfHxfHnggh4pz7U8QkItlLsBNQEdX4R5+zwRN66g2ZSX/shaa/EkVnihUhD7r +njP9I51ORWucTQD6OvgooaNQZCkQ/Se9TzdakwWKS2XSIFXiY/e2E5ZgKI/pfKDU +iA/KessxddPb7nP/05OIJqg9AoDrD4vmehLzAQD+zsUS3LDU1m9/cG4LMsQbT2VK +Te4HqbGIAle+eu/asQf8DDJMrbZpiJZvADum9j0TJ0oep6VdMbzo9RSDKvlLKT9m +kG63H8oDWnCZm1a+HmGq9YIX+JHWmsLXXsFLeEouLzHO+mZo0X28eji3V2T87hyR +MmUM0wFo4k7jK8uVmkDXv3XwNp2uByWxUKZd7EnWmcEZWqIiexJ7XpCS0Pg3tRaI +zxve0SRe/dxfUPnTk/9KQ9hS6DWroBKquL182zx1Fggh4LIWWE2zq+UYn8BI0E8A +rmIDFJdF8ymFQGRrEy6g79NnkPmkrZWsgMRYY65P6v4zLVmqohJKkpm3/Uxa6QAP +CCoPh/JTOvPeCP2bOJH8z4Z9Py3ouMIjofQW8sXqRgf/RIHbh0KsINHrwwZ4gVIr +MK3RofpaYxw1ztPIWb4cMWoWZHH1Pxh7ggTGSBpAhKXkiWw2Rxat8QF5aA7e962c +bLvVv8dqsPrD/RnVJHag89cbPTzjn7gY9elE8EM8ithV3oQkwHTr4avYlpDZsgNd +hUW3YgRwGo31tdzxoG04AcpV2t+07P8XMPr9hsfWs4rHohXPi38Hseu1Ji+dBoWQ +3+1w/HH3o55s+jy4Ruaz78AIrjbmAJq+6rA2mIcCgrhw3DnzuwQAKeBvSeqn9zfS +ZC812osMBVmkycwelpaIh64WZ0vWL3GvdXDctV2kXM+qVpDTLEny0LuiXxrwCKQL +Ev4HAwK9uQBcreDEEud7pfRb8EYP5lzO2ZA7RaIvje6EWAGBvJGMRT0QQE5SGqc7 +Fw5geigBdt+vVyRuNNhg3c2fdn/OBQaYu0J/8AiOogG8EaM8tCFlbGdhbWFsQGRz +YS5jb20gPGVsZ2FtYWxAZHNhLmNvbT6IkAQTEQgAOBYhBI+gnfiHQxB35/Dp0XAQ +aE/rsWC5BQJffzC7AhsDBQsJCAcCBhUKCQgLAgQWAgMBAh4BAheAAAoJEHAQaE/r +sWC5A4EA/0GcJmyPtN+Klc7b9sVT3JgKTRnB/URxOJfYJofP0hZLAQCkqyMO+adV +JvbgDH0zaITQWZSSXPqpgMpCA6juTrDsd50CawRffzC7EAgAxFFFSAAEQzWTgKU5 +EBtpxxoPzHqcChawTHRxHxjcELXzmUBS5PzfA1HXSPnNqK/x3Ut5ycC3CsW41Fnt +Gm3706Wu9VFbFZVn55F9lPiplUo61n5pqMvOr1gmuQsdXiTa0t5FRa4TZ2VSiHFw +vdAVSPTUsT4ZxJ1rPyFYRtq1n3pQcvdZowd07r0JnzTMjLLMFYCKhwIowoOC4zqJ +iB8enjwOlpaqBATRm9xpVF7SJkroPF6/B1vdhj7E3c1aJyHlo0PYBAg756sSHWHg +UuLyUQ4TA0hcCVenn/L/aSY2LnbdZB1EBhlYjA7dTCgwIqsQhfQmPkjz6g64A7+Y +HbbrLwADBQgAk14QIEQ+J/VHetpQV/jt2pNsFK1kVK7mXK0spTExaC2yj2sXlHjL +Ie3bO5T/KqmIaBEB5db5fA5xK9cZt79qrQHDKsEqUetUeMUWLBx77zBsus3grIgy +bwDZKseRzQ715pwxquxQlScGoDIBKEh08HpwHkq140eIj3w+MAIfndaZaSCNaxaP +Snky7BQmJ7Wc7qrIwoQP6yrnUqyW2yNi81nJYUhxjChqaFSlwzLs/iNGryBKo0ic +BqVIRjikKHBlwBng6WyrltQo/Vt9GG8w+lqaAVXbJRlaBZJUR+2NKi/YhP3qQse3 +v8fi4kns0gh5LK+2C01RvdX4T49QSExuIf4HAwLJqYIGwadA2uem5v7/765ZtFWV +oL0iZ0ueTJDby4wTFDpLVzzDi/uVcB0ZRFrGOp7w6OYcNYTtV8n3xmli2Q5Trw0c +wZVzvg+ABKWiv7faBjMczIFF8y6WZKOIeAQYEQgAIBYhBI+gnfiHQxB35/Dp0XAQ +aE/rsWC5BQJffzC7AhsMAAoJEHAQaE/rsWC5ZmIA/jhS4r4lClbvjuPWt0Yqdn7R +fss2SPMYvMrrDh42aE0OAQD8xn4G6CN8UtW9xihXOY6FpxiJ/sMc2VaneeUd34oa +4g== +=XZm8 +-----END PGP PRIVATE KEY BLOCK-----` + +// https://tests.sequoia-pgp.org/#Certificate_expiration +// P _ U p +const expiringPrimaryUIDKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +xsDNBF2lnPIBDAC5cL9PQoQLTMuhjbYvb4Ncuuo0bfmgPRFywX53jPhoFf4Zg6mv +/seOXpgecTdOcVttfzC8ycIKrt3aQTiwOG/ctaR4Bk/t6ayNFfdUNxHWk4WCKzdz +/56fW2O0F23qIRd8UUJp5IIlN4RDdRCtdhVQIAuzvp2oVy/LaS2kxQoKvph/5pQ/ +5whqsyroEWDJoSV0yOb25B/iwk/pLUFoyhDG9bj0kIzDxrEqW+7Ba8nocQlecMF3 +X5KMN5kp2zraLv9dlBBpWW43XktjcCZgMy20SouraVma8Je/ECwUWYUiAZxLIlMv +9CurEOtxUw6N3RdOtLmYZS9uEnn5y1UkF88o8Nku890uk6BrewFzJyLAx5wRZ4F0 +qV/yq36UWQ0JB/AUGhHVPdFf6pl6eaxBwT5GXvbBUibtf8YI2og5RsgTWtXfU7eb +SGXrl5ZMpbA6mbfhd0R8aPxWfmDWiIOhBufhMCvUHh1sApMKVZnvIff9/0Dca3wb +vLIwa3T4CyshfT0AEQEAAc0hQm9iIEJhYmJhZ2UgPGJvYkBvcGVucGdwLmV4YW1w +bGU+wsFcBBMBCgCQBYJhesp/BYkEWQPJBQsJCAcCCRD7/MgqAV5zMEcUAAAAAAAe +ACBzYWx0QG5vdGF0aW9ucy5zZXF1b2lhLXBncC5vcmeEOQlNyTLFkc9I/elp+BpY +495V7KatqtDmsyDr+zDAdwYVCgkICwIEFgIDAQIXgAIbAwIeARYhBNGmbhojsYLJ +mA94jPv8yCoBXnMwAABSCQv/av8hKyynMtXVKFuWOGJw0mR8auDm84WdhMFRZg8t +yTJ1L88+Ny4WUAFeqo2j7DU2yPGrm5rmuvzlEedFYFeOWt+A4adz+oumgRd0nsgG +Lf3QYUWQhLWVlz+H7zubgKqSB2A2RqV65S7mTTVro42nb2Mng6rvGWiqeKG5nrXN +/01p1mIBQGR/KnZSqYLzA2Pw2PiJoSkXT26PDz/kiEMXpjKMR6sicV4bKVlEdUvm +pIImIPBHZq1EsKXEyWtWC41w/pc+FofGE+uSFs2aef1vvEHFkj3BHSK8gRcH3kfR +eFroTET8C2q9V1AOELWm+Ys6PzGzF72URK1MKXlThuL4t4LjvXWGNA78IKW+/RQH +DzK4U0jqSO0mL6qxqVS5Ij6jjL6OTrVEGdtDf5n0vI8tcUTBKtVqYAYk+t2YGT05 +ayxALtb7viVKo8f10WEcCuKshn0gdsEFMRZQzJ89uQIY3R3FbsdRCaE6OEaDgKMQ +UTFROyfhthgzRKbRxfcplMUCzsDNBF2lnPIBDADWML9cbGMrp12CtF9b2P6z9TTT +74S8iyBOzaSvdGDQY/sUtZXRg21HWamXnn9sSXvIDEINOQ6A9QxdxoqWdCHrOuW3 +ofneYXoG+zeKc4dC86wa1TR2q9vW+RMXSO4uImA+Uzula/6k1DogDf28qhCxMwG/ +i/m9g1c/0aApuDyKdQ1PXsHHNlgd/Dn6rrd5y2AObaifV7wIhEJnvqgFXDN2RXGj +LeCOHV4Q2WTYPg/S4k1nMXVDwZXrvIsA0YwIMgIT86Rafp1qKlgPNbiIlC1g9RY/ +iFaGN2b4Ir6GDohBQSfZW2+LXoPZuVE/wGlQ01rh827KVZW4lXvqsge+wtnWlszc +selGATyzqOK9LdHPdZGzROZYI2e8c+paLNDdVPL6vdRBUnkCaEkOtl1mr2JpQi5n +TU+gTX4IeInC7E+1a9UDF/Y85ybUz8XV8rUnR76UqVC7KidNepdHbZjjXCt8/Zo+ +Tec9JNbYNQB/e9ExmDntmlHEsSEQzFwzj8sxH48AEQEAAcLA9gQYAQoAIBYhBNGm +bhojsYLJmA94jPv8yCoBXnMwBQJdpZzyAhsMAAoJEPv8yCoBXnMw6f8L/26C34dk +jBffTzMj5Bdzm8MtF67OYneJ4TQMw7+41IL4rVcSKhIhk/3Ud5knaRtP2ef1+5F6 +6h9/RPQOJ5+tvBwhBAcUWSupKnUrdVaZQanYmtSxcVV2PL9+QEiNN3tzluhaWO// +rACxJ+K/ZXQlIzwQVTpNhfGzAaMVV9zpf3u0k14itcv6alKY8+rLZvO1wIIeRZLm +U0tZDD5HtWDvUV7rIFI1WuoLb+KZgbYn3OWjCPHVdTrdZ2CqnZbG3SXw6awH9bzR +LV9EXkbhIMez0deCVdeo+wFFklh8/5VK2b0vk/+wqMJxfpa1lHvJLobzOP9fvrsw +sr92MA2+k901WeISR7qEzcI0Fdg8AyFAExaEK6VyjP7SXGLwvfisw34OxuZr3qmx +1Sufu4toH3XrB7QJN8XyqqbsGxUCBqWif9RSK4xjzRTe56iPeiSJJOIciMP9i2ld +I+KgLycyeDvGoBj0HCLO3gVaBe4ubVrj5KjhX2PVNEJd3XZRzaXZE2aAMQ== +=AmgT +-----END PGP PUBLIC KEY BLOCK-----` + +const rsa2048PrivateKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- +Comment: gpg (GnuPG) 2.2.27 with libgcrypt 1.9.4 + +lQPGBGL07P0BCADL0etN8efyAXA6sL2WfQvHe5wEKYXPWeN2+jiqSppfeRZAOlzP +kZ3U+cloeJriplYvVJwI3ID2aw52Z/TRn8iKRP5eOUFrEgcgl06lazLtOndK7o7p +oBV5mLtHEirFHm6W61fNt10jzM0jx0PV6nseLhFB2J42F1cmU/aBgFo41wjLSZYr +owR+v+O9S5sUXblQF6sEDcY01sBEu09zrIgT49VFwQ1Cvdh9XZEOTQBfdiugoj5a +DS3fAqAka3r1VoQK4eR7/upnYSgSACGeaQ4pUelKku5rpm50gdWTY8ppq0k9e1eT +y2x0OQcW3hWE+j4os1ca0ZEADMdqr/99MOxrABEBAAH+BwMCJWxU4VOZOJ7/I6vX +FxdfBhIBEXlJ52FM3S/oYtXqLhkGyrtmZOeEazVvUtuCe3M3ScHI8xCthcmE8E0j +bi+ZEHPS2NiBZtgHFF27BLn7zZuTc+oD5WKduZdK3463egnyThTqIIMl25WZBuab +k5ycwYrWwBH0jfA4gwJ13ai4pufKC2RM8qIu6YAVPglYBKFLKGvvJHa5vI+LuA0E +K+k35hIic7yVUcQneNnAF2598X5yWiieYnOZpmHlRw1zfbMwOJr3ZNj2v94u7b+L +sTa/1Uv9887Vb6sJp0c2Sh4cwEccoPYkvMqFn3ZrJUr3UdDu1K2vWohPtswzhrYV ++RdPZE5RLoCQufKvlPezk0Pzhzb3bBU7XjUbdGY1nH/EyQeBNp+Gw6qldKvzcBaB +cyOK1c6hPSszpJX93m5UxCN55IeifmcNjmbDh8vGCCdajy6d56qV2n4F3k7vt1J1 +0UlxIGhqijJoaTCX66xjLMC6VXkSz6aHQ35rnXosm/cqPcQshsZTdlfSyWkorfdr +4Hj8viBER26mjYurTMLBKDtUN724ZrR0Ev5jorX9uoKlgl87bDZHty2Ku2S+vR68 +VAvnj6Fi1BYNclnDoqxdRB2z5T9JbWE52HuG83/QsplhEqXxESDxriTyTHMbNxEe +88soVCDh4tgflZFa2ucUr6gEKJKij7jgahARnyaXfPZlQBUAS1YUeILYmN+VR+M/ +sHENpwDWc7TInn8VN638nJV+ScZGMih3AwWZTIoiLju3MMt1K0YZ3NuiqwGH4Jwg +/BbEdTWeCci9y3NEQHQ3uZZ5p6j2CwFVlK11idemCMvAiTVxF+gKdaLMkeCwKxru +J3YzhKEo+iDVYbPYBYizx/EHBn2U5kITQ5SBXzjTaaFMNZJEf9JYsL1ybPB6HOFY +VNVB2KT8CGVwtCJHb2xhbmcgR29waGVyIDxnb2xhbmdAZXhhbXBsZS5vcmc+iQFO +BBMBCgA4FiEEC6K7U7f4qesybTnqSkra7gHusm0FAmL07P0CGwMFCwkIBwIGFQoJ +CAsCBBYCAwECHgECF4AACgkQSkra7gHusm1MvwgAxpClWkeSqIhMQfbiuz0+lOkE +89y1DCFw8bHjZoUf4/4K8hFA3dGkk+q72XFgiyaCpfXxMt6Gi+dN47t+tTv9NIqC +sukbaoJBmJDhN6+djmJOgOYy+FWsW2LAk2LOwKYulpnBZdcA5rlMAhBg7gevQpF+ +ruSU69P7UUaFJl/DC7hDmaIcj+4cjBE/HO26SnVQjoTfjZT82rDh1Wsuf8LnkJUk +b3wezBLpXKjDvdHikdv4gdlR4AputVM38aZntYYglh/EASo5TneyZ7ZscdLNRdcF +r5O2fKqrOJLOdaoYRFZZWOvP5GtEVFDU7WGivOSVfiszBE0wZR3dgZRJipHCXJ0D +xgRi9Oz9AQgAtMJcJqLLVANJHl90tWuoizDkm+Imcwq2ubQAjpclnNrODnDK+7o4 +pBsWmXbZSdkC4gY+LhOQA6bPDD0JEHM58DOnrm49BddxXAyK0HPsk4sGGt2SS86B +OawWNdfJVyqw4bAiHWDmQg4PcjBbt3ocOIxAR6I5kBSiQVxuGQs9T+Zvg3G1r3Or +fS6DzlgY3HFUML5YsGH4lOxNSOoKAP68GIH/WNdUZ+feiRg9knIib6I3Hgtf5eO8 +JRH7aWE/TD7eNu36bLLjT5TZPq5r6xaD2plbtPOyXbNPWs9qI1yG+VnErfaLY0w8 +Qo0aqzbgID+CTZVomXSOpOcQseaFKw8ZfQARAQAB/gcDArha6+/+d4OY/w9N32K9 +hFNYt4LufTETMQ+k/sBeaMuAVzmT47DlAXzkrZhGW4dZOtXMu1rXaUwHlqkhEyzL +L4MYEWVXfD+LbZNEK3MEFss6RK+UAMeT/PTV9aA8cXQVPcSJYzfBXHQ1U1hnOgrO +apn92MN8RmkhX8wJLyeWTMMuP4lXByJMmmGo8WvifeRD2kFY4y0WVBDAXJAV4Ljf +Di/bBiwoc5a+gxHuZT2W9ZSxBQJNXdt4Un2IlyZuo58s5MLx2N0EaNJ8PwRUE6fM +RZYO8aZCEPUtINE4njbvsWOMCtrblsMPwZ1B0SiIaWmLaNyGdCNKea+fCIW7kasC +JYMhnLumpUTXg5HNexkCsl7ABWj0PYBflOE61h8EjWpnQ7JBBVKS2ua4lMjwHRX7 +5o5yxym9k5UZNFdGoXVL7xpizCcdGawxTJvwhs3vBqu1ZWYCegOAZWDrOkCyhUpq +8uKMROZFbn+FwE+7tjt+v2ed62FVEvD6g4V3ThCA6mQqeOARfJWN8GZY8BDm8lht +crOXriUkrx+FlrgGtm2CkwjW5/9Xd7AhFpHnQdFeozOHyq1asNSgJF9sNi9Lz94W +skQSVRi0IExxSXYGI3Y0nnAZUe2BAQflYPJdEveSr3sKlUqXiETTA1VXsTPK3kOC +92CbLzj/Hz199jZvywwyu53I+GKMpF42rMq7zxr2oa61YWY4YE/GDezwwys/wLx/ +QpCW4X3ppI7wJjCSSqEV0baYZSSli1ayheS6dxi8QnSpX1Bmpz6gU7m/M9Sns+hl +J7ZvgpjCAiV7KJTjtclr5/S02zP78LTVkoTWoz/6MOTROwaP63VBUXX8pbJhf/vu +DLmNnDk8joMJxoDXWeNU0EnNl4hP7Z/jExRBOEO4oAnUf/Sf6gCWQhL5qcajtg6w +tGv7vx3f2IkBNgQYAQoAIBYhBAuiu1O3+KnrMm056kpK2u4B7rJtBQJi9Oz9AhsM +AAoJEEpK2u4B7rJt6lgIAMBWqP4BCOGnQXBbgJ0+ACVghpkFUXZTb/tXJc8UUvTM +8uov6k/RsqDGZrvhhufD7Wwt7j9v7dD7VPp7bPyjVWyimglQzWguTUUqLDGlstYH +5uYv1pzma0ZsAGNqFeGlTLsKOSGKFMH4rB2KfN2n51L8POvtp1y7GKZQbWIWneaB +cZr3BINU5GMvYYU7pAYcoR+mJPdJx5Up3Ocn+bn8Tu1sy9C/ArtCQucazGnoE9u1 +HhNLrh0CdzzX7TNH6TQ8LwPOvq0K5l/WqbN9lE0WBBhMv2HydxhluO8AhU+A5GqC +C+wET7nVDnhoOm/fstIeb7/LN7OYejKPeHdFBJEL9GA= +=u442 +-----END PGP PRIVATE KEY BLOCK-----` + +const curve25519PrivateKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- +Comment: gpg (GnuPG) 2.2.27 with libgcrypt 1.9.4 + +lFgEYvTtQBYJKwYBBAHaRw8BAQdAxsNXLbrk5xOjpO24VhOMvQ0/F+JcyIkckMDH +X3FIGxcAAQDFOlunZWYuPsCx5JLp78vKqUTfgef9TGG4oD6I/Sa0zBMstCJHb2xh +bmcgR29waGVyIDxnb2xhbmdAZXhhbXBsZS5vcmc+iJAEExYIADgWIQSFQHEOazmo +h1ldII4MvfnLQ4JBNwUCYvTtQAIbAwULCQgHAgYVCgkICwIEFgIDAQIeAQIXgAAK +CRAMvfnLQ4JBN5yeAQCKdry8B5ScCPrev2+UByMCss7Sdu5RhomCFsHdNPLcKAEA +8ugei+1owHsV+3cGwWWzKk6sLa8ZN87i3SKuOGp9DQycXQRi9O1AEgorBgEEAZdV +AQUBAQdA5CubPp8l7lrVQ25h7Hx5XN2C8xanRnnpcjzEooCaEA0DAQgHAAD/Rpc+ +sOZUXrFk9HOWB1XU41LoWbDBoG8sP8RWAVYwD5AQRYh4BBgWCAAgFiEEhUBxDms5 +qIdZXSCODL35y0OCQTcFAmL07UACGwwACgkQDL35y0OCQTcvdwEA7lb5g/YisrEf +iq660uwMGoepLUfvtqKzuQ6heYe83y0BAN65Ffg5HYOJzUEi0kZQRf7OhdtuL2kJ +SRXn8DmCTfEB +=cELM +-----END PGP PRIVATE KEY BLOCK-----` + +const curve448PrivateKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- +Comment: C1DB 65D5 80D7 B922 7254 4B1E A699 9895 FABA CE52 + +xYUEYV2UmRYDK2VxAc9AFyxgh5xnSbyt50TWl558mw9xdMN+/UBLr5+UMP8IsrvV +MdXuTIE8CyaUQKSotHtH2RkYEXj5nsMAAAHPQIbTMSzjIWug8UFECzAex5FHgAgH +gYF3RK+TS8D24wX8kOu2C/NoVxwGY+p+i0JHaB+7yljriSKAGxs6wsBEBB8WCgCD +BYJhXZSZBYkFpI+9AwsJBwkQppmYlfq6zlJHFAAAAAAAHgAgc2FsdEBub3RhdGlv +bnMuc2VxdW9pYS1wZ3Aub3Jn5wSpIutJ5HncJWk4ruUV8GzQF390rR5+qWEAnAoY +akcDFQoIApsBAh4BFiEEwdtl1YDXuSJyVEseppmYlfq6zlIAALzdA5dA/fsgYg/J +qaQriYKaPUkyHL7EB3BXhV2d1h/gk+qJLvXQuU2WEJ/XSs3GrsBRiiZwvPH4o+7b +mleAxjy5wpS523vqrrBR2YZ5FwIku7WS4litSdn4AtVam/TlLdMNIf41CtFeZKBe +c5R5VNdQy8y7qy8AAADNEUN1cnZlNDQ4IE9wdGlvbiA4wsBHBBMWCgCGBYJhXZSZ +BYkFpI+9AwsJBwkQppmYlfq6zlJHFAAAAAAAHgAgc2FsdEBub3RhdGlvbnMuc2Vx +dW9pYS1wZ3Aub3JnD55UsYMzE6OACP+mgw5zvT+BBgol8/uFQjHg4krjUCMDFQoI +ApkBApsBAh4BFiEEwdtl1YDXuSJyVEseppmYlfq6zlIAAPQJA5dA0Xqwzn/0uwCq +RlsOVCB3f5NOj1exKnlBvRw0xT1VBee1yxvlUt5eIAoCxWoRlWBJob3TTkhm9AEA +8dyhwPmyGfWHzPw5NFG3xsXrZdNXNvit9WMVAPcmsyR7teXuDlJItxRAdJJc/qfJ +YVbBFoaNrhYAAADHhQRhXZSZFgMrZXEBz0BL7THZ9MnCLfSPJ1FMLim9eGkQ3Bfn +M3he5rOwO3t14QI1LjI96OjkeJipMgcFAmEP1Bq/ZHGO7oAAAc9AFnE8iNBaT3OU +EFtxkmWHXtdaYMmGGRdopw9JPXr/UxuunDln5o9dxPxf7q7z26zXrZen+qed/Isa +HsDCwSwEGBYKAWsFgmFdlJkFiQWkj70JEKaZmJX6us5SRxQAAAAAAB4AIHNhbHRA +bm90YXRpb25zLnNlcXVvaWEtcGdwLm9yZxREUizdTcepBzgSMOv2VWQCWbl++3CZ +EbgAWDryvSsyApsCwDGgBBkWCgBvBYJhXZSZCRBKo3SL4S5djkcUAAAAAAAeACBz +YWx0QG5vdGF0aW9ucy5zZXF1b2lhLXBncC5vcmemoGTDjmNQiIzw6HOEddvS0OB7 +UZ/P07jM/EVmnYxTlBYhBAxsnkGpx1UCiH6gUUqjdIvhLl2OAAALYQOXQAMB1oKq +OWxSFmvmgCKNcbAAyA3piF5ERIqs4z07oJvqDYrOWt75UsEIH/04gU/vHc4EmfG2 +JDLJgOLlyTUPkL/08f0ydGZPofFQBhn8HkuFFjnNtJ5oz3GIP4cdWMQFaUw0uvjb +PM9Tm3ptENGd6Ts1AAAAFiEEwdtl1YDXuSJyVEseppmYlfq6zlIAAGpTA5dATR6i +U2GrpUcQgpG+JqfAsGmF4yAOhgFxc1UfidFk3nTup3fLgjipkYY170WLRNbyKkVO +Sodx93GAs58rizO1acDAWiLq3cyEPBFXbyFThbcNPcLl+/77Uk/mgkYrPQFAQWdK +1kSRm4SizDBK37K8ChAAAADHhwRhXZSZEgMrZW8Bx0DMhzvhQo+OsXeqQ6QVw4sF +CaexHh6rLohh7TzL3hQSjoJ27fV6JBkIWdn0LfrMlJIDbSv2SLdlgQMBCgkAAcdA +MO7Dc1myF6Co1fAH+EuP+OxhxP/7V6ljuSCZENDfA49tQkzTta+PniG+pOVB2LHb +huyaKBkqiaogo8LAOQQYFgoAeAWCYV2UmQWJBaSPvQkQppmYlfq6zlJHFAAAAAAA +HgAgc2FsdEBub3RhdGlvbnMuc2VxdW9pYS1wZ3Aub3JnEjBMQAmc/2u45u5FQGmB +QAytjSG2LM3JQN+PPVl5vEkCmwwWIQTB22XVgNe5InJUSx6mmZiV+rrOUgAASdYD +l0DXEHQ9ykNP2rZP35ET1dmiFagFtTj/hLQcWlg16LqvJNGqOgYXuqTerbiOOt02 +XLCBln+wdewpU4ChEffMUDRBfqfQco/YsMqWV7bHJHAO0eC/DMKCjyU90xdH7R/d +QgqsfguR1PqPuJxpXV4bSr6CGAAAAA== +=MSvh +-----END PGP PRIVATE KEY BLOCK-----` + +const keyWithNotation = `-----BEGIN PGP PRIVATE KEY BLOCK----- + +xVgEY9gIshYJKwYBBAHaRw8BAQdAF25fSM8OpFlXZhop4Qpqo5ywGZ4jgWlR +ppjhIKDthREAAQC+LFpzFcMJYcjxGKzBGHN0Px2jU4d04YSRnFAik+lVVQ6u +zRdUZXN0IDx0ZXN0QGV4YW1wbGUuY29tPsLACgQQFgoAfAUCY9gIsgQLCQcI +CRD/utJOCym8pR0UgAAAAAAQAAR0ZXh0QGV4YW1wbGUuY29tdGVzdB8UAAAA +AAASAARiaW5hcnlAZXhhbXBsZS5jb20AAQIDAxUICgQWAAIBAhkBAhsDAh4B +FiEEEMCQTUVGKgCX5rDQ/7rSTgspvKUAAPl5AP9Npz90LxzrB97Qr2DrGwfG +wuYn4FSYwtuPfZHHeoIabwD/QEbvpQJ/NBb9EAZuow4Rirlt1yv19mmnF+j5 +8yUzhQjHXQRj2AiyEgorBgEEAZdVAQUBAQdARXAo30DmKcyUg6co7OUm0RNT +z9iqFbDBzA8A47JEt1MDAQgHAAD/XKK3lBm0SqMR558HLWdBrNG6NqKuqb5X +joCML987ZNgRD8J4BBgWCAAqBQJj2AiyCRD/utJOCym8pQIbDBYhBBDAkE1F +RioAl+aw0P+60k4LKbylAADRxgEAg7UfBDiDPp5LHcW9D+SgFHk6+GyEU4ev +VppQxdtxPvAA/34snHBX7Twnip1nMt7P4e2hDiw/hwQ7oqioOvc6jMkP +=Z8YJ +-----END PGP PRIVATE KEY BLOCK----- +` diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go new file mode 100644 index 00000000..fec41a0e --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go @@ -0,0 +1,67 @@ +// Copyright (C) 2019 ProtonTech AG + +package packet + +import "math/bits" + +// CipherSuite contains a combination of Cipher and Mode +type CipherSuite struct { + // The cipher function + Cipher CipherFunction + // The AEAD mode of operation. + Mode AEADMode +} + +// AEADConfig collects a number of AEAD parameters along with sensible defaults. +// A nil AEADConfig is valid and results in all default values. +type AEADConfig struct { + // The AEAD mode of operation. + DefaultMode AEADMode + // Amount of octets in each chunk of data + ChunkSize uint64 +} + +// Mode returns the AEAD mode of operation. +func (conf *AEADConfig) Mode() AEADMode { + // If no preference is specified, OCB is used (which is mandatory to implement). + if conf == nil || conf.DefaultMode == 0 { + return AEADModeOCB + } + + mode := conf.DefaultMode + if mode != AEADModeEAX && mode != AEADModeOCB && mode != AEADModeGCM { + panic("AEAD mode unsupported") + } + return mode +} + +// ChunkSizeByte returns the byte indicating the chunk size. The effective +// chunk size is computed with the formula uint64(1) << (chunkSizeByte + 6) +// limit to 16 = 4 MiB +// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2 +func (conf *AEADConfig) ChunkSizeByte() byte { + if conf == nil || conf.ChunkSize == 0 { + return 12 // 1 << (12 + 6) == 262144 bytes + } + + chunkSize := conf.ChunkSize + exponent := bits.Len64(chunkSize) - 1 + switch { + case exponent < 6: + exponent = 6 + case exponent > 16: + exponent = 16 + } + + return byte(exponent - 6) +} + +// decodeAEADChunkSize returns the effective chunk size. In 32-bit systems, the +// maximum returned value is 1 << 30. +func decodeAEADChunkSize(c byte) int { + size := uint64(1 << (c + 6)) + if size != uint64(int(size)) { + return 1 << 30 + } + return int(size) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go new file mode 100644 index 00000000..cee83bdc --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go @@ -0,0 +1,264 @@ +// Copyright (C) 2019 ProtonTech AG + +package packet + +import ( + "bytes" + "crypto/cipher" + "encoding/binary" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// aeadCrypter is an AEAD opener/sealer, its configuration, and data for en/decryption. +type aeadCrypter struct { + aead cipher.AEAD + chunkSize int + initialNonce []byte + associatedData []byte // Chunk-independent associated data + chunkIndex []byte // Chunk counter + packetTag packetType // SEIP packet (v2) or AEAD Encrypted Data packet + bytesProcessed int // Amount of plaintext bytes encrypted/decrypted + buffer bytes.Buffer // Buffered bytes across chunks +} + +// computeNonce takes the incremental index and computes an eXclusive OR with +// the least significant 8 bytes of the receivers' initial nonce (see sec. +// 5.16.1 and 5.16.2). It returns the resulting nonce. +func (wo *aeadCrypter) computeNextNonce() (nonce []byte) { + if wo.packetTag == packetTypeSymmetricallyEncryptedIntegrityProtected { + return append(wo.initialNonce, wo.chunkIndex...) + } + + nonce = make([]byte, len(wo.initialNonce)) + copy(nonce, wo.initialNonce) + offset := len(wo.initialNonce) - 8 + for i := 0; i < 8; i++ { + nonce[i+offset] ^= wo.chunkIndex[i] + } + return +} + +// incrementIndex performs an integer increment by 1 of the integer represented by the +// slice, modifying it accordingly. +func (wo *aeadCrypter) incrementIndex() error { + index := wo.chunkIndex + if len(index) == 0 { + return errors.AEADError("Index has length 0") + } + for i := len(index) - 1; i >= 0; i-- { + if index[i] < 255 { + index[i]++ + return nil + } + index[i] = 0 + } + return errors.AEADError("cannot further increment index") +} + +// aeadDecrypter reads and decrypts bytes. It buffers extra decrypted bytes when +// necessary, similar to aeadEncrypter. +type aeadDecrypter struct { + aeadCrypter // Embedded ciphertext opener + reader io.Reader // 'reader' is a partialLengthReader + peekedBytes []byte // Used to detect last chunk + eof bool +} + +// Read decrypts bytes and reads them into dst. It decrypts when necessary and +// buffers extra decrypted bytes. It returns the number of bytes copied into dst +// and an error. +func (ar *aeadDecrypter) Read(dst []byte) (n int, err error) { + // Return buffered plaintext bytes from previous calls + if ar.buffer.Len() > 0 { + return ar.buffer.Read(dst) + } + + // Return EOF if we've previously validated the final tag + if ar.eof { + return 0, io.EOF + } + + // Read a chunk + tagLen := ar.aead.Overhead() + cipherChunkBuf := new(bytes.Buffer) + _, errRead := io.CopyN(cipherChunkBuf, ar.reader, int64(ar.chunkSize+tagLen)) + cipherChunk := cipherChunkBuf.Bytes() + if errRead != nil && errRead != io.EOF { + return 0, errRead + } + decrypted, errChunk := ar.openChunk(cipherChunk) + if errChunk != nil { + return 0, errChunk + } + + // Return decrypted bytes, buffering if necessary + if len(dst) < len(decrypted) { + n = copy(dst, decrypted[:len(dst)]) + ar.buffer.Write(decrypted[len(dst):]) + } else { + n = copy(dst, decrypted) + } + + // Check final authentication tag + if errRead == io.EOF { + errChunk := ar.validateFinalTag(ar.peekedBytes) + if errChunk != nil { + return n, errChunk + } + ar.eof = true // Mark EOF for when we've returned all buffered data + } + return +} + +// Close is noOp. The final authentication tag of the stream was already +// checked in the last Read call. In the future, this function could be used to +// wipe the reader and peeked, decrypted bytes, if necessary. +func (ar *aeadDecrypter) Close() (err error) { + return nil +} + +// openChunk decrypts and checks integrity of an encrypted chunk, returning +// the underlying plaintext and an error. It accesses peeked bytes from next +// chunk, to identify the last chunk and decrypt/validate accordingly. +func (ar *aeadDecrypter) openChunk(data []byte) ([]byte, error) { + tagLen := ar.aead.Overhead() + // Restore carried bytes from last call + chunkExtra := append(ar.peekedBytes, data...) + // 'chunk' contains encrypted bytes, followed by an authentication tag. + chunk := chunkExtra[:len(chunkExtra)-tagLen] + ar.peekedBytes = chunkExtra[len(chunkExtra)-tagLen:] + + adata := ar.associatedData + if ar.aeadCrypter.packetTag == packetTypeAEADEncrypted { + adata = append(ar.associatedData, ar.chunkIndex...) + } + + nonce := ar.computeNextNonce() + plainChunk, err := ar.aead.Open(nil, nonce, chunk, adata) + if err != nil { + return nil, err + } + ar.bytesProcessed += len(plainChunk) + if err = ar.aeadCrypter.incrementIndex(); err != nil { + return nil, err + } + return plainChunk, nil +} + +// Checks the summary tag. It takes into account the total decrypted bytes into +// the associated data. It returns an error, or nil if the tag is valid. +func (ar *aeadDecrypter) validateFinalTag(tag []byte) error { + // Associated: tag, version, cipher, aead, chunk size, ... + amountBytes := make([]byte, 8) + binary.BigEndian.PutUint64(amountBytes, uint64(ar.bytesProcessed)) + + adata := ar.associatedData + if ar.aeadCrypter.packetTag == packetTypeAEADEncrypted { + // ... index ... + adata = append(ar.associatedData, ar.chunkIndex...) + } + + // ... and total number of encrypted octets + adata = append(adata, amountBytes...) + nonce := ar.computeNextNonce() + _, err := ar.aead.Open(nil, nonce, tag, adata) + if err != nil { + return err + } + return nil +} + +// aeadEncrypter encrypts and writes bytes. It encrypts when necessary according +// to the AEAD block size, and buffers the extra encrypted bytes for next write. +type aeadEncrypter struct { + aeadCrypter // Embedded plaintext sealer + writer io.WriteCloser // 'writer' is a partialLengthWriter +} + +// Write encrypts and writes bytes. It encrypts when necessary and buffers extra +// plaintext bytes for next call. When the stream is finished, Close() MUST be +// called to append the final tag. +func (aw *aeadEncrypter) Write(plaintextBytes []byte) (n int, err error) { + // Append plaintextBytes to existing buffered bytes + n, err = aw.buffer.Write(plaintextBytes) + if err != nil { + return n, err + } + // Encrypt and write chunks + for aw.buffer.Len() >= aw.chunkSize { + plainChunk := aw.buffer.Next(aw.chunkSize) + encryptedChunk, err := aw.sealChunk(plainChunk) + if err != nil { + return n, err + } + _, err = aw.writer.Write(encryptedChunk) + if err != nil { + return n, err + } + } + return +} + +// Close encrypts and writes the remaining buffered plaintext if any, appends +// the final authentication tag, and closes the embedded writer. This function +// MUST be called at the end of a stream. +func (aw *aeadEncrypter) Close() (err error) { + // Encrypt and write a chunk if there's buffered data left, or if we haven't + // written any chunks yet. + if aw.buffer.Len() > 0 || aw.bytesProcessed == 0 { + plainChunk := aw.buffer.Bytes() + lastEncryptedChunk, err := aw.sealChunk(plainChunk) + if err != nil { + return err + } + _, err = aw.writer.Write(lastEncryptedChunk) + if err != nil { + return err + } + } + // Compute final tag (associated data: packet tag, version, cipher, aead, + // chunk size... + adata := aw.associatedData + + if aw.aeadCrypter.packetTag == packetTypeAEADEncrypted { + // ... index ... + adata = append(aw.associatedData, aw.chunkIndex...) + } + + // ... and total number of encrypted octets + amountBytes := make([]byte, 8) + binary.BigEndian.PutUint64(amountBytes, uint64(aw.bytesProcessed)) + adata = append(adata, amountBytes...) + + nonce := aw.computeNextNonce() + finalTag := aw.aead.Seal(nil, nonce, nil, adata) + _, err = aw.writer.Write(finalTag) + if err != nil { + return err + } + return aw.writer.Close() +} + +// sealChunk Encrypts and authenticates the given chunk. +func (aw *aeadEncrypter) sealChunk(data []byte) ([]byte, error) { + if len(data) > aw.chunkSize { + return nil, errors.AEADError("chunk exceeds maximum length") + } + if aw.associatedData == nil { + return nil, errors.AEADError("can't seal without headers") + } + adata := aw.associatedData + if aw.aeadCrypter.packetTag == packetTypeAEADEncrypted { + adata = append(aw.associatedData, aw.chunkIndex...) + } + + nonce := aw.computeNextNonce() + encrypted := aw.aead.Seal(nil, nonce, data, adata) + aw.bytesProcessed += len(data) + if err := aw.aeadCrypter.incrementIndex(); err != nil { + return nil, err + } + return encrypted, nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go new file mode 100644 index 00000000..98bd876b --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go @@ -0,0 +1,96 @@ +// Copyright (C) 2019 ProtonTech AG + +package packet + +import ( + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" +) + +// AEADEncrypted represents an AEAD Encrypted Packet. +// See https://www.ietf.org/archive/id/draft-koch-openpgp-2015-rfc4880bis-00.html#name-aead-encrypted-data-packet-t +type AEADEncrypted struct { + cipher CipherFunction + mode AEADMode + chunkSizeByte byte + Contents io.Reader // Encrypted chunks and tags + initialNonce []byte // Referred to as IV in RFC4880-bis +} + +// Only currently defined version +const aeadEncryptedVersion = 1 + +func (ae *AEADEncrypted) parse(buf io.Reader) error { + headerData := make([]byte, 4) + if n, err := io.ReadFull(buf, headerData); n < 4 { + return errors.AEADError("could not read aead header:" + err.Error()) + } + // Read initial nonce + mode := AEADMode(headerData[2]) + nonceLen := mode.IvLength() + + // This packet supports only EAX and OCB + // https://www.ietf.org/archive/id/draft-koch-openpgp-2015-rfc4880bis-00.html#name-aead-encrypted-data-packet-t + if nonceLen == 0 || mode > AEADModeOCB { + return errors.AEADError("unknown mode") + } + + initialNonce := make([]byte, nonceLen) + if n, err := io.ReadFull(buf, initialNonce); n < nonceLen { + return errors.AEADError("could not read aead nonce:" + err.Error()) + } + ae.Contents = buf + ae.initialNonce = initialNonce + c := headerData[1] + if _, ok := algorithm.CipherById[c]; !ok { + return errors.UnsupportedError("unknown cipher: " + string(c)) + } + ae.cipher = CipherFunction(c) + ae.mode = mode + ae.chunkSizeByte = headerData[3] + return nil +} + +// Decrypt returns a io.ReadCloser from which decrypted bytes can be read, or +// an error. +func (ae *AEADEncrypted) Decrypt(ciph CipherFunction, key []byte) (io.ReadCloser, error) { + return ae.decrypt(key) +} + +// decrypt prepares an aeadCrypter and returns a ReadCloser from which +// decrypted bytes can be read (see aeadDecrypter.Read()). +func (ae *AEADEncrypted) decrypt(key []byte) (io.ReadCloser, error) { + blockCipher := ae.cipher.new(key) + aead := ae.mode.new(blockCipher) + // Carry the first tagLen bytes + tagLen := ae.mode.TagLength() + peekedBytes := make([]byte, tagLen) + n, err := io.ReadFull(ae.Contents, peekedBytes) + if n < tagLen || (err != nil && err != io.EOF) { + return nil, errors.AEADError("Not enough data to decrypt:" + err.Error()) + } + chunkSize := decodeAEADChunkSize(ae.chunkSizeByte) + return &aeadDecrypter{ + aeadCrypter: aeadCrypter{ + aead: aead, + chunkSize: chunkSize, + initialNonce: ae.initialNonce, + associatedData: ae.associatedData(), + chunkIndex: make([]byte, 8), + packetTag: packetTypeAEADEncrypted, + }, + reader: ae.Contents, + peekedBytes: peekedBytes}, nil +} + +// associatedData for chunks: tag, version, cipher, mode, chunk size byte +func (ae *AEADEncrypted) associatedData() []byte { + return []byte{ + 0xD4, + aeadEncryptedVersion, + byte(ae.cipher), + byte(ae.mode), + ae.chunkSizeByte} +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/compressed.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/compressed.go new file mode 100644 index 00000000..2f5cad71 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/compressed.go @@ -0,0 +1,125 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "compress/bzip2" + "compress/flate" + "compress/zlib" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "io" + "strconv" +) + +// Compressed represents a compressed OpenPGP packet. The decompressed contents +// will contain more OpenPGP packets. See RFC 4880, section 5.6. +type Compressed struct { + Body io.Reader +} + +const ( + NoCompression = flate.NoCompression + BestSpeed = flate.BestSpeed + BestCompression = flate.BestCompression + DefaultCompression = flate.DefaultCompression +) + +// CompressionConfig contains compressor configuration settings. +type CompressionConfig struct { + // Level is the compression level to use. It must be set to + // between -1 and 9, with -1 causing the compressor to use the + // default compression level, 0 causing the compressor to use + // no compression and 1 to 9 representing increasing (better, + // slower) compression levels. If Level is less than -1 or + // more then 9, a non-nil error will be returned during + // encryption. See the constants above for convenient common + // settings for Level. + Level int +} + +func (c *Compressed) parse(r io.Reader) error { + var buf [1]byte + _, err := readFull(r, buf[:]) + if err != nil { + return err + } + + switch buf[0] { + case 0: + c.Body = r + case 1: + c.Body = flate.NewReader(r) + case 2: + c.Body, err = zlib.NewReader(r) + case 3: + c.Body = bzip2.NewReader(r) + default: + err = errors.UnsupportedError("unknown compression algorithm: " + strconv.Itoa(int(buf[0]))) + } + + return err +} + +// compressedWriterCloser represents the serialized compression stream +// header and the compressor. Its Close() method ensures that both the +// compressor and serialized stream header are closed. Its Write() +// method writes to the compressor. +type compressedWriteCloser struct { + sh io.Closer // Stream Header + c io.WriteCloser // Compressor +} + +func (cwc compressedWriteCloser) Write(p []byte) (int, error) { + return cwc.c.Write(p) +} + +func (cwc compressedWriteCloser) Close() (err error) { + err = cwc.c.Close() + if err != nil { + return err + } + + return cwc.sh.Close() +} + +// SerializeCompressed serializes a compressed data packet to w and +// returns a WriteCloser to which the literal data packets themselves +// can be written and which MUST be closed on completion. If cc is +// nil, sensible defaults will be used to configure the compression +// algorithm. +func SerializeCompressed(w io.WriteCloser, algo CompressionAlgo, cc *CompressionConfig) (literaldata io.WriteCloser, err error) { + compressed, err := serializeStreamHeader(w, packetTypeCompressed) + if err != nil { + return + } + + _, err = compressed.Write([]byte{uint8(algo)}) + if err != nil { + return + } + + level := DefaultCompression + if cc != nil { + level = cc.Level + } + + var compressor io.WriteCloser + switch algo { + case CompressionZIP: + compressor, err = flate.NewWriter(compressed, level) + case CompressionZLIB: + compressor, err = zlib.NewWriterLevel(compressed, level) + default: + s := strconv.Itoa(int(algo)) + err = errors.UnsupportedError("Unsupported compression algorithm: " + s) + } + if err != nil { + return + } + + literaldata = compressedWriteCloser{compressed, compressor} + + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/config.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/config.go new file mode 100644 index 00000000..04994bec --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/config.go @@ -0,0 +1,248 @@ +// Copyright 2012 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto" + "crypto/rand" + "io" + "math/big" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/s2k" +) + +// Config collects a number of parameters along with sensible defaults. +// A nil *Config is valid and results in all default values. +type Config struct { + // Rand provides the source of entropy. + // If nil, the crypto/rand Reader is used. + Rand io.Reader + // DefaultHash is the default hash function to be used. + // If zero, SHA-256 is used. + DefaultHash crypto.Hash + // DefaultCipher is the cipher to be used. + // If zero, AES-128 is used. + DefaultCipher CipherFunction + // Time returns the current time as the number of seconds since the + // epoch. If Time is nil, time.Now is used. + Time func() time.Time + // DefaultCompressionAlgo is the compression algorithm to be + // applied to the plaintext before encryption. If zero, no + // compression is done. + DefaultCompressionAlgo CompressionAlgo + // CompressionConfig configures the compression settings. + CompressionConfig *CompressionConfig + // S2K (String to Key) config, used for key derivation in the context of secret key encryption + // and password-encrypted data. + // If nil, the default configuration is used + S2KConfig *s2k.Config + // Iteration count for Iterated S2K (String to Key). + // Only used if sk2.Mode is nil. + // This value is duplicated here from s2k.Config for backwards compatibility. + // It determines the strength of the passphrase stretching when + // the said passphrase is hashed to produce a key. S2KCount + // should be between 65536 and 65011712, inclusive. If Config + // is nil or S2KCount is 0, the value 16777216 used. Not all + // values in the above range can be represented. S2KCount will + // be rounded up to the next representable value if it cannot + // be encoded exactly. When set, it is strongly encrouraged to + // use a value that is at least 65536. See RFC 4880 Section + // 3.7.1.3. + // + // Deprecated: SK2Count should be configured in S2KConfig instead. + S2KCount int + // RSABits is the number of bits in new RSA keys made with NewEntity. + // If zero, then 2048 bit keys are created. + RSABits int + // The public key algorithm to use - will always create a signing primary + // key and encryption subkey. + Algorithm PublicKeyAlgorithm + // Some known primes that are optionally prepopulated by the caller + RSAPrimes []*big.Int + // Curve configures the desired packet.Curve if the Algorithm is PubKeyAlgoECDSA, + // PubKeyAlgoEdDSA, or PubKeyAlgoECDH. If empty Curve25519 is used. + Curve Curve + // AEADConfig configures the use of the new AEAD Encrypted Data Packet, + // defined in the draft of the next version of the OpenPGP specification. + // If a non-nil AEADConfig is passed, usage of this packet is enabled. By + // default, it is disabled. See the documentation of AEADConfig for more + // configuration options related to AEAD. + // **Note: using this option may break compatibility with other OpenPGP + // implementations, as well as future versions of this library.** + AEADConfig *AEADConfig + // V5Keys configures version 5 key generation. If false, this package still + // supports version 5 keys, but produces version 4 keys. + V5Keys bool + // "The validity period of the key. This is the number of seconds after + // the key creation time that the key expires. If this is not present + // or has a value of zero, the key never expires. This is found only on + // a self-signature."" + // https://tools.ietf.org/html/rfc4880#section-5.2.3.6 + KeyLifetimeSecs uint32 + // "The validity period of the signature. This is the number of seconds + // after the signature creation time that the signature expires. If + // this is not present or has a value of zero, it never expires." + // https://tools.ietf.org/html/rfc4880#section-5.2.3.10 + SigLifetimeSecs uint32 + // SigningKeyId is used to specify the signing key to use (by Key ID). + // By default, the signing key is selected automatically, preferring + // signing subkeys if available. + SigningKeyId uint64 + // SigningIdentity is used to specify a user ID (packet Signer's User ID, type 28) + // when producing a generic certification signature onto an existing user ID. + // The identity must be present in the signer Entity. + SigningIdentity string + // InsecureAllowUnauthenticatedMessages controls, whether it is tolerated to read + // encrypted messages without Modification Detection Code (MDC). + // MDC is mandated by the IETF OpenPGP Crypto Refresh draft and has long been implemented + // in most OpenPGP implementations. Messages without MDC are considered unnecessarily + // insecure and should be prevented whenever possible. + // In case one needs to deal with messages from very old OpenPGP implementations, there + // might be no other way than to tolerate the missing MDC. Setting this flag, allows this + // mode of operation. It should be considered a measure of last resort. + InsecureAllowUnauthenticatedMessages bool + // KnownNotations is a map of Notation Data names to bools, which controls + // the notation names that are allowed to be present in critical Notation Data + // signature subpackets. + KnownNotations map[string]bool + // SignatureNotations is a list of Notations to be added to any signatures. + SignatureNotations []*Notation +} + +func (c *Config) Random() io.Reader { + if c == nil || c.Rand == nil { + return rand.Reader + } + return c.Rand +} + +func (c *Config) Hash() crypto.Hash { + if c == nil || uint(c.DefaultHash) == 0 { + return crypto.SHA256 + } + return c.DefaultHash +} + +func (c *Config) Cipher() CipherFunction { + if c == nil || uint8(c.DefaultCipher) == 0 { + return CipherAES128 + } + return c.DefaultCipher +} + +func (c *Config) Now() time.Time { + if c == nil || c.Time == nil { + return time.Now().Truncate(time.Second) + } + return c.Time().Truncate(time.Second) +} + +// KeyLifetime returns the validity period of the key. +func (c *Config) KeyLifetime() uint32 { + if c == nil { + return 0 + } + return c.KeyLifetimeSecs +} + +// SigLifetime returns the validity period of the signature. +func (c *Config) SigLifetime() uint32 { + if c == nil { + return 0 + } + return c.SigLifetimeSecs +} + +func (c *Config) Compression() CompressionAlgo { + if c == nil { + return CompressionNone + } + return c.DefaultCompressionAlgo +} + +func (c *Config) RSAModulusBits() int { + if c == nil || c.RSABits == 0 { + return 2048 + } + return c.RSABits +} + +func (c *Config) PublicKeyAlgorithm() PublicKeyAlgorithm { + if c == nil || c.Algorithm == 0 { + return PubKeyAlgoRSA + } + return c.Algorithm +} + +func (c *Config) CurveName() Curve { + if c == nil || c.Curve == "" { + return Curve25519 + } + return c.Curve +} + +// Deprecated: The hash iterations should now be queried via the S2K() method. +func (c *Config) PasswordHashIterations() int { + if c == nil || c.S2KCount == 0 { + return 0 + } + return c.S2KCount +} + +func (c *Config) S2K() *s2k.Config { + if c == nil { + return nil + } + // for backwards compatibility + if c != nil && c.S2KCount > 0 && c.S2KConfig == nil { + return &s2k.Config{ + S2KCount: c.S2KCount, + } + } + return c.S2KConfig +} + +func (c *Config) AEAD() *AEADConfig { + if c == nil { + return nil + } + return c.AEADConfig +} + +func (c *Config) SigningKey() uint64 { + if c == nil { + return 0 + } + return c.SigningKeyId +} + +func (c *Config) SigningUserId() string { + if c == nil { + return "" + } + return c.SigningIdentity +} + +func (c *Config) AllowUnauthenticatedMessages() bool { + if c == nil { + return false + } + return c.InsecureAllowUnauthenticatedMessages +} + +func (c *Config) KnownNotation(notationName string) bool { + if c == nil { + return false + } + return c.KnownNotations[notationName] +} + +func (c *Config) Notations() []*Notation { + if c == nil { + return nil + } + return c.SignatureNotations +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/encrypted_key.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/encrypted_key.go new file mode 100644 index 00000000..eeff2902 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/encrypted_key.go @@ -0,0 +1,286 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto" + "crypto/rsa" + "encoding/binary" + "io" + "math/big" + "strconv" + + "github.com/ProtonMail/go-crypto/openpgp/ecdh" + "github.com/ProtonMail/go-crypto/openpgp/elgamal" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/encoding" +) + +const encryptedKeyVersion = 3 + +// EncryptedKey represents a public-key encrypted session key. See RFC 4880, +// section 5.1. +type EncryptedKey struct { + KeyId uint64 + Algo PublicKeyAlgorithm + CipherFunc CipherFunction // only valid after a successful Decrypt for a v3 packet + Key []byte // only valid after a successful Decrypt + + encryptedMPI1, encryptedMPI2 encoding.Field +} + +func (e *EncryptedKey) parse(r io.Reader) (err error) { + var buf [10]byte + _, err = readFull(r, buf[:]) + if err != nil { + return + } + if buf[0] != encryptedKeyVersion { + return errors.UnsupportedError("unknown EncryptedKey version " + strconv.Itoa(int(buf[0]))) + } + e.KeyId = binary.BigEndian.Uint64(buf[1:9]) + e.Algo = PublicKeyAlgorithm(buf[9]) + switch e.Algo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly: + e.encryptedMPI1 = new(encoding.MPI) + if _, err = e.encryptedMPI1.ReadFrom(r); err != nil { + return + } + case PubKeyAlgoElGamal: + e.encryptedMPI1 = new(encoding.MPI) + if _, err = e.encryptedMPI1.ReadFrom(r); err != nil { + return + } + + e.encryptedMPI2 = new(encoding.MPI) + if _, err = e.encryptedMPI2.ReadFrom(r); err != nil { + return + } + case PubKeyAlgoECDH: + e.encryptedMPI1 = new(encoding.MPI) + if _, err = e.encryptedMPI1.ReadFrom(r); err != nil { + return + } + + e.encryptedMPI2 = new(encoding.OID) + if _, err = e.encryptedMPI2.ReadFrom(r); err != nil { + return + } + } + _, err = consumeAll(r) + return +} + +func checksumKeyMaterial(key []byte) uint16 { + var checksum uint16 + for _, v := range key { + checksum += uint16(v) + } + return checksum +} + +// Decrypt decrypts an encrypted session key with the given private key. The +// private key must have been decrypted first. +// If config is nil, sensible defaults will be used. +func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error { + if e.KeyId != 0 && e.KeyId != priv.KeyId { + return errors.InvalidArgumentError("cannot decrypt encrypted session key for key id " + strconv.FormatUint(e.KeyId, 16) + " with private key id " + strconv.FormatUint(priv.KeyId, 16)) + } + if e.Algo != priv.PubKeyAlgo { + return errors.InvalidArgumentError("cannot decrypt encrypted session key of type " + strconv.Itoa(int(e.Algo)) + " with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo))) + } + if priv.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + + var err error + var b []byte + + // TODO(agl): use session key decryption routines here to avoid + // padding oracle attacks. + switch priv.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly: + // Supports both *rsa.PrivateKey and crypto.Decrypter + k := priv.PrivateKey.(crypto.Decrypter) + b, err = k.Decrypt(config.Random(), padToKeySize(k.Public().(*rsa.PublicKey), e.encryptedMPI1.Bytes()), nil) + case PubKeyAlgoElGamal: + c1 := new(big.Int).SetBytes(e.encryptedMPI1.Bytes()) + c2 := new(big.Int).SetBytes(e.encryptedMPI2.Bytes()) + b, err = elgamal.Decrypt(priv.PrivateKey.(*elgamal.PrivateKey), c1, c2) + case PubKeyAlgoECDH: + vsG := e.encryptedMPI1.Bytes() + m := e.encryptedMPI2.Bytes() + oid := priv.PublicKey.oid.EncodedBytes() + b, err = ecdh.Decrypt(priv.PrivateKey.(*ecdh.PrivateKey), vsG, m, oid, priv.PublicKey.Fingerprint[:]) + default: + err = errors.InvalidArgumentError("cannot decrypt encrypted session key with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo))) + } + + if err != nil { + return err + } + + e.CipherFunc = CipherFunction(b[0]) + if !e.CipherFunc.IsSupported() { + return errors.UnsupportedError("unsupported encryption function") + } + + e.Key = b[1 : len(b)-2] + expectedChecksum := uint16(b[len(b)-2])<<8 | uint16(b[len(b)-1]) + checksum := checksumKeyMaterial(e.Key) + if checksum != expectedChecksum { + return errors.StructuralError("EncryptedKey checksum incorrect") + } + + return nil +} + +// Serialize writes the encrypted key packet, e, to w. +func (e *EncryptedKey) Serialize(w io.Writer) error { + var mpiLen int + switch e.Algo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly: + mpiLen = int(e.encryptedMPI1.EncodedLength()) + case PubKeyAlgoElGamal: + mpiLen = int(e.encryptedMPI1.EncodedLength()) + int(e.encryptedMPI2.EncodedLength()) + case PubKeyAlgoECDH: + mpiLen = int(e.encryptedMPI1.EncodedLength()) + int(e.encryptedMPI2.EncodedLength()) + default: + return errors.InvalidArgumentError("don't know how to serialize encrypted key type " + strconv.Itoa(int(e.Algo))) + } + + err := serializeHeader(w, packetTypeEncryptedKey, 1 /* version */ +8 /* key id */ +1 /* algo */ +mpiLen) + if err != nil { + return err + } + + w.Write([]byte{encryptedKeyVersion}) + binary.Write(w, binary.BigEndian, e.KeyId) + w.Write([]byte{byte(e.Algo)}) + + switch e.Algo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly: + _, err := w.Write(e.encryptedMPI1.EncodedBytes()) + return err + case PubKeyAlgoElGamal: + if _, err := w.Write(e.encryptedMPI1.EncodedBytes()); err != nil { + return err + } + _, err := w.Write(e.encryptedMPI2.EncodedBytes()) + return err + case PubKeyAlgoECDH: + if _, err := w.Write(e.encryptedMPI1.EncodedBytes()); err != nil { + return err + } + _, err := w.Write(e.encryptedMPI2.EncodedBytes()) + return err + default: + panic("internal error") + } +} + +// SerializeEncryptedKey serializes an encrypted key packet to w that contains +// key, encrypted to pub. +// If config is nil, sensible defaults will be used. +func SerializeEncryptedKey(w io.Writer, pub *PublicKey, cipherFunc CipherFunction, key []byte, config *Config) error { + var buf [10]byte + buf[0] = encryptedKeyVersion + binary.BigEndian.PutUint64(buf[1:9], pub.KeyId) + buf[9] = byte(pub.PubKeyAlgo) + + keyBlock := make([]byte, 1 /* cipher type */ +len(key)+2 /* checksum */) + keyBlock[0] = byte(cipherFunc) + copy(keyBlock[1:], key) + checksum := checksumKeyMaterial(key) + keyBlock[1+len(key)] = byte(checksum >> 8) + keyBlock[1+len(key)+1] = byte(checksum) + + switch pub.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly: + return serializeEncryptedKeyRSA(w, config.Random(), buf, pub.PublicKey.(*rsa.PublicKey), keyBlock) + case PubKeyAlgoElGamal: + return serializeEncryptedKeyElGamal(w, config.Random(), buf, pub.PublicKey.(*elgamal.PublicKey), keyBlock) + case PubKeyAlgoECDH: + return serializeEncryptedKeyECDH(w, config.Random(), buf, pub.PublicKey.(*ecdh.PublicKey), keyBlock, pub.oid, pub.Fingerprint) + case PubKeyAlgoDSA, PubKeyAlgoRSASignOnly: + return errors.InvalidArgumentError("cannot encrypt to public key of type " + strconv.Itoa(int(pub.PubKeyAlgo))) + } + + return errors.UnsupportedError("encrypting a key to public key of type " + strconv.Itoa(int(pub.PubKeyAlgo))) +} + +func serializeEncryptedKeyRSA(w io.Writer, rand io.Reader, header [10]byte, pub *rsa.PublicKey, keyBlock []byte) error { + cipherText, err := rsa.EncryptPKCS1v15(rand, pub, keyBlock) + if err != nil { + return errors.InvalidArgumentError("RSA encryption failed: " + err.Error()) + } + + cipherMPI := encoding.NewMPI(cipherText) + packetLen := 10 /* header length */ + int(cipherMPI.EncodedLength()) + + err = serializeHeader(w, packetTypeEncryptedKey, packetLen) + if err != nil { + return err + } + _, err = w.Write(header[:]) + if err != nil { + return err + } + _, err = w.Write(cipherMPI.EncodedBytes()) + return err +} + +func serializeEncryptedKeyElGamal(w io.Writer, rand io.Reader, header [10]byte, pub *elgamal.PublicKey, keyBlock []byte) error { + c1, c2, err := elgamal.Encrypt(rand, pub, keyBlock) + if err != nil { + return errors.InvalidArgumentError("ElGamal encryption failed: " + err.Error()) + } + + packetLen := 10 /* header length */ + packetLen += 2 /* mpi size */ + (c1.BitLen()+7)/8 + packetLen += 2 /* mpi size */ + (c2.BitLen()+7)/8 + + err = serializeHeader(w, packetTypeEncryptedKey, packetLen) + if err != nil { + return err + } + _, err = w.Write(header[:]) + if err != nil { + return err + } + if _, err = w.Write(new(encoding.MPI).SetBig(c1).EncodedBytes()); err != nil { + return err + } + _, err = w.Write(new(encoding.MPI).SetBig(c2).EncodedBytes()) + return err +} + +func serializeEncryptedKeyECDH(w io.Writer, rand io.Reader, header [10]byte, pub *ecdh.PublicKey, keyBlock []byte, oid encoding.Field, fingerprint []byte) error { + vsG, c, err := ecdh.Encrypt(rand, pub, keyBlock, oid.EncodedBytes(), fingerprint) + if err != nil { + return errors.InvalidArgumentError("ECDH encryption failed: " + err.Error()) + } + + g := encoding.NewMPI(vsG) + m := encoding.NewOID(c) + + packetLen := 10 /* header length */ + packetLen += int(g.EncodedLength()) + int(m.EncodedLength()) + + err = serializeHeader(w, packetTypeEncryptedKey, packetLen) + if err != nil { + return err + } + + _, err = w.Write(header[:]) + if err != nil { + return err + } + if _, err = w.Write(g.EncodedBytes()); err != nil { + return err + } + _, err = w.Write(m.EncodedBytes()) + return err +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/literal.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/literal.go new file mode 100644 index 00000000..4be98760 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/literal.go @@ -0,0 +1,91 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "encoding/binary" + "io" +) + +// LiteralData represents an encrypted file. See RFC 4880, section 5.9. +type LiteralData struct { + Format uint8 + IsBinary bool + FileName string + Time uint32 // Unix epoch time. Either creation time or modification time. 0 means undefined. + Body io.Reader +} + +// ForEyesOnly returns whether the contents of the LiteralData have been marked +// as especially sensitive. +func (l *LiteralData) ForEyesOnly() bool { + return l.FileName == "_CONSOLE" +} + +func (l *LiteralData) parse(r io.Reader) (err error) { + var buf [256]byte + + _, err = readFull(r, buf[:2]) + if err != nil { + return + } + + l.Format = buf[0] + l.IsBinary = l.Format == 'b' + fileNameLen := int(buf[1]) + + _, err = readFull(r, buf[:fileNameLen]) + if err != nil { + return + } + + l.FileName = string(buf[:fileNameLen]) + + _, err = readFull(r, buf[:4]) + if err != nil { + return + } + + l.Time = binary.BigEndian.Uint32(buf[:4]) + l.Body = r + return +} + +// SerializeLiteral serializes a literal data packet to w and returns a +// WriteCloser to which the data itself can be written and which MUST be closed +// on completion. The fileName is truncated to 255 bytes. +func SerializeLiteral(w io.WriteCloser, isBinary bool, fileName string, time uint32) (plaintext io.WriteCloser, err error) { + var buf [4]byte + buf[0] = 't' + if isBinary { + buf[0] = 'b' + } + if len(fileName) > 255 { + fileName = fileName[:255] + } + buf[1] = byte(len(fileName)) + + inner, err := serializeStreamHeader(w, packetTypeLiteralData) + if err != nil { + return + } + + _, err = inner.Write(buf[:2]) + if err != nil { + return + } + _, err = inner.Write([]byte(fileName)) + if err != nil { + return + } + binary.BigEndian.PutUint32(buf[:], time) + _, err = inner.Write(buf[:]) + if err != nil { + return + } + + plaintext = inner + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/notation.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/notation.go new file mode 100644 index 00000000..2c3e3f50 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/notation.go @@ -0,0 +1,29 @@ +package packet + +// Notation type represents a Notation Data subpacket +// see https://tools.ietf.org/html/rfc4880#section-5.2.3.16 +type Notation struct { + Name string + Value []byte + IsCritical bool + IsHumanReadable bool +} + +func (notation *Notation) getData() []byte { + nameData := []byte(notation.Name) + nameLen := len(nameData) + valueLen := len(notation.Value) + + data := make([]byte, 8+nameLen+valueLen) + if notation.IsHumanReadable { + data[0] = 0x80 + } + + data[4] = byte(nameLen >> 8) + data[5] = byte(nameLen) + data[6] = byte(valueLen >> 8) + data[7] = byte(valueLen) + copy(data[8:8+nameLen], nameData) + copy(data[8+nameLen:], notation.Value) + return data +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/ocfb.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/ocfb.go new file mode 100644 index 00000000..4f26d0a0 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/ocfb.go @@ -0,0 +1,137 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// OpenPGP CFB Mode. http://tools.ietf.org/html/rfc4880#section-13.9 + +package packet + +import ( + "crypto/cipher" +) + +type ocfbEncrypter struct { + b cipher.Block + fre []byte + outUsed int +} + +// An OCFBResyncOption determines if the "resynchronization step" of OCFB is +// performed. +type OCFBResyncOption bool + +const ( + OCFBResync OCFBResyncOption = true + OCFBNoResync OCFBResyncOption = false +) + +// NewOCFBEncrypter returns a cipher.Stream which encrypts data with OpenPGP's +// cipher feedback mode using the given cipher.Block, and an initial amount of +// ciphertext. randData must be random bytes and be the same length as the +// cipher.Block's block size. Resync determines if the "resynchronization step" +// from RFC 4880, 13.9 step 7 is performed. Different parts of OpenPGP vary on +// this point. +func NewOCFBEncrypter(block cipher.Block, randData []byte, resync OCFBResyncOption) (cipher.Stream, []byte) { + blockSize := block.BlockSize() + if len(randData) != blockSize { + return nil, nil + } + + x := &ocfbEncrypter{ + b: block, + fre: make([]byte, blockSize), + outUsed: 0, + } + prefix := make([]byte, blockSize+2) + + block.Encrypt(x.fre, x.fre) + for i := 0; i < blockSize; i++ { + prefix[i] = randData[i] ^ x.fre[i] + } + + block.Encrypt(x.fre, prefix[:blockSize]) + prefix[blockSize] = x.fre[0] ^ randData[blockSize-2] + prefix[blockSize+1] = x.fre[1] ^ randData[blockSize-1] + + if resync { + block.Encrypt(x.fre, prefix[2:]) + } else { + x.fre[0] = prefix[blockSize] + x.fre[1] = prefix[blockSize+1] + x.outUsed = 2 + } + return x, prefix +} + +func (x *ocfbEncrypter) XORKeyStream(dst, src []byte) { + for i := 0; i < len(src); i++ { + if x.outUsed == len(x.fre) { + x.b.Encrypt(x.fre, x.fre) + x.outUsed = 0 + } + + x.fre[x.outUsed] ^= src[i] + dst[i] = x.fre[x.outUsed] + x.outUsed++ + } +} + +type ocfbDecrypter struct { + b cipher.Block + fre []byte + outUsed int +} + +// NewOCFBDecrypter returns a cipher.Stream which decrypts data with OpenPGP's +// cipher feedback mode using the given cipher.Block. Prefix must be the first +// blockSize + 2 bytes of the ciphertext, where blockSize is the cipher.Block's +// block size. On successful exit, blockSize+2 bytes of decrypted data are written into +// prefix. Resync determines if the "resynchronization step" from RFC 4880, +// 13.9 step 7 is performed. Different parts of OpenPGP vary on this point. +func NewOCFBDecrypter(block cipher.Block, prefix []byte, resync OCFBResyncOption) cipher.Stream { + blockSize := block.BlockSize() + if len(prefix) != blockSize+2 { + return nil + } + + x := &ocfbDecrypter{ + b: block, + fre: make([]byte, blockSize), + outUsed: 0, + } + prefixCopy := make([]byte, len(prefix)) + copy(prefixCopy, prefix) + + block.Encrypt(x.fre, x.fre) + for i := 0; i < blockSize; i++ { + prefixCopy[i] ^= x.fre[i] + } + + block.Encrypt(x.fre, prefix[:blockSize]) + prefixCopy[blockSize] ^= x.fre[0] + prefixCopy[blockSize+1] ^= x.fre[1] + + if resync { + block.Encrypt(x.fre, prefix[2:]) + } else { + x.fre[0] = prefix[blockSize] + x.fre[1] = prefix[blockSize+1] + x.outUsed = 2 + } + copy(prefix, prefixCopy) + return x +} + +func (x *ocfbDecrypter) XORKeyStream(dst, src []byte) { + for i := 0; i < len(src); i++ { + if x.outUsed == len(x.fre) { + x.b.Encrypt(x.fre, x.fre) + x.outUsed = 0 + } + + c := src[i] + dst[i] = x.fre[x.outUsed] ^ src[i] + x.fre[x.outUsed] = c + x.outUsed++ + } +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/one_pass_signature.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/one_pass_signature.go new file mode 100644 index 00000000..033fb2d7 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/one_pass_signature.go @@ -0,0 +1,73 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto" + "encoding/binary" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "io" + "strconv" +) + +// OnePassSignature represents a one-pass signature packet. See RFC 4880, +// section 5.4. +type OnePassSignature struct { + SigType SignatureType + Hash crypto.Hash + PubKeyAlgo PublicKeyAlgorithm + KeyId uint64 + IsLast bool +} + +const onePassSignatureVersion = 3 + +func (ops *OnePassSignature) parse(r io.Reader) (err error) { + var buf [13]byte + + _, err = readFull(r, buf[:]) + if err != nil { + return + } + if buf[0] != onePassSignatureVersion { + err = errors.UnsupportedError("one-pass-signature packet version " + strconv.Itoa(int(buf[0]))) + } + + var ok bool + ops.Hash, ok = algorithm.HashIdToHashWithSha1(buf[2]) + if !ok { + return errors.UnsupportedError("hash function: " + strconv.Itoa(int(buf[2]))) + } + + ops.SigType = SignatureType(buf[1]) + ops.PubKeyAlgo = PublicKeyAlgorithm(buf[3]) + ops.KeyId = binary.BigEndian.Uint64(buf[4:12]) + ops.IsLast = buf[12] != 0 + return +} + +// Serialize marshals the given OnePassSignature to w. +func (ops *OnePassSignature) Serialize(w io.Writer) error { + var buf [13]byte + buf[0] = onePassSignatureVersion + buf[1] = uint8(ops.SigType) + var ok bool + buf[2], ok = algorithm.HashToHashIdWithSha1(ops.Hash) + if !ok { + return errors.UnsupportedError("hash type: " + strconv.Itoa(int(ops.Hash))) + } + buf[3] = uint8(ops.PubKeyAlgo) + binary.BigEndian.PutUint64(buf[4:12], ops.KeyId) + if ops.IsLast { + buf[12] = 1 + } + + if err := serializeHeader(w, packetTypeOnePassSignature, len(buf)); err != nil { + return err + } + _, err := w.Write(buf[:]) + return err +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/opaque.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/opaque.go new file mode 100644 index 00000000..4f820407 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/opaque.go @@ -0,0 +1,171 @@ +// Copyright 2012 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "bytes" + "io" + "io/ioutil" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// OpaquePacket represents an OpenPGP packet as raw, unparsed data. This is +// useful for splitting and storing the original packet contents separately, +// handling unsupported packet types or accessing parts of the packet not yet +// implemented by this package. +type OpaquePacket struct { + // Packet type + Tag uint8 + // Reason why the packet was parsed opaquely + Reason error + // Binary contents of the packet data + Contents []byte +} + +func (op *OpaquePacket) parse(r io.Reader) (err error) { + op.Contents, err = ioutil.ReadAll(r) + return +} + +// Serialize marshals the packet to a writer in its original form, including +// the packet header. +func (op *OpaquePacket) Serialize(w io.Writer) (err error) { + err = serializeHeader(w, packetType(op.Tag), len(op.Contents)) + if err == nil { + _, err = w.Write(op.Contents) + } + return +} + +// Parse attempts to parse the opaque contents into a structure supported by +// this package. If the packet is not known then the result will be another +// OpaquePacket. +func (op *OpaquePacket) Parse() (p Packet, err error) { + hdr := bytes.NewBuffer(nil) + err = serializeHeader(hdr, packetType(op.Tag), len(op.Contents)) + if err != nil { + op.Reason = err + return op, err + } + p, err = Read(io.MultiReader(hdr, bytes.NewBuffer(op.Contents))) + if err != nil { + op.Reason = err + p = op + } + return +} + +// OpaqueReader reads OpaquePackets from an io.Reader. +type OpaqueReader struct { + r io.Reader +} + +func NewOpaqueReader(r io.Reader) *OpaqueReader { + return &OpaqueReader{r: r} +} + +// Read the next OpaquePacket. +func (or *OpaqueReader) Next() (op *OpaquePacket, err error) { + tag, _, contents, err := readHeader(or.r) + if err != nil { + return + } + op = &OpaquePacket{Tag: uint8(tag), Reason: err} + err = op.parse(contents) + if err != nil { + consumeAll(contents) + } + return +} + +// OpaqueSubpacket represents an unparsed OpenPGP subpacket, +// as found in signature and user attribute packets. +type OpaqueSubpacket struct { + SubType uint8 + EncodedLength []byte // Store the original encoded length for signature verifications. + Contents []byte +} + +// OpaqueSubpackets extracts opaque, unparsed OpenPGP subpackets from +// their byte representation. +func OpaqueSubpackets(contents []byte) (result []*OpaqueSubpacket, err error) { + var ( + subHeaderLen int + subPacket *OpaqueSubpacket + ) + for len(contents) > 0 { + subHeaderLen, subPacket, err = nextSubpacket(contents) + if err != nil { + break + } + result = append(result, subPacket) + contents = contents[subHeaderLen+len(subPacket.Contents):] + } + return +} + +func nextSubpacket(contents []byte) (subHeaderLen int, subPacket *OpaqueSubpacket, err error) { + // RFC 4880, section 5.2.3.1 + var subLen uint32 + var encodedLength []byte + if len(contents) < 1 { + goto Truncated + } + subPacket = &OpaqueSubpacket{} + switch { + case contents[0] < 192: + subHeaderLen = 2 // 1 length byte, 1 subtype byte + if len(contents) < subHeaderLen { + goto Truncated + } + encodedLength = contents[0:1] + subLen = uint32(contents[0]) + contents = contents[1:] + case contents[0] < 255: + subHeaderLen = 3 // 2 length bytes, 1 subtype + if len(contents) < subHeaderLen { + goto Truncated + } + encodedLength = contents[0:2] + subLen = uint32(contents[0]-192)<<8 + uint32(contents[1]) + 192 + contents = contents[2:] + default: + subHeaderLen = 6 // 5 length bytes, 1 subtype + if len(contents) < subHeaderLen { + goto Truncated + } + encodedLength = contents[0:5] + subLen = uint32(contents[1])<<24 | + uint32(contents[2])<<16 | + uint32(contents[3])<<8 | + uint32(contents[4]) + contents = contents[5:] + + } + if subLen > uint32(len(contents)) || subLen == 0 { + goto Truncated + } + subPacket.SubType = contents[0] + subPacket.EncodedLength = encodedLength + subPacket.Contents = contents[1:subLen] + return +Truncated: + err = errors.StructuralError("subpacket truncated") + return +} + +func (osp *OpaqueSubpacket) Serialize(w io.Writer) (err error) { + buf := make([]byte, 6) + copy(buf, osp.EncodedLength) + n := len(osp.EncodedLength) + + buf[n] = osp.SubType + if _, err = w.Write(buf[:n+1]); err != nil { + return + } + _, err = w.Write(osp.Contents) + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/packet.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/packet.go new file mode 100644 index 00000000..4d86a7da --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/packet.go @@ -0,0 +1,551 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package packet implements parsing and serialization of OpenPGP packets, as +// specified in RFC 4880. +package packet // import "github.com/ProtonMail/go-crypto/openpgp/packet" + +import ( + "bytes" + "crypto/cipher" + "crypto/rsa" + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" +) + +// readFull is the same as io.ReadFull except that reading zero bytes returns +// ErrUnexpectedEOF rather than EOF. +func readFull(r io.Reader, buf []byte) (n int, err error) { + n, err = io.ReadFull(r, buf) + if err == io.EOF { + err = io.ErrUnexpectedEOF + } + return +} + +// readLength reads an OpenPGP length from r. See RFC 4880, section 4.2.2. +func readLength(r io.Reader) (length int64, isPartial bool, err error) { + var buf [4]byte + _, err = readFull(r, buf[:1]) + if err != nil { + return + } + switch { + case buf[0] < 192: + length = int64(buf[0]) + case buf[0] < 224: + length = int64(buf[0]-192) << 8 + _, err = readFull(r, buf[0:1]) + if err != nil { + return + } + length += int64(buf[0]) + 192 + case buf[0] < 255: + length = int64(1) << (buf[0] & 0x1f) + isPartial = true + default: + _, err = readFull(r, buf[0:4]) + if err != nil { + return + } + length = int64(buf[0])<<24 | + int64(buf[1])<<16 | + int64(buf[2])<<8 | + int64(buf[3]) + } + return +} + +// partialLengthReader wraps an io.Reader and handles OpenPGP partial lengths. +// The continuation lengths are parsed and removed from the stream and EOF is +// returned at the end of the packet. See RFC 4880, section 4.2.2.4. +type partialLengthReader struct { + r io.Reader + remaining int64 + isPartial bool +} + +func (r *partialLengthReader) Read(p []byte) (n int, err error) { + for r.remaining == 0 { + if !r.isPartial { + return 0, io.EOF + } + r.remaining, r.isPartial, err = readLength(r.r) + if err != nil { + return 0, err + } + } + + toRead := int64(len(p)) + if toRead > r.remaining { + toRead = r.remaining + } + + n, err = r.r.Read(p[:int(toRead)]) + r.remaining -= int64(n) + if n < int(toRead) && err == io.EOF { + err = io.ErrUnexpectedEOF + } + return +} + +// partialLengthWriter writes a stream of data using OpenPGP partial lengths. +// See RFC 4880, section 4.2.2.4. +type partialLengthWriter struct { + w io.WriteCloser + buf bytes.Buffer + lengthByte [1]byte +} + +func (w *partialLengthWriter) Write(p []byte) (n int, err error) { + bufLen := w.buf.Len() + if bufLen > 512 { + for power := uint(30); ; power-- { + l := 1 << power + if bufLen >= l { + w.lengthByte[0] = 224 + uint8(power) + _, err = w.w.Write(w.lengthByte[:]) + if err != nil { + return + } + var m int + m, err = w.w.Write(w.buf.Next(l)) + if err != nil { + return + } + if m != l { + return 0, io.ErrShortWrite + } + break + } + } + } + return w.buf.Write(p) +} + +func (w *partialLengthWriter) Close() (err error) { + len := w.buf.Len() + err = serializeLength(w.w, len) + if err != nil { + return err + } + _, err = w.buf.WriteTo(w.w) + if err != nil { + return err + } + return w.w.Close() +} + +// A spanReader is an io.LimitReader, but it returns ErrUnexpectedEOF if the +// underlying Reader returns EOF before the limit has been reached. +type spanReader struct { + r io.Reader + n int64 +} + +func (l *spanReader) Read(p []byte) (n int, err error) { + if l.n <= 0 { + return 0, io.EOF + } + if int64(len(p)) > l.n { + p = p[0:l.n] + } + n, err = l.r.Read(p) + l.n -= int64(n) + if l.n > 0 && err == io.EOF { + err = io.ErrUnexpectedEOF + } + return +} + +// readHeader parses a packet header and returns an io.Reader which will return +// the contents of the packet. See RFC 4880, section 4.2. +func readHeader(r io.Reader) (tag packetType, length int64, contents io.Reader, err error) { + var buf [4]byte + _, err = io.ReadFull(r, buf[:1]) + if err != nil { + return + } + if buf[0]&0x80 == 0 { + err = errors.StructuralError("tag byte does not have MSB set") + return + } + if buf[0]&0x40 == 0 { + // Old format packet + tag = packetType((buf[0] & 0x3f) >> 2) + lengthType := buf[0] & 3 + if lengthType == 3 { + length = -1 + contents = r + return + } + lengthBytes := 1 << lengthType + _, err = readFull(r, buf[0:lengthBytes]) + if err != nil { + return + } + for i := 0; i < lengthBytes; i++ { + length <<= 8 + length |= int64(buf[i]) + } + contents = &spanReader{r, length} + return + } + + // New format packet + tag = packetType(buf[0] & 0x3f) + length, isPartial, err := readLength(r) + if err != nil { + return + } + if isPartial { + contents = &partialLengthReader{ + remaining: length, + isPartial: true, + r: r, + } + length = -1 + } else { + contents = &spanReader{r, length} + } + return +} + +// serializeHeader writes an OpenPGP packet header to w. See RFC 4880, section +// 4.2. +func serializeHeader(w io.Writer, ptype packetType, length int) (err error) { + err = serializeType(w, ptype) + if err != nil { + return + } + return serializeLength(w, length) +} + +// serializeType writes an OpenPGP packet type to w. See RFC 4880, section +// 4.2. +func serializeType(w io.Writer, ptype packetType) (err error) { + var buf [1]byte + buf[0] = 0x80 | 0x40 | byte(ptype) + _, err = w.Write(buf[:]) + return +} + +// serializeLength writes an OpenPGP packet length to w. See RFC 4880, section +// 4.2.2. +func serializeLength(w io.Writer, length int) (err error) { + var buf [5]byte + var n int + + if length < 192 { + buf[0] = byte(length) + n = 1 + } else if length < 8384 { + length -= 192 + buf[0] = 192 + byte(length>>8) + buf[1] = byte(length) + n = 2 + } else { + buf[0] = 255 + buf[1] = byte(length >> 24) + buf[2] = byte(length >> 16) + buf[3] = byte(length >> 8) + buf[4] = byte(length) + n = 5 + } + + _, err = w.Write(buf[:n]) + return +} + +// serializeStreamHeader writes an OpenPGP packet header to w where the +// length of the packet is unknown. It returns a io.WriteCloser which can be +// used to write the contents of the packet. See RFC 4880, section 4.2. +func serializeStreamHeader(w io.WriteCloser, ptype packetType) (out io.WriteCloser, err error) { + err = serializeType(w, ptype) + if err != nil { + return + } + out = &partialLengthWriter{w: w} + return +} + +// Packet represents an OpenPGP packet. Users are expected to try casting +// instances of this interface to specific packet types. +type Packet interface { + parse(io.Reader) error +} + +// consumeAll reads from the given Reader until error, returning the number of +// bytes read. +func consumeAll(r io.Reader) (n int64, err error) { + var m int + var buf [1024]byte + + for { + m, err = r.Read(buf[:]) + n += int64(m) + if err == io.EOF { + err = nil + return + } + if err != nil { + return + } + } +} + +// packetType represents the numeric ids of the different OpenPGP packet types. See +// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-2 +type packetType uint8 + +const ( + packetTypeEncryptedKey packetType = 1 + packetTypeSignature packetType = 2 + packetTypeSymmetricKeyEncrypted packetType = 3 + packetTypeOnePassSignature packetType = 4 + packetTypePrivateKey packetType = 5 + packetTypePublicKey packetType = 6 + packetTypePrivateSubkey packetType = 7 + packetTypeCompressed packetType = 8 + packetTypeSymmetricallyEncrypted packetType = 9 + packetTypeLiteralData packetType = 11 + packetTypeUserId packetType = 13 + packetTypePublicSubkey packetType = 14 + packetTypeUserAttribute packetType = 17 + packetTypeSymmetricallyEncryptedIntegrityProtected packetType = 18 + packetTypeAEADEncrypted packetType = 20 +) + +// EncryptedDataPacket holds encrypted data. It is currently implemented by +// SymmetricallyEncrypted and AEADEncrypted. +type EncryptedDataPacket interface { + Decrypt(CipherFunction, []byte) (io.ReadCloser, error) +} + +// Read reads a single OpenPGP packet from the given io.Reader. If there is an +// error parsing a packet, the whole packet is consumed from the input. +func Read(r io.Reader) (p Packet, err error) { + tag, _, contents, err := readHeader(r) + if err != nil { + return + } + + switch tag { + case packetTypeEncryptedKey: + p = new(EncryptedKey) + case packetTypeSignature: + p = new(Signature) + case packetTypeSymmetricKeyEncrypted: + p = new(SymmetricKeyEncrypted) + case packetTypeOnePassSignature: + p = new(OnePassSignature) + case packetTypePrivateKey, packetTypePrivateSubkey: + pk := new(PrivateKey) + if tag == packetTypePrivateSubkey { + pk.IsSubkey = true + } + p = pk + case packetTypePublicKey, packetTypePublicSubkey: + isSubkey := tag == packetTypePublicSubkey + p = &PublicKey{IsSubkey: isSubkey} + case packetTypeCompressed: + p = new(Compressed) + case packetTypeSymmetricallyEncrypted: + p = new(SymmetricallyEncrypted) + case packetTypeLiteralData: + p = new(LiteralData) + case packetTypeUserId: + p = new(UserId) + case packetTypeUserAttribute: + p = new(UserAttribute) + case packetTypeSymmetricallyEncryptedIntegrityProtected: + se := new(SymmetricallyEncrypted) + se.IntegrityProtected = true + p = se + case packetTypeAEADEncrypted: + p = new(AEADEncrypted) + default: + err = errors.UnknownPacketTypeError(tag) + } + if p != nil { + err = p.parse(contents) + } + if err != nil { + consumeAll(contents) + } + return +} + +// SignatureType represents the different semantic meanings of an OpenPGP +// signature. See RFC 4880, section 5.2.1. +type SignatureType uint8 + +const ( + SigTypeBinary SignatureType = 0x00 + SigTypeText = 0x01 + SigTypeGenericCert = 0x10 + SigTypePersonaCert = 0x11 + SigTypeCasualCert = 0x12 + SigTypePositiveCert = 0x13 + SigTypeSubkeyBinding = 0x18 + SigTypePrimaryKeyBinding = 0x19 + SigTypeDirectSignature = 0x1F + SigTypeKeyRevocation = 0x20 + SigTypeSubkeyRevocation = 0x28 + SigTypeCertificationRevocation = 0x30 +) + +// PublicKeyAlgorithm represents the different public key system specified for +// OpenPGP. See +// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-12 +type PublicKeyAlgorithm uint8 + +const ( + PubKeyAlgoRSA PublicKeyAlgorithm = 1 + PubKeyAlgoElGamal PublicKeyAlgorithm = 16 + PubKeyAlgoDSA PublicKeyAlgorithm = 17 + // RFC 6637, Section 5. + PubKeyAlgoECDH PublicKeyAlgorithm = 18 + PubKeyAlgoECDSA PublicKeyAlgorithm = 19 + // https://www.ietf.org/archive/id/draft-koch-eddsa-for-openpgp-04.txt + PubKeyAlgoEdDSA PublicKeyAlgorithm = 22 + + // Deprecated in RFC 4880, Section 13.5. Use key flags instead. + PubKeyAlgoRSAEncryptOnly PublicKeyAlgorithm = 2 + PubKeyAlgoRSASignOnly PublicKeyAlgorithm = 3 +) + +// CanEncrypt returns true if it's possible to encrypt a message to a public +// key of the given type. +func (pka PublicKeyAlgorithm) CanEncrypt() bool { + switch pka { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoElGamal, PubKeyAlgoECDH: + return true + } + return false +} + +// CanSign returns true if it's possible for a public key of the given type to +// sign a message. +func (pka PublicKeyAlgorithm) CanSign() bool { + switch pka { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA: + return true + } + return false +} + +// CipherFunction represents the different block ciphers specified for OpenPGP. See +// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-13 +type CipherFunction algorithm.CipherFunction + +const ( + Cipher3DES CipherFunction = 2 + CipherCAST5 CipherFunction = 3 + CipherAES128 CipherFunction = 7 + CipherAES192 CipherFunction = 8 + CipherAES256 CipherFunction = 9 +) + +// KeySize returns the key size, in bytes, of cipher. +func (cipher CipherFunction) KeySize() int { + return algorithm.CipherFunction(cipher).KeySize() +} + +// IsSupported returns true if the cipher is supported from the library +func (cipher CipherFunction) IsSupported() bool { + return algorithm.CipherFunction(cipher).KeySize() > 0 +} + +// blockSize returns the block size, in bytes, of cipher. +func (cipher CipherFunction) blockSize() int { + return algorithm.CipherFunction(cipher).BlockSize() +} + +// new returns a fresh instance of the given cipher. +func (cipher CipherFunction) new(key []byte) (block cipher.Block) { + return algorithm.CipherFunction(cipher).New(key) +} + +// padToKeySize left-pads a MPI with zeroes to match the length of the +// specified RSA public. +func padToKeySize(pub *rsa.PublicKey, b []byte) []byte { + k := (pub.N.BitLen() + 7) / 8 + if len(b) >= k { + return b + } + bb := make([]byte, k) + copy(bb[len(bb)-len(b):], b) + return bb +} + +// CompressionAlgo Represents the different compression algorithms +// supported by OpenPGP (except for BZIP2, which is not currently +// supported). See Section 9.3 of RFC 4880. +type CompressionAlgo uint8 + +const ( + CompressionNone CompressionAlgo = 0 + CompressionZIP CompressionAlgo = 1 + CompressionZLIB CompressionAlgo = 2 +) + +// AEADMode represents the different Authenticated Encryption with Associated +// Data specified for OpenPGP. +// See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.6 +type AEADMode algorithm.AEADMode + +const ( + AEADModeEAX AEADMode = 1 + AEADModeOCB AEADMode = 2 + AEADModeGCM AEADMode = 3 +) + +func (mode AEADMode) IvLength() int { + return algorithm.AEADMode(mode).NonceLength() +} + +func (mode AEADMode) TagLength() int { + return algorithm.AEADMode(mode).TagLength() +} + +// new returns a fresh instance of the given mode. +func (mode AEADMode) new(block cipher.Block) cipher.AEAD { + return algorithm.AEADMode(mode).New(block) +} + +// ReasonForRevocation represents a revocation reason code as per RFC4880 +// section 5.2.3.23. +type ReasonForRevocation uint8 + +const ( + NoReason ReasonForRevocation = 0 + KeySuperseded ReasonForRevocation = 1 + KeyCompromised ReasonForRevocation = 2 + KeyRetired ReasonForRevocation = 3 +) + +// Curve is a mapping to supported ECC curves for key generation. +// See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-06.html#name-curve-specific-wire-formats +type Curve string + +const ( + Curve25519 Curve = "Curve25519" + Curve448 Curve = "Curve448" + CurveNistP256 Curve = "P256" + CurveNistP384 Curve = "P384" + CurveNistP521 Curve = "P521" + CurveSecP256k1 Curve = "SecP256k1" + CurveBrainpoolP256 Curve = "BrainpoolP256" + CurveBrainpoolP384 Curve = "BrainpoolP384" + CurveBrainpoolP512 Curve = "BrainpoolP512" +) + +// TrustLevel represents a trust level per RFC4880 5.2.3.13 +type TrustLevel uint8 + +// TrustAmount represents a trust amount per RFC4880 5.2.3.13 +type TrustAmount uint8 diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go new file mode 100644 index 00000000..2fc43864 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go @@ -0,0 +1,837 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "bytes" + "crypto" + "crypto/cipher" + "crypto/dsa" + "crypto/rand" + "crypto/rsa" + "crypto/sha1" + "io" + "io/ioutil" + "math/big" + "strconv" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/ecdh" + "github.com/ProtonMail/go-crypto/openpgp/ecdsa" + "github.com/ProtonMail/go-crypto/openpgp/eddsa" + "github.com/ProtonMail/go-crypto/openpgp/elgamal" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/encoding" + "github.com/ProtonMail/go-crypto/openpgp/s2k" +) + +// PrivateKey represents a possibly encrypted private key. See RFC 4880, +// section 5.5.3. +type PrivateKey struct { + PublicKey + Encrypted bool // if true then the private key is unavailable until Decrypt has been called. + encryptedData []byte + cipher CipherFunction + s2k func(out, in []byte) + // An *{rsa|dsa|elgamal|ecdh|ecdsa|ed25519}.PrivateKey or + // crypto.Signer/crypto.Decrypter (Decryptor RSA only). + PrivateKey interface{} + sha1Checksum bool + iv []byte + + // Type of encryption of the S2K packet + // Allowed values are 0 (Not encrypted), 254 (SHA1), or + // 255 (2-byte checksum) + s2kType S2KType + // Full parameters of the S2K packet + s2kParams *s2k.Params +} + +// S2KType s2k packet type +type S2KType uint8 + +const ( + // S2KNON unencrypt + S2KNON S2KType = 0 + // S2KSHA1 sha1 sum check + S2KSHA1 S2KType = 254 + // S2KCHECKSUM sum check + S2KCHECKSUM S2KType = 255 +) + +func NewRSAPrivateKey(creationTime time.Time, priv *rsa.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +func NewDSAPrivateKey(creationTime time.Time, priv *dsa.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewDSAPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +func NewElGamalPrivateKey(creationTime time.Time, priv *elgamal.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +func NewECDSAPrivateKey(creationTime time.Time, priv *ecdsa.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewECDSAPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +func NewEdDSAPrivateKey(creationTime time.Time, priv *eddsa.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewEdDSAPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +func NewECDHPrivateKey(creationTime time.Time, priv *ecdh.PrivateKey) *PrivateKey { + pk := new(PrivateKey) + pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey) + pk.PrivateKey = priv + return pk +} + +// NewSignerPrivateKey creates a PrivateKey from a crypto.Signer that +// implements RSA, ECDSA or EdDSA. +func NewSignerPrivateKey(creationTime time.Time, signer interface{}) *PrivateKey { + pk := new(PrivateKey) + // In general, the public Keys should be used as pointers. We still + // type-switch on the values, for backwards-compatibility. + switch pubkey := signer.(type) { + case *rsa.PrivateKey: + pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey) + case rsa.PrivateKey: + pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey) + case *ecdsa.PrivateKey: + pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey) + case ecdsa.PrivateKey: + pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey) + case *eddsa.PrivateKey: + pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey) + case eddsa.PrivateKey: + pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey) + default: + panic("openpgp: unknown signer type in NewSignerPrivateKey") + } + pk.PrivateKey = signer + return pk +} + +// NewDecrypterPrivateKey creates a PrivateKey from a *{rsa|elgamal|ecdh}.PrivateKey. +func NewDecrypterPrivateKey(creationTime time.Time, decrypter interface{}) *PrivateKey { + pk := new(PrivateKey) + switch priv := decrypter.(type) { + case *rsa.PrivateKey: + pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey) + case *elgamal.PrivateKey: + pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey) + case *ecdh.PrivateKey: + pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey) + default: + panic("openpgp: unknown decrypter type in NewDecrypterPrivateKey") + } + pk.PrivateKey = decrypter + return pk +} + +func (pk *PrivateKey) parse(r io.Reader) (err error) { + err = (&pk.PublicKey).parse(r) + if err != nil { + return + } + v5 := pk.PublicKey.Version == 5 + + var buf [1]byte + _, err = readFull(r, buf[:]) + if err != nil { + return + } + pk.s2kType = S2KType(buf[0]) + var optCount [1]byte + if v5 { + if _, err = readFull(r, optCount[:]); err != nil { + return + } + } + + switch pk.s2kType { + case S2KNON: + pk.s2k = nil + pk.Encrypted = false + case S2KSHA1, S2KCHECKSUM: + if v5 && pk.s2kType == S2KCHECKSUM { + return errors.StructuralError("wrong s2k identifier for version 5") + } + _, err = readFull(r, buf[:]) + if err != nil { + return + } + pk.cipher = CipherFunction(buf[0]) + if pk.cipher != 0 && !pk.cipher.IsSupported() { + return errors.UnsupportedError("unsupported cipher function in private key") + } + pk.s2kParams, err = s2k.ParseIntoParams(r) + if err != nil { + return + } + if pk.s2kParams.Dummy() { + return + } + pk.s2k, err = pk.s2kParams.Function() + if err != nil { + return + } + pk.Encrypted = true + if pk.s2kType == S2KSHA1 { + pk.sha1Checksum = true + } + default: + return errors.UnsupportedError("deprecated s2k function in private key") + } + + if pk.Encrypted { + blockSize := pk.cipher.blockSize() + if blockSize == 0 { + return errors.UnsupportedError("unsupported cipher in private key: " + strconv.Itoa(int(pk.cipher))) + } + pk.iv = make([]byte, blockSize) + _, err = readFull(r, pk.iv) + if err != nil { + return + } + } + + var privateKeyData []byte + if v5 { + var n [4]byte /* secret material four octet count */ + _, err = readFull(r, n[:]) + if err != nil { + return + } + count := uint32(uint32(n[0])<<24 | uint32(n[1])<<16 | uint32(n[2])<<8 | uint32(n[3])) + if !pk.Encrypted { + count = count + 2 /* two octet checksum */ + } + privateKeyData = make([]byte, count) + _, err = readFull(r, privateKeyData) + if err != nil { + return + } + } else { + privateKeyData, err = ioutil.ReadAll(r) + if err != nil { + return + } + } + if !pk.Encrypted { + if len(privateKeyData) < 2 { + return errors.StructuralError("truncated private key data") + } + var sum uint16 + for i := 0; i < len(privateKeyData)-2; i++ { + sum += uint16(privateKeyData[i]) + } + if privateKeyData[len(privateKeyData)-2] != uint8(sum>>8) || + privateKeyData[len(privateKeyData)-1] != uint8(sum) { + return errors.StructuralError("private key checksum failure") + } + privateKeyData = privateKeyData[:len(privateKeyData)-2] + return pk.parsePrivateKey(privateKeyData) + } + + pk.encryptedData = privateKeyData + return +} + +// Dummy returns true if the private key is a dummy key. This is a GNU extension. +func (pk *PrivateKey) Dummy() bool { + return pk.s2kParams.Dummy() +} + +func mod64kHash(d []byte) uint16 { + var h uint16 + for _, b := range d { + h += uint16(b) + } + return h +} + +func (pk *PrivateKey) Serialize(w io.Writer) (err error) { + contents := bytes.NewBuffer(nil) + err = pk.PublicKey.serializeWithoutHeaders(contents) + if err != nil { + return + } + if _, err = contents.Write([]byte{uint8(pk.s2kType)}); err != nil { + return + } + + optional := bytes.NewBuffer(nil) + if pk.Encrypted || pk.Dummy() { + optional.Write([]byte{uint8(pk.cipher)}) + if err := pk.s2kParams.Serialize(optional); err != nil { + return err + } + if pk.Encrypted { + optional.Write(pk.iv) + } + } + if pk.Version == 5 { + contents.Write([]byte{uint8(optional.Len())}) + } + io.Copy(contents, optional) + + if !pk.Dummy() { + l := 0 + var priv []byte + if !pk.Encrypted { + buf := bytes.NewBuffer(nil) + err = pk.serializePrivateKey(buf) + if err != nil { + return err + } + l = buf.Len() + checksum := mod64kHash(buf.Bytes()) + buf.Write([]byte{byte(checksum >> 8), byte(checksum)}) + priv = buf.Bytes() + } else { + priv, l = pk.encryptedData, len(pk.encryptedData) + } + + if pk.Version == 5 { + contents.Write([]byte{byte(l >> 24), byte(l >> 16), byte(l >> 8), byte(l)}) + } + contents.Write(priv) + } + + ptype := packetTypePrivateKey + if pk.IsSubkey { + ptype = packetTypePrivateSubkey + } + err = serializeHeader(w, ptype, contents.Len()) + if err != nil { + return + } + _, err = io.Copy(w, contents) + if err != nil { + return + } + return +} + +func serializeRSAPrivateKey(w io.Writer, priv *rsa.PrivateKey) error { + if _, err := w.Write(new(encoding.MPI).SetBig(priv.D).EncodedBytes()); err != nil { + return err + } + if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[1]).EncodedBytes()); err != nil { + return err + } + if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[0]).EncodedBytes()); err != nil { + return err + } + _, err := w.Write(new(encoding.MPI).SetBig(priv.Precomputed.Qinv).EncodedBytes()) + return err +} + +func serializeDSAPrivateKey(w io.Writer, priv *dsa.PrivateKey) error { + _, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes()) + return err +} + +func serializeElGamalPrivateKey(w io.Writer, priv *elgamal.PrivateKey) error { + _, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes()) + return err +} + +func serializeECDSAPrivateKey(w io.Writer, priv *ecdsa.PrivateKey) error { + _, err := w.Write(encoding.NewMPI(priv.MarshalIntegerSecret()).EncodedBytes()) + return err +} + +func serializeEdDSAPrivateKey(w io.Writer, priv *eddsa.PrivateKey) error { + _, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes()) + return err +} + +func serializeECDHPrivateKey(w io.Writer, priv *ecdh.PrivateKey) error { + _, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes()) + return err +} + +// decrypt decrypts an encrypted private key using a decryption key. +func (pk *PrivateKey) decrypt(decryptionKey []byte) error { + if pk.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + if !pk.Encrypted { + return nil + } + + block := pk.cipher.new(decryptionKey) + cfb := cipher.NewCFBDecrypter(block, pk.iv) + + data := make([]byte, len(pk.encryptedData)) + cfb.XORKeyStream(data, pk.encryptedData) + + if pk.sha1Checksum { + if len(data) < sha1.Size { + return errors.StructuralError("truncated private key data") + } + h := sha1.New() + h.Write(data[:len(data)-sha1.Size]) + sum := h.Sum(nil) + if !bytes.Equal(sum, data[len(data)-sha1.Size:]) { + return errors.StructuralError("private key checksum failure") + } + data = data[:len(data)-sha1.Size] + } else { + if len(data) < 2 { + return errors.StructuralError("truncated private key data") + } + var sum uint16 + for i := 0; i < len(data)-2; i++ { + sum += uint16(data[i]) + } + if data[len(data)-2] != uint8(sum>>8) || + data[len(data)-1] != uint8(sum) { + return errors.StructuralError("private key checksum failure") + } + data = data[:len(data)-2] + } + + err := pk.parsePrivateKey(data) + if _, ok := err.(errors.KeyInvalidError); ok { + return errors.KeyInvalidError("invalid key parameters") + } + if err != nil { + return err + } + + // Mark key as unencrypted + pk.s2kType = S2KNON + pk.s2k = nil + pk.Encrypted = false + pk.encryptedData = nil + + return nil +} + +func (pk *PrivateKey) decryptWithCache(passphrase []byte, keyCache *s2k.Cache) error { + if pk.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + if !pk.Encrypted { + return nil + } + + key, err := keyCache.GetOrComputeDerivedKey(passphrase, pk.s2kParams, pk.cipher.KeySize()) + if err != nil { + return err + } + return pk.decrypt(key) +} + +// Decrypt decrypts an encrypted private key using a passphrase. +func (pk *PrivateKey) Decrypt(passphrase []byte) error { + if pk.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + if !pk.Encrypted { + return nil + } + + key := make([]byte, pk.cipher.KeySize()) + pk.s2k(key, passphrase) + return pk.decrypt(key) +} + +// DecryptPrivateKeys decrypts all encrypted keys with the given config and passphrase. +// Avoids recomputation of similar s2k key derivations. +func DecryptPrivateKeys(keys []*PrivateKey, passphrase []byte) error { + // Create a cache to avoid recomputation of key derviations for the same passphrase. + s2kCache := &s2k.Cache{} + for _, key := range keys { + if key != nil && !key.Dummy() && key.Encrypted { + err := key.decryptWithCache(passphrase, s2kCache) + if err != nil { + return err + } + } + } + return nil +} + +// encrypt encrypts an unencrypted private key. +func (pk *PrivateKey) encrypt(key []byte, params *s2k.Params, cipherFunction CipherFunction) error { + if pk.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + if pk.Encrypted { + return nil + } + // check if encryptionKey has the correct size + if len(key) != cipherFunction.KeySize() { + return errors.InvalidArgumentError("supplied encryption key has the wrong size") + } + + priv := bytes.NewBuffer(nil) + err := pk.serializePrivateKey(priv) + if err != nil { + return err + } + + pk.cipher = cipherFunction + pk.s2kParams = params + pk.s2k, err = pk.s2kParams.Function() + if err != nil { + return err + } + + privateKeyBytes := priv.Bytes() + pk.sha1Checksum = true + block := pk.cipher.new(key) + pk.iv = make([]byte, pk.cipher.blockSize()) + _, err = rand.Read(pk.iv) + if err != nil { + return err + } + cfb := cipher.NewCFBEncrypter(block, pk.iv) + + if pk.sha1Checksum { + pk.s2kType = S2KSHA1 + h := sha1.New() + h.Write(privateKeyBytes) + sum := h.Sum(nil) + privateKeyBytes = append(privateKeyBytes, sum...) + } else { + pk.s2kType = S2KCHECKSUM + var sum uint16 + for _, b := range privateKeyBytes { + sum += uint16(b) + } + priv.Write([]byte{uint8(sum >> 8), uint8(sum)}) + } + + pk.encryptedData = make([]byte, len(privateKeyBytes)) + cfb.XORKeyStream(pk.encryptedData, privateKeyBytes) + pk.Encrypted = true + pk.PrivateKey = nil + return err +} + +// EncryptWithConfig encrypts an unencrypted private key using the passphrase and the config. +func (pk *PrivateKey) EncryptWithConfig(passphrase []byte, config *Config) error { + params, err := s2k.Generate(config.Random(), config.S2K()) + if err != nil { + return err + } + // Derive an encryption key with the configured s2k function. + key := make([]byte, config.Cipher().KeySize()) + s2k, err := params.Function() + if err != nil { + return err + } + s2k(key, passphrase) + // Encrypt the private key with the derived encryption key. + return pk.encrypt(key, params, config.Cipher()) +} + +// EncryptPrivateKeys encrypts all unencrypted keys with the given config and passphrase. +// Only derives one key from the passphrase, which is then used to encrypt each key. +func EncryptPrivateKeys(keys []*PrivateKey, passphrase []byte, config *Config) error { + params, err := s2k.Generate(config.Random(), config.S2K()) + if err != nil { + return err + } + // Derive an encryption key with the configured s2k function. + encryptionKey := make([]byte, config.Cipher().KeySize()) + s2k, err := params.Function() + if err != nil { + return err + } + s2k(encryptionKey, passphrase) + for _, key := range keys { + if key != nil && !key.Dummy() && !key.Encrypted { + err = key.encrypt(encryptionKey, params, config.Cipher()) + if err != nil { + return err + } + } + } + return nil +} + +// Encrypt encrypts an unencrypted private key using a passphrase. +func (pk *PrivateKey) Encrypt(passphrase []byte) error { + // Default config of private key encryption + config := &Config{ + S2KConfig: &s2k.Config{ + S2KMode: s2k.IteratedSaltedS2K, + S2KCount: 65536, + Hash: crypto.SHA256, + } , + DefaultCipher: CipherAES256, + } + return pk.EncryptWithConfig(passphrase, config) +} + +func (pk *PrivateKey) serializePrivateKey(w io.Writer) (err error) { + switch priv := pk.PrivateKey.(type) { + case *rsa.PrivateKey: + err = serializeRSAPrivateKey(w, priv) + case *dsa.PrivateKey: + err = serializeDSAPrivateKey(w, priv) + case *elgamal.PrivateKey: + err = serializeElGamalPrivateKey(w, priv) + case *ecdsa.PrivateKey: + err = serializeECDSAPrivateKey(w, priv) + case *eddsa.PrivateKey: + err = serializeEdDSAPrivateKey(w, priv) + case *ecdh.PrivateKey: + err = serializeECDHPrivateKey(w, priv) + default: + err = errors.InvalidArgumentError("unknown private key type") + } + return +} + +func (pk *PrivateKey) parsePrivateKey(data []byte) (err error) { + switch pk.PublicKey.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoRSAEncryptOnly: + return pk.parseRSAPrivateKey(data) + case PubKeyAlgoDSA: + return pk.parseDSAPrivateKey(data) + case PubKeyAlgoElGamal: + return pk.parseElGamalPrivateKey(data) + case PubKeyAlgoECDSA: + return pk.parseECDSAPrivateKey(data) + case PubKeyAlgoECDH: + return pk.parseECDHPrivateKey(data) + case PubKeyAlgoEdDSA: + return pk.parseEdDSAPrivateKey(data) + } + panic("impossible") +} + +func (pk *PrivateKey) parseRSAPrivateKey(data []byte) (err error) { + rsaPub := pk.PublicKey.PublicKey.(*rsa.PublicKey) + rsaPriv := new(rsa.PrivateKey) + rsaPriv.PublicKey = *rsaPub + + buf := bytes.NewBuffer(data) + d := new(encoding.MPI) + if _, err := d.ReadFrom(buf); err != nil { + return err + } + + p := new(encoding.MPI) + if _, err := p.ReadFrom(buf); err != nil { + return err + } + + q := new(encoding.MPI) + if _, err := q.ReadFrom(buf); err != nil { + return err + } + + rsaPriv.D = new(big.Int).SetBytes(d.Bytes()) + rsaPriv.Primes = make([]*big.Int, 2) + rsaPriv.Primes[0] = new(big.Int).SetBytes(p.Bytes()) + rsaPriv.Primes[1] = new(big.Int).SetBytes(q.Bytes()) + if err := rsaPriv.Validate(); err != nil { + return errors.KeyInvalidError(err.Error()) + } + rsaPriv.Precompute() + pk.PrivateKey = rsaPriv + + return nil +} + +func (pk *PrivateKey) parseDSAPrivateKey(data []byte) (err error) { + dsaPub := pk.PublicKey.PublicKey.(*dsa.PublicKey) + dsaPriv := new(dsa.PrivateKey) + dsaPriv.PublicKey = *dsaPub + + buf := bytes.NewBuffer(data) + x := new(encoding.MPI) + if _, err := x.ReadFrom(buf); err != nil { + return err + } + + dsaPriv.X = new(big.Int).SetBytes(x.Bytes()) + if err := validateDSAParameters(dsaPriv); err != nil { + return err + } + pk.PrivateKey = dsaPriv + + return nil +} + +func (pk *PrivateKey) parseElGamalPrivateKey(data []byte) (err error) { + pub := pk.PublicKey.PublicKey.(*elgamal.PublicKey) + priv := new(elgamal.PrivateKey) + priv.PublicKey = *pub + + buf := bytes.NewBuffer(data) + x := new(encoding.MPI) + if _, err := x.ReadFrom(buf); err != nil { + return err + } + + priv.X = new(big.Int).SetBytes(x.Bytes()) + if err := validateElGamalParameters(priv); err != nil { + return err + } + pk.PrivateKey = priv + + return nil +} + +func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) { + ecdsaPub := pk.PublicKey.PublicKey.(*ecdsa.PublicKey) + ecdsaPriv := ecdsa.NewPrivateKey(*ecdsaPub) + + buf := bytes.NewBuffer(data) + d := new(encoding.MPI) + if _, err := d.ReadFrom(buf); err != nil { + return err + } + + if err := ecdsaPriv.UnmarshalIntegerSecret(d.Bytes()); err != nil { + return err + } + if err := ecdsa.Validate(ecdsaPriv); err != nil { + return err + } + pk.PrivateKey = ecdsaPriv + + return nil +} + +func (pk *PrivateKey) parseECDHPrivateKey(data []byte) (err error) { + ecdhPub := pk.PublicKey.PublicKey.(*ecdh.PublicKey) + ecdhPriv := ecdh.NewPrivateKey(*ecdhPub) + + buf := bytes.NewBuffer(data) + d := new(encoding.MPI) + if _, err := d.ReadFrom(buf); err != nil { + return err + } + + if err := ecdhPriv.UnmarshalByteSecret(d.Bytes()); err != nil { + return err + } + + if err := ecdh.Validate(ecdhPriv); err != nil { + return err + } + + pk.PrivateKey = ecdhPriv + + return nil +} + +func (pk *PrivateKey) parseEdDSAPrivateKey(data []byte) (err error) { + eddsaPub := pk.PublicKey.PublicKey.(*eddsa.PublicKey) + eddsaPriv := eddsa.NewPrivateKey(*eddsaPub) + eddsaPriv.PublicKey = *eddsaPub + + buf := bytes.NewBuffer(data) + d := new(encoding.MPI) + if _, err := d.ReadFrom(buf); err != nil { + return err + } + + if err = eddsaPriv.UnmarshalByteSecret(d.Bytes()); err != nil { + return err + } + + if err := eddsa.Validate(eddsaPriv); err != nil { + return err + } + + pk.PrivateKey = eddsaPriv + + return nil +} + +func validateDSAParameters(priv *dsa.PrivateKey) error { + p := priv.P // group prime + q := priv.Q // subgroup order + g := priv.G // g has order q mod p + x := priv.X // secret + y := priv.Y // y == g**x mod p + one := big.NewInt(1) + // expect g, y >= 2 and g < p + if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 { + return errors.KeyInvalidError("dsa: invalid group") + } + // expect p > q + if p.Cmp(q) <= 0 { + return errors.KeyInvalidError("dsa: invalid group prime") + } + // q should be large enough and divide p-1 + pSub1 := new(big.Int).Sub(p, one) + if q.BitLen() < 150 || new(big.Int).Mod(pSub1, q).Cmp(big.NewInt(0)) != 0 { + return errors.KeyInvalidError("dsa: invalid order") + } + // confirm that g has order q mod p + if !q.ProbablyPrime(32) || new(big.Int).Exp(g, q, p).Cmp(one) != 0 { + return errors.KeyInvalidError("dsa: invalid order") + } + // check y + if new(big.Int).Exp(g, x, p).Cmp(y) != 0 { + return errors.KeyInvalidError("dsa: mismatching values") + } + + return nil +} + +func validateElGamalParameters(priv *elgamal.PrivateKey) error { + p := priv.P // group prime + g := priv.G // g has order p-1 mod p + x := priv.X // secret + y := priv.Y // y == g**x mod p + one := big.NewInt(1) + // Expect g, y >= 2 and g < p + if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 { + return errors.KeyInvalidError("elgamal: invalid group") + } + if p.BitLen() < 1024 { + return errors.KeyInvalidError("elgamal: group order too small") + } + pSub1 := new(big.Int).Sub(p, one) + if new(big.Int).Exp(g, pSub1, p).Cmp(one) != 0 { + return errors.KeyInvalidError("elgamal: invalid group") + } + // Since p-1 is not prime, g might have a smaller order that divides p-1. + // We cannot confirm the exact order of g, but we make sure it is not too small. + gExpI := new(big.Int).Set(g) + i := 1 + threshold := 2 << 17 // we want order > threshold + for i < threshold { + i++ // we check every order to make sure key validation is not easily bypassed by guessing y' + gExpI.Mod(new(big.Int).Mul(gExpI, g), p) + if gExpI.Cmp(one) == 0 { + return errors.KeyInvalidError("elgamal: order too small") + } + } + // Check y + if new(big.Int).Exp(g, x, p).Cmp(y) != 0 { + return errors.KeyInvalidError("elgamal: mismatching values") + } + + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go new file mode 100644 index 00000000..029b8f1a --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go @@ -0,0 +1,12 @@ +package packet + +// Generated with `gpg --export-secret-keys "Test Key 2"` +const privKeyRSAHex = "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" + +// Generated by `gpg --export-secret-keys` followed by a manual extraction of +// the ElGamal subkey from the packets. +const privKeyElGamalHex = "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" + +// pkcs1PrivKeyHex is a PKCS#1, RSA private key. +// Generated by `openssl genrsa 1024 | openssl rsa -outform DER | xxd -p` +const pkcs1PrivKeyHex = "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" diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go new file mode 100644 index 00000000..3402b8c1 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go @@ -0,0 +1,806 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto" + "crypto/dsa" + "crypto/rsa" + "crypto/sha1" + "crypto/sha256" + _ "crypto/sha512" + "encoding/binary" + "fmt" + "hash" + "io" + "math/big" + "strconv" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/ecdh" + "github.com/ProtonMail/go-crypto/openpgp/ecdsa" + "github.com/ProtonMail/go-crypto/openpgp/eddsa" + "github.com/ProtonMail/go-crypto/openpgp/elgamal" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/internal/ecc" + "github.com/ProtonMail/go-crypto/openpgp/internal/encoding" +) + +type kdfHashFunction byte +type kdfAlgorithm byte + +// PublicKey represents an OpenPGP public key. See RFC 4880, section 5.5.2. +type PublicKey struct { + Version int + CreationTime time.Time + PubKeyAlgo PublicKeyAlgorithm + PublicKey interface{} // *rsa.PublicKey, *dsa.PublicKey, *ecdsa.PublicKey or *eddsa.PublicKey + Fingerprint []byte + KeyId uint64 + IsSubkey bool + + // RFC 4880 fields + n, e, p, q, g, y encoding.Field + + // RFC 6637 fields + // oid contains the OID byte sequence identifying the elliptic curve used + oid encoding.Field + + // kdf stores key derivation function parameters + // used for ECDH encryption. See RFC 6637, Section 9. + kdf encoding.Field +} + +// UpgradeToV5 updates the version of the key to v5, and updates all necessary +// fields. +func (pk *PublicKey) UpgradeToV5() { + pk.Version = 5 + pk.setFingerprintAndKeyId() +} + +// signingKey provides a convenient abstraction over signature verification +// for v3 and v4 public keys. +type signingKey interface { + SerializeForHash(io.Writer) error + SerializeSignaturePrefix(io.Writer) + serializeWithoutHeaders(io.Writer) error +} + +// NewRSAPublicKey returns a PublicKey that wraps the given rsa.PublicKey. +func NewRSAPublicKey(creationTime time.Time, pub *rsa.PublicKey) *PublicKey { + pk := &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoRSA, + PublicKey: pub, + n: new(encoding.MPI).SetBig(pub.N), + e: new(encoding.MPI).SetBig(big.NewInt(int64(pub.E))), + } + + pk.setFingerprintAndKeyId() + return pk +} + +// NewDSAPublicKey returns a PublicKey that wraps the given dsa.PublicKey. +func NewDSAPublicKey(creationTime time.Time, pub *dsa.PublicKey) *PublicKey { + pk := &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoDSA, + PublicKey: pub, + p: new(encoding.MPI).SetBig(pub.P), + q: new(encoding.MPI).SetBig(pub.Q), + g: new(encoding.MPI).SetBig(pub.G), + y: new(encoding.MPI).SetBig(pub.Y), + } + + pk.setFingerprintAndKeyId() + return pk +} + +// NewElGamalPublicKey returns a PublicKey that wraps the given elgamal.PublicKey. +func NewElGamalPublicKey(creationTime time.Time, pub *elgamal.PublicKey) *PublicKey { + pk := &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoElGamal, + PublicKey: pub, + p: new(encoding.MPI).SetBig(pub.P), + g: new(encoding.MPI).SetBig(pub.G), + y: new(encoding.MPI).SetBig(pub.Y), + } + + pk.setFingerprintAndKeyId() + return pk +} + +func NewECDSAPublicKey(creationTime time.Time, pub *ecdsa.PublicKey) *PublicKey { + pk := &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoECDSA, + PublicKey: pub, + p: encoding.NewMPI(pub.MarshalPoint()), + } + + curveInfo := ecc.FindByCurve(pub.GetCurve()) + if curveInfo == nil { + panic("unknown elliptic curve") + } + pk.oid = curveInfo.Oid + pk.setFingerprintAndKeyId() + return pk +} + +func NewECDHPublicKey(creationTime time.Time, pub *ecdh.PublicKey) *PublicKey { + var pk *PublicKey + var kdf = encoding.NewOID([]byte{0x1, pub.Hash.Id(), pub.Cipher.Id()}) + pk = &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoECDH, + PublicKey: pub, + p: encoding.NewMPI(pub.MarshalPoint()), + kdf: kdf, + } + + curveInfo := ecc.FindByCurve(pub.GetCurve()) + + if curveInfo == nil { + panic("unknown elliptic curve") + } + + pk.oid = curveInfo.Oid + pk.setFingerprintAndKeyId() + return pk +} + +func NewEdDSAPublicKey(creationTime time.Time, pub *eddsa.PublicKey) *PublicKey { + curveInfo := ecc.FindByCurve(pub.GetCurve()) + pk := &PublicKey{ + Version: 4, + CreationTime: creationTime, + PubKeyAlgo: PubKeyAlgoEdDSA, + PublicKey: pub, + oid: curveInfo.Oid, + // Native point format, see draft-koch-eddsa-for-openpgp-04, Appendix B + p: encoding.NewMPI(pub.MarshalPoint()), + } + + pk.setFingerprintAndKeyId() + return pk +} + +func (pk *PublicKey) parse(r io.Reader) (err error) { + // RFC 4880, section 5.5.2 + var buf [6]byte + _, err = readFull(r, buf[:]) + if err != nil { + return + } + if buf[0] != 4 && buf[0] != 5 { + return errors.UnsupportedError("public key version " + strconv.Itoa(int(buf[0]))) + } + + pk.Version = int(buf[0]) + if pk.Version == 5 { + var n [4]byte + _, err = readFull(r, n[:]) + if err != nil { + return + } + } + pk.CreationTime = time.Unix(int64(uint32(buf[1])<<24|uint32(buf[2])<<16|uint32(buf[3])<<8|uint32(buf[4])), 0) + pk.PubKeyAlgo = PublicKeyAlgorithm(buf[5]) + switch pk.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly: + err = pk.parseRSA(r) + case PubKeyAlgoDSA: + err = pk.parseDSA(r) + case PubKeyAlgoElGamal: + err = pk.parseElGamal(r) + case PubKeyAlgoECDSA: + err = pk.parseECDSA(r) + case PubKeyAlgoECDH: + err = pk.parseECDH(r) + case PubKeyAlgoEdDSA: + err = pk.parseEdDSA(r) + default: + err = errors.UnsupportedError("public key type: " + strconv.Itoa(int(pk.PubKeyAlgo))) + } + if err != nil { + return + } + + pk.setFingerprintAndKeyId() + return +} + +func (pk *PublicKey) setFingerprintAndKeyId() { + // RFC 4880, section 12.2 + if pk.Version == 5 { + fingerprint := sha256.New() + pk.SerializeForHash(fingerprint) + pk.Fingerprint = make([]byte, 32) + copy(pk.Fingerprint, fingerprint.Sum(nil)) + pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[:8]) + } else { + fingerprint := sha1.New() + pk.SerializeForHash(fingerprint) + pk.Fingerprint = make([]byte, 20) + copy(pk.Fingerprint, fingerprint.Sum(nil)) + pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[12:20]) + } +} + +// parseRSA parses RSA public key material from the given Reader. See RFC 4880, +// section 5.5.2. +func (pk *PublicKey) parseRSA(r io.Reader) (err error) { + pk.n = new(encoding.MPI) + if _, err = pk.n.ReadFrom(r); err != nil { + return + } + pk.e = new(encoding.MPI) + if _, err = pk.e.ReadFrom(r); err != nil { + return + } + + if len(pk.e.Bytes()) > 3 { + err = errors.UnsupportedError("large public exponent") + return + } + rsa := &rsa.PublicKey{ + N: new(big.Int).SetBytes(pk.n.Bytes()), + E: 0, + } + for i := 0; i < len(pk.e.Bytes()); i++ { + rsa.E <<= 8 + rsa.E |= int(pk.e.Bytes()[i]) + } + pk.PublicKey = rsa + return +} + +// parseDSA parses DSA public key material from the given Reader. See RFC 4880, +// section 5.5.2. +func (pk *PublicKey) parseDSA(r io.Reader) (err error) { + pk.p = new(encoding.MPI) + if _, err = pk.p.ReadFrom(r); err != nil { + return + } + pk.q = new(encoding.MPI) + if _, err = pk.q.ReadFrom(r); err != nil { + return + } + pk.g = new(encoding.MPI) + if _, err = pk.g.ReadFrom(r); err != nil { + return + } + pk.y = new(encoding.MPI) + if _, err = pk.y.ReadFrom(r); err != nil { + return + } + + dsa := new(dsa.PublicKey) + dsa.P = new(big.Int).SetBytes(pk.p.Bytes()) + dsa.Q = new(big.Int).SetBytes(pk.q.Bytes()) + dsa.G = new(big.Int).SetBytes(pk.g.Bytes()) + dsa.Y = new(big.Int).SetBytes(pk.y.Bytes()) + pk.PublicKey = dsa + return +} + +// parseElGamal parses ElGamal public key material from the given Reader. See +// RFC 4880, section 5.5.2. +func (pk *PublicKey) parseElGamal(r io.Reader) (err error) { + pk.p = new(encoding.MPI) + if _, err = pk.p.ReadFrom(r); err != nil { + return + } + pk.g = new(encoding.MPI) + if _, err = pk.g.ReadFrom(r); err != nil { + return + } + pk.y = new(encoding.MPI) + if _, err = pk.y.ReadFrom(r); err != nil { + return + } + + elgamal := new(elgamal.PublicKey) + elgamal.P = new(big.Int).SetBytes(pk.p.Bytes()) + elgamal.G = new(big.Int).SetBytes(pk.g.Bytes()) + elgamal.Y = new(big.Int).SetBytes(pk.y.Bytes()) + pk.PublicKey = elgamal + return +} + +// parseECDSA parses ECDSA public key material from the given Reader. See +// RFC 6637, Section 9. +func (pk *PublicKey) parseECDSA(r io.Reader) (err error) { + pk.oid = new(encoding.OID) + if _, err = pk.oid.ReadFrom(r); err != nil { + return + } + pk.p = new(encoding.MPI) + if _, err = pk.p.ReadFrom(r); err != nil { + return + } + + curveInfo := ecc.FindByOid(pk.oid) + if curveInfo == nil { + return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid)) + } + + c, ok := curveInfo.Curve.(ecc.ECDSACurve) + if !ok { + return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid)) + } + + ecdsaKey := ecdsa.NewPublicKey(c) + err = ecdsaKey.UnmarshalPoint(pk.p.Bytes()) + pk.PublicKey = ecdsaKey + + return +} + +// parseECDH parses ECDH public key material from the given Reader. See +// RFC 6637, Section 9. +func (pk *PublicKey) parseECDH(r io.Reader) (err error) { + pk.oid = new(encoding.OID) + if _, err = pk.oid.ReadFrom(r); err != nil { + return + } + pk.p = new(encoding.MPI) + if _, err = pk.p.ReadFrom(r); err != nil { + return + } + pk.kdf = new(encoding.OID) + if _, err = pk.kdf.ReadFrom(r); err != nil { + return + } + + curveInfo := ecc.FindByOid(pk.oid) + + if curveInfo == nil { + return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid)) + } + + c, ok := curveInfo.Curve.(ecc.ECDHCurve) + if !ok { + return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid)) + } + + if kdfLen := len(pk.kdf.Bytes()); kdfLen < 3 { + return errors.UnsupportedError("unsupported ECDH KDF length: " + strconv.Itoa(kdfLen)) + } + if reserved := pk.kdf.Bytes()[0]; reserved != 0x01 { + return errors.UnsupportedError("unsupported KDF reserved field: " + strconv.Itoa(int(reserved))) + } + kdfHash, ok := algorithm.HashById[pk.kdf.Bytes()[1]] + if !ok { + return errors.UnsupportedError("unsupported ECDH KDF hash: " + strconv.Itoa(int(pk.kdf.Bytes()[1]))) + } + kdfCipher, ok := algorithm.CipherById[pk.kdf.Bytes()[2]] + if !ok { + return errors.UnsupportedError("unsupported ECDH KDF cipher: " + strconv.Itoa(int(pk.kdf.Bytes()[2]))) + } + + ecdhKey := ecdh.NewPublicKey(c, kdfHash, kdfCipher) + err = ecdhKey.UnmarshalPoint(pk.p.Bytes()) + pk.PublicKey = ecdhKey + + return +} + +func (pk *PublicKey) parseEdDSA(r io.Reader) (err error) { + pk.oid = new(encoding.OID) + if _, err = pk.oid.ReadFrom(r); err != nil { + return + } + curveInfo := ecc.FindByOid(pk.oid) + if curveInfo == nil { + return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid)) + } + + c, ok := curveInfo.Curve.(ecc.EdDSACurve) + if !ok { + return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid)) + } + + pk.p = new(encoding.MPI) + if _, err = pk.p.ReadFrom(r); err != nil { + return + } + + if len(pk.p.Bytes()) == 0 { + return errors.StructuralError("empty EdDSA public key") + } + + pub := eddsa.NewPublicKey(c) + + switch flag := pk.p.Bytes()[0]; flag { + case 0x04: + // TODO: see _grcy_ecc_eddsa_ensure_compact in grcypt + return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag))) + case 0x40: + err = pub.UnmarshalPoint(pk.p.Bytes()) + default: + return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag))) + } + + pk.PublicKey = pub + return +} + +// SerializeForHash serializes the PublicKey to w with the special packet +// header format needed for hashing. +func (pk *PublicKey) SerializeForHash(w io.Writer) error { + pk.SerializeSignaturePrefix(w) + return pk.serializeWithoutHeaders(w) +} + +// SerializeSignaturePrefix writes the prefix for this public key to the given Writer. +// The prefix is used when calculating a signature over this public key. See +// RFC 4880, section 5.2.4. +func (pk *PublicKey) SerializeSignaturePrefix(w io.Writer) { + var pLength = pk.algorithmSpecificByteCount() + if pk.Version == 5 { + pLength += 10 // version, timestamp (4), algorithm, key octet count (4). + w.Write([]byte{ + 0x9A, + byte(pLength >> 24), + byte(pLength >> 16), + byte(pLength >> 8), + byte(pLength), + }) + return + } + pLength += 6 + w.Write([]byte{0x99, byte(pLength >> 8), byte(pLength)}) +} + +func (pk *PublicKey) Serialize(w io.Writer) (err error) { + length := 6 // 6 byte header + length += pk.algorithmSpecificByteCount() + if pk.Version == 5 { + length += 4 // octet key count + } + packetType := packetTypePublicKey + if pk.IsSubkey { + packetType = packetTypePublicSubkey + } + err = serializeHeader(w, packetType, length) + if err != nil { + return + } + return pk.serializeWithoutHeaders(w) +} + +func (pk *PublicKey) algorithmSpecificByteCount() int { + length := 0 + switch pk.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly: + length += int(pk.n.EncodedLength()) + length += int(pk.e.EncodedLength()) + case PubKeyAlgoDSA: + length += int(pk.p.EncodedLength()) + length += int(pk.q.EncodedLength()) + length += int(pk.g.EncodedLength()) + length += int(pk.y.EncodedLength()) + case PubKeyAlgoElGamal: + length += int(pk.p.EncodedLength()) + length += int(pk.g.EncodedLength()) + length += int(pk.y.EncodedLength()) + case PubKeyAlgoECDSA: + length += int(pk.oid.EncodedLength()) + length += int(pk.p.EncodedLength()) + case PubKeyAlgoECDH: + length += int(pk.oid.EncodedLength()) + length += int(pk.p.EncodedLength()) + length += int(pk.kdf.EncodedLength()) + case PubKeyAlgoEdDSA: + length += int(pk.oid.EncodedLength()) + length += int(pk.p.EncodedLength()) + default: + panic("unknown public key algorithm") + } + return length +} + +// serializeWithoutHeaders marshals the PublicKey to w in the form of an +// OpenPGP public key packet, not including the packet header. +func (pk *PublicKey) serializeWithoutHeaders(w io.Writer) (err error) { + t := uint32(pk.CreationTime.Unix()) + if _, err = w.Write([]byte{ + byte(pk.Version), + byte(t >> 24), byte(t >> 16), byte(t >> 8), byte(t), + byte(pk.PubKeyAlgo), + }); err != nil { + return + } + + if pk.Version == 5 { + n := pk.algorithmSpecificByteCount() + if _, err = w.Write([]byte{ + byte(n >> 24), byte(n >> 16), byte(n >> 8), byte(n), + }); err != nil { + return + } + } + + switch pk.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly: + if _, err = w.Write(pk.n.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.e.EncodedBytes()) + return + case PubKeyAlgoDSA: + if _, err = w.Write(pk.p.EncodedBytes()); err != nil { + return + } + if _, err = w.Write(pk.q.EncodedBytes()); err != nil { + return + } + if _, err = w.Write(pk.g.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.y.EncodedBytes()) + return + case PubKeyAlgoElGamal: + if _, err = w.Write(pk.p.EncodedBytes()); err != nil { + return + } + if _, err = w.Write(pk.g.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.y.EncodedBytes()) + return + case PubKeyAlgoECDSA: + if _, err = w.Write(pk.oid.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.p.EncodedBytes()) + return + case PubKeyAlgoECDH: + if _, err = w.Write(pk.oid.EncodedBytes()); err != nil { + return + } + if _, err = w.Write(pk.p.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.kdf.EncodedBytes()) + return + case PubKeyAlgoEdDSA: + if _, err = w.Write(pk.oid.EncodedBytes()); err != nil { + return + } + _, err = w.Write(pk.p.EncodedBytes()) + return + } + return errors.InvalidArgumentError("bad public-key algorithm") +} + +// CanSign returns true iff this public key can generate signatures +func (pk *PublicKey) CanSign() bool { + return pk.PubKeyAlgo != PubKeyAlgoRSAEncryptOnly && pk.PubKeyAlgo != PubKeyAlgoElGamal && pk.PubKeyAlgo != PubKeyAlgoECDH +} + +// VerifySignature returns nil iff sig is a valid signature, made by this +// public key, of the data hashed into signed. signed is mutated by this call. +func (pk *PublicKey) VerifySignature(signed hash.Hash, sig *Signature) (err error) { + if !pk.CanSign() { + return errors.InvalidArgumentError("public key cannot generate signatures") + } + if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) { + sig.AddMetadataToHashSuffix() + } + signed.Write(sig.HashSuffix) + hashBytes := signed.Sum(nil) + if sig.Version == 5 && (hashBytes[0] != sig.HashTag[0] || hashBytes[1] != sig.HashTag[1]) { + return errors.SignatureError("hash tag doesn't match") + } + + if pk.PubKeyAlgo != sig.PubKeyAlgo { + return errors.InvalidArgumentError("public key and signature use different algorithms") + } + + switch pk.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly: + rsaPublicKey, _ := pk.PublicKey.(*rsa.PublicKey) + err = rsa.VerifyPKCS1v15(rsaPublicKey, sig.Hash, hashBytes, padToKeySize(rsaPublicKey, sig.RSASignature.Bytes())) + if err != nil { + return errors.SignatureError("RSA verification failure") + } + return nil + case PubKeyAlgoDSA: + dsaPublicKey, _ := pk.PublicKey.(*dsa.PublicKey) + // Need to truncate hashBytes to match FIPS 186-3 section 4.6. + subgroupSize := (dsaPublicKey.Q.BitLen() + 7) / 8 + if len(hashBytes) > subgroupSize { + hashBytes = hashBytes[:subgroupSize] + } + if !dsa.Verify(dsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.DSASigR.Bytes()), new(big.Int).SetBytes(sig.DSASigS.Bytes())) { + return errors.SignatureError("DSA verification failure") + } + return nil + case PubKeyAlgoECDSA: + ecdsaPublicKey := pk.PublicKey.(*ecdsa.PublicKey) + if !ecdsa.Verify(ecdsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.ECDSASigR.Bytes()), new(big.Int).SetBytes(sig.ECDSASigS.Bytes())) { + return errors.SignatureError("ECDSA verification failure") + } + return nil + case PubKeyAlgoEdDSA: + eddsaPublicKey := pk.PublicKey.(*eddsa.PublicKey) + if !eddsa.Verify(eddsaPublicKey, hashBytes, sig.EdDSASigR.Bytes(), sig.EdDSASigS.Bytes()) { + return errors.SignatureError("EdDSA verification failure") + } + return nil + default: + return errors.SignatureError("Unsupported public key algorithm used in signature") + } +} + +// keySignatureHash returns a Hash of the message that needs to be signed for +// pk to assert a subkey relationship to signed. +func keySignatureHash(pk, signed signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) { + if !hashFunc.Available() { + return nil, errors.UnsupportedError("hash function") + } + h = hashFunc.New() + + // RFC 4880, section 5.2.4 + err = pk.SerializeForHash(h) + if err != nil { + return nil, err + } + + err = signed.SerializeForHash(h) + return +} + +// VerifyKeySignature returns nil iff sig is a valid signature, made by this +// public key, of signed. +func (pk *PublicKey) VerifyKeySignature(signed *PublicKey, sig *Signature) error { + h, err := keySignatureHash(pk, signed, sig.Hash) + if err != nil { + return err + } + if err = pk.VerifySignature(h, sig); err != nil { + return err + } + + if sig.FlagSign { + // Signing subkeys must be cross-signed. See + // https://www.gnupg.org/faq/subkey-cross-certify.html. + if sig.EmbeddedSignature == nil { + return errors.StructuralError("signing subkey is missing cross-signature") + } + // Verify the cross-signature. This is calculated over the same + // data as the main signature, so we cannot just recursively + // call signed.VerifyKeySignature(...) + if h, err = keySignatureHash(pk, signed, sig.EmbeddedSignature.Hash); err != nil { + return errors.StructuralError("error while hashing for cross-signature: " + err.Error()) + } + if err := signed.VerifySignature(h, sig.EmbeddedSignature); err != nil { + return errors.StructuralError("error while verifying cross-signature: " + err.Error()) + } + } + + return nil +} + +func keyRevocationHash(pk signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) { + if !hashFunc.Available() { + return nil, errors.UnsupportedError("hash function") + } + h = hashFunc.New() + + // RFC 4880, section 5.2.4 + err = pk.SerializeForHash(h) + + return +} + +// VerifyRevocationSignature returns nil iff sig is a valid signature, made by this +// public key. +func (pk *PublicKey) VerifyRevocationSignature(sig *Signature) (err error) { + h, err := keyRevocationHash(pk, sig.Hash) + if err != nil { + return err + } + return pk.VerifySignature(h, sig) +} + +// VerifySubkeyRevocationSignature returns nil iff sig is a valid subkey revocation signature, +// made by this public key, of signed. +func (pk *PublicKey) VerifySubkeyRevocationSignature(sig *Signature, signed *PublicKey) (err error) { + h, err := keySignatureHash(pk, signed, sig.Hash) + if err != nil { + return err + } + return pk.VerifySignature(h, sig) +} + +// userIdSignatureHash returns a Hash of the message that needs to be signed +// to assert that pk is a valid key for id. +func userIdSignatureHash(id string, pk *PublicKey, hashFunc crypto.Hash) (h hash.Hash, err error) { + if !hashFunc.Available() { + return nil, errors.UnsupportedError("hash function") + } + h = hashFunc.New() + + // RFC 4880, section 5.2.4 + pk.SerializeSignaturePrefix(h) + pk.serializeWithoutHeaders(h) + + var buf [5]byte + buf[0] = 0xb4 + buf[1] = byte(len(id) >> 24) + buf[2] = byte(len(id) >> 16) + buf[3] = byte(len(id) >> 8) + buf[4] = byte(len(id)) + h.Write(buf[:]) + h.Write([]byte(id)) + + return +} + +// VerifyUserIdSignature returns nil iff sig is a valid signature, made by this +// public key, that id is the identity of pub. +func (pk *PublicKey) VerifyUserIdSignature(id string, pub *PublicKey, sig *Signature) (err error) { + h, err := userIdSignatureHash(id, pub, sig.Hash) + if err != nil { + return err + } + return pk.VerifySignature(h, sig) +} + +// KeyIdString returns the public key's fingerprint in capital hex +// (e.g. "6C7EE1B8621CC013"). +func (pk *PublicKey) KeyIdString() string { + return fmt.Sprintf("%X", pk.Fingerprint[12:20]) +} + +// KeyIdShortString returns the short form of public key's fingerprint +// in capital hex, as shown by gpg --list-keys (e.g. "621CC013"). +func (pk *PublicKey) KeyIdShortString() string { + return fmt.Sprintf("%X", pk.Fingerprint[16:20]) +} + +// BitLength returns the bit length for the given public key. +func (pk *PublicKey) BitLength() (bitLength uint16, err error) { + switch pk.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly: + bitLength = pk.n.BitLength() + case PubKeyAlgoDSA: + bitLength = pk.p.BitLength() + case PubKeyAlgoElGamal: + bitLength = pk.p.BitLength() + case PubKeyAlgoECDSA: + bitLength = pk.p.BitLength() + case PubKeyAlgoECDH: + bitLength = pk.p.BitLength() + case PubKeyAlgoEdDSA: + bitLength = pk.p.BitLength() + default: + err = errors.InvalidArgumentError("bad public-key algorithm") + } + return +} + +// KeyExpired returns whether sig is a self-signature of a key that has +// expired or is created in the future. +func (pk *PublicKey) KeyExpired(sig *Signature, currentTime time.Time) bool { + if pk.CreationTime.After(currentTime) { + return true + } + if sig.KeyLifetimeSecs == nil || *sig.KeyLifetimeSecs == 0 { + return false + } + expiry := pk.CreationTime.Add(time.Duration(*sig.KeyLifetimeSecs) * time.Second) + return currentTime.After(expiry) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go new file mode 100644 index 00000000..b255f1f6 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go @@ -0,0 +1,24 @@ +package packet + +const rsaFingerprintHex = "5fb74b1d03b1e3cb31bc2f8aa34d7e18c20c31bb" + +const rsaPkDataHex = "988d044d3c5c10010400b1d13382944bd5aba23a4312968b5095d14f947f600eb478e14a6fcb16b0e0cac764884909c020bc495cfcc39a935387c661507bdb236a0612fb582cac3af9b29cc2c8c70090616c41b662f4da4c1201e195472eb7f4ae1ccbcbf9940fe21d985e379a5563dde5b9a23d35f1cfaa5790da3b79db26f23695107bfaca8e7b5bcd0011010001" + +const dsaFingerprintHex = "eece4c094db002103714c63c8e8fbe54062f19ed" + +const dsaPkDataHex = "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" + +const ecdsaFingerprintHex = "9892270b38b8980b05c8d56d43fe956c542ca00b" + +const ecdsaPkDataHex = "9893045071c29413052b8104002304230401f4867769cedfa52c325018896245443968e52e51d0c2df8d939949cb5b330f2921711fbee1c9b9dddb95d15cb0255e99badeddda7cc23d9ddcaacbc290969b9f24019375d61c2e4e3b36953a28d8b2bc95f78c3f1d592fb24499be348656a7b17e3963187b4361afe497bc5f9f81213f04069f8e1fb9e6a6290ae295ca1a92b894396cb4" + +const ecdhFingerprintHex = "722354df2475a42164d1d49faa8b938f9a201946" + +const ecdhPkDataHex = "b90073044d53059212052b810400220303042faa84024a20b6735c4897efa5bfb41bf85b7eefeab5ca0cb9ffc8ea04a46acb25534a577694f9e25340a4ab5223a9dd1eda530c8aa2e6718db10d7e672558c7736fe09369ea5739a2a3554bf16d41faa50562f11c6d39bbd5dffb6b9a9ec91803010909" + +const eddsaFingerprintHex = "b2d5e5ec0e6deca6bc8eeeb00907e75e1dd99ad8" + +const eddsaPkDataHex = "98330456e2132b16092b06010401da470f01010740bbda39266affa511a8c2d02edf690fb784b0499c4406185811a163539ef11dc1b41d74657374696e67203c74657374696e674074657374696e672e636f6d3e8879041316080021050256e2132b021b03050b09080702061508090a0b020416020301021e01021780000a09100907e75e1dd99ad86d0c00fe39d2008359352782bc9b61ac382584cd8eff3f57a18c2287e3afeeb05d1f04ba00fe2d0bc1ddf3ff8adb9afa3e7d9287244b4ec567f3db4d60b74a9b5465ed528203" + +// Source: https://sites.google.com/site/brainhub/pgpecckeys#TOC-ECC-NIST-P-384-key +const ecc384PubHex = `99006f044d53059213052b81040022030304f6b8c5aced5b84ef9f4a209db2e4a9dfb70d28cb8c10ecd57674a9fa5a67389942b62d5e51367df4c7bfd3f8e500feecf07ed265a621a8ebbbe53e947ec78c677eba143bd1533c2b350e1c29f82313e1e1108eba063be1e64b10e6950e799c2db42465635f6473615f64685f333834203c6f70656e70677040627261696e6875622e6f72673e8900cb04101309005305024d530592301480000000002000077072656665727265642d656d61696c2d656e636f64696e67407067702e636f6d7067706d696d65040b090807021901051b03000000021602051e010000000415090a08000a0910098033880f54719fca2b0180aa37350968bd5f115afd8ce7bc7b103822152dbff06d0afcda835329510905b98cb469ba208faab87c7412b799e7b633017f58364ea480e8a1a3f253a0c5f22c446e8be9a9fce6210136ee30811abbd49139de28b5bdf8dc36d06ae748579e9ff503b90073044d53059212052b810400220303042faa84024a20b6735c4897efa5bfb41bf85b7eefeab5ca0cb9ffc8ea04a46acb25534a577694f9e25340a4ab5223a9dd1eda530c8aa2e6718db10d7e672558c7736fe09369ea5739a2a3554bf16d41faa50562f11c6d39bbd5dffb6b9a9ec9180301090989008404181309000c05024d530592051b0c000000000a0910098033880f54719f80970180eee7a6d8fcee41ee4f9289df17f9bcf9d955dca25c583b94336f3a2b2d4986dc5cf417b8d2dc86f741a9e1a6d236c0e3017d1c76575458a0cfb93ae8a2b274fcc65ceecd7a91eec83656ba13219969f06945b48c56bd04152c3a0553c5f2f4bd1267` diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/reader.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/reader.go new file mode 100644 index 00000000..10215fe5 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/reader.go @@ -0,0 +1,86 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// Reader reads packets from an io.Reader and allows packets to be 'unread' so +// that they result from the next call to Next. +type Reader struct { + q []Packet + readers []io.Reader +} + +// New io.Readers are pushed when a compressed or encrypted packet is processed +// and recursively treated as a new source of packets. However, a carefully +// crafted packet can trigger an infinite recursive sequence of packets. See +// http://mumble.net/~campbell/misc/pgp-quine +// https://web.nvd.nist.gov/view/vuln/detail?vulnId=CVE-2013-4402 +// This constant limits the number of recursive packets that may be pushed. +const maxReaders = 32 + +// Next returns the most recently unread Packet, or reads another packet from +// the top-most io.Reader. Unknown packet types are skipped. +func (r *Reader) Next() (p Packet, err error) { + if len(r.q) > 0 { + p = r.q[len(r.q)-1] + r.q = r.q[:len(r.q)-1] + return + } + + for len(r.readers) > 0 { + p, err = Read(r.readers[len(r.readers)-1]) + if err == nil { + return + } + if err == io.EOF { + r.readers = r.readers[:len(r.readers)-1] + continue + } + // TODO: Add strict mode that rejects unknown packets, instead of ignoring them. + if _, ok := err.(errors.UnknownPacketTypeError); ok { + continue + } + if _, ok := err.(errors.UnsupportedError); ok { + switch p.(type) { + case *SymmetricallyEncrypted, *AEADEncrypted, *Compressed, *LiteralData: + return nil, err + } + continue + } + return nil, err + } + + return nil, io.EOF +} + +// Push causes the Reader to start reading from a new io.Reader. When an EOF +// error is seen from the new io.Reader, it is popped and the Reader continues +// to read from the next most recent io.Reader. Push returns a StructuralError +// if pushing the reader would exceed the maximum recursion level, otherwise it +// returns nil. +func (r *Reader) Push(reader io.Reader) (err error) { + if len(r.readers) >= maxReaders { + return errors.StructuralError("too many layers of packets") + } + r.readers = append(r.readers, reader) + return nil +} + +// Unread causes the given Packet to be returned from the next call to Next. +func (r *Reader) Unread(p Packet) { + r.q = append(r.q, p) +} + +func NewReader(r io.Reader) *Reader { + return &Reader{ + q: nil, + readers: []io.Reader{r}, + } +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/signature.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/signature.go new file mode 100644 index 00000000..80d0bb98 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/signature.go @@ -0,0 +1,1084 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "bytes" + "crypto" + "crypto/dsa" + "encoding/binary" + "hash" + "io" + "strconv" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/ecdsa" + "github.com/ProtonMail/go-crypto/openpgp/eddsa" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/internal/encoding" +) + +const ( + // See RFC 4880, section 5.2.3.21 for details. + KeyFlagCertify = 1 << iota + KeyFlagSign + KeyFlagEncryptCommunications + KeyFlagEncryptStorage + KeyFlagSplitKey + KeyFlagAuthenticate + _ + KeyFlagGroupKey +) + +// Signature represents a signature. See RFC 4880, section 5.2. +type Signature struct { + Version int + SigType SignatureType + PubKeyAlgo PublicKeyAlgorithm + Hash crypto.Hash + + // HashSuffix is extra data that is hashed in after the signed data. + HashSuffix []byte + // HashTag contains the first two bytes of the hash for fast rejection + // of bad signed data. + HashTag [2]byte + + // Metadata includes format, filename and time, and is protected by v5 + // signatures of type 0x00 or 0x01. This metadata is included into the hash + // computation; if nil, six 0x00 bytes are used instead. See section 5.2.4. + Metadata *LiteralData + + CreationTime time.Time + + RSASignature encoding.Field + DSASigR, DSASigS encoding.Field + ECDSASigR, ECDSASigS encoding.Field + EdDSASigR, EdDSASigS encoding.Field + + // rawSubpackets contains the unparsed subpackets, in order. + rawSubpackets []outputSubpacket + + // The following are optional so are nil when not included in the + // signature. + + SigLifetimeSecs, KeyLifetimeSecs *uint32 + PreferredSymmetric, PreferredHash, PreferredCompression []uint8 + PreferredCipherSuites [][2]uint8 + IssuerKeyId *uint64 + IssuerFingerprint []byte + SignerUserId *string + IsPrimaryId *bool + Notations []*Notation + + // TrustLevel and TrustAmount can be set by the signer to assert that + // the key is not only valid but also trustworthy at the specified + // level. + // See RFC 4880, section 5.2.3.13 for details. + TrustLevel TrustLevel + TrustAmount TrustAmount + + // TrustRegularExpression can be used in conjunction with trust Signature + // packets to limit the scope of the trust that is extended. + // See RFC 4880, section 5.2.3.14 for details. + TrustRegularExpression *string + + // PolicyURI can be set to the URI of a document that describes the + // policy under which the signature was issued. See RFC 4880, section + // 5.2.3.20 for details. + PolicyURI string + + // FlagsValid is set if any flags were given. See RFC 4880, section + // 5.2.3.21 for details. + FlagsValid bool + FlagCertify, FlagSign, FlagEncryptCommunications, FlagEncryptStorage, FlagSplitKey, FlagAuthenticate, FlagGroupKey bool + + // RevocationReason is set if this signature has been revoked. + // See RFC 4880, section 5.2.3.23 for details. + RevocationReason *ReasonForRevocation + RevocationReasonText string + + // In a self-signature, these flags are set there is a features subpacket + // indicating that the issuer implementation supports these features + // see https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh#features-subpacket + SEIPDv1, SEIPDv2 bool + + // EmbeddedSignature, if non-nil, is a signature of the parent key, by + // this key. This prevents an attacker from claiming another's signing + // subkey as their own. + EmbeddedSignature *Signature + + outSubpackets []outputSubpacket +} + +func (sig *Signature) parse(r io.Reader) (err error) { + // RFC 4880, section 5.2.3 + var buf [5]byte + _, err = readFull(r, buf[:1]) + if err != nil { + return + } + if buf[0] != 4 && buf[0] != 5 { + err = errors.UnsupportedError("signature packet version " + strconv.Itoa(int(buf[0]))) + return + } + sig.Version = int(buf[0]) + _, err = readFull(r, buf[:5]) + if err != nil { + return + } + sig.SigType = SignatureType(buf[0]) + sig.PubKeyAlgo = PublicKeyAlgorithm(buf[1]) + switch sig.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA: + default: + err = errors.UnsupportedError("public key algorithm " + strconv.Itoa(int(sig.PubKeyAlgo))) + return + } + + var ok bool + + if sig.Version < 5 { + sig.Hash, ok = algorithm.HashIdToHashWithSha1(buf[2]) + } else { + sig.Hash, ok = algorithm.HashIdToHash(buf[2]) + } + + if !ok { + return errors.UnsupportedError("hash function " + strconv.Itoa(int(buf[2]))) + } + + hashedSubpacketsLength := int(buf[3])<<8 | int(buf[4]) + hashedSubpackets := make([]byte, hashedSubpacketsLength) + _, err = readFull(r, hashedSubpackets) + if err != nil { + return + } + err = sig.buildHashSuffix(hashedSubpackets) + if err != nil { + return + } + + err = parseSignatureSubpackets(sig, hashedSubpackets, true) + if err != nil { + return + } + + _, err = readFull(r, buf[:2]) + if err != nil { + return + } + unhashedSubpacketsLength := int(buf[0])<<8 | int(buf[1]) + unhashedSubpackets := make([]byte, unhashedSubpacketsLength) + _, err = readFull(r, unhashedSubpackets) + if err != nil { + return + } + err = parseSignatureSubpackets(sig, unhashedSubpackets, false) + if err != nil { + return + } + + _, err = readFull(r, sig.HashTag[:2]) + if err != nil { + return + } + + switch sig.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly: + sig.RSASignature = new(encoding.MPI) + _, err = sig.RSASignature.ReadFrom(r) + case PubKeyAlgoDSA: + sig.DSASigR = new(encoding.MPI) + if _, err = sig.DSASigR.ReadFrom(r); err != nil { + return + } + + sig.DSASigS = new(encoding.MPI) + _, err = sig.DSASigS.ReadFrom(r) + case PubKeyAlgoECDSA: + sig.ECDSASigR = new(encoding.MPI) + if _, err = sig.ECDSASigR.ReadFrom(r); err != nil { + return + } + + sig.ECDSASigS = new(encoding.MPI) + _, err = sig.ECDSASigS.ReadFrom(r) + case PubKeyAlgoEdDSA: + sig.EdDSASigR = new(encoding.MPI) + if _, err = sig.EdDSASigR.ReadFrom(r); err != nil { + return + } + + sig.EdDSASigS = new(encoding.MPI) + if _, err = sig.EdDSASigS.ReadFrom(r); err != nil { + return + } + default: + panic("unreachable") + } + return +} + +// parseSignatureSubpackets parses subpackets of the main signature packet. See +// RFC 4880, section 5.2.3.1. +func parseSignatureSubpackets(sig *Signature, subpackets []byte, isHashed bool) (err error) { + for len(subpackets) > 0 { + subpackets, err = parseSignatureSubpacket(sig, subpackets, isHashed) + if err != nil { + return + } + } + + if sig.CreationTime.IsZero() { + err = errors.StructuralError("no creation time in signature") + } + + return +} + +type signatureSubpacketType uint8 + +const ( + creationTimeSubpacket signatureSubpacketType = 2 + signatureExpirationSubpacket signatureSubpacketType = 3 + trustSubpacket signatureSubpacketType = 5 + regularExpressionSubpacket signatureSubpacketType = 6 + keyExpirationSubpacket signatureSubpacketType = 9 + prefSymmetricAlgosSubpacket signatureSubpacketType = 11 + issuerSubpacket signatureSubpacketType = 16 + notationDataSubpacket signatureSubpacketType = 20 + prefHashAlgosSubpacket signatureSubpacketType = 21 + prefCompressionSubpacket signatureSubpacketType = 22 + primaryUserIdSubpacket signatureSubpacketType = 25 + policyUriSubpacket signatureSubpacketType = 26 + keyFlagsSubpacket signatureSubpacketType = 27 + signerUserIdSubpacket signatureSubpacketType = 28 + reasonForRevocationSubpacket signatureSubpacketType = 29 + featuresSubpacket signatureSubpacketType = 30 + embeddedSignatureSubpacket signatureSubpacketType = 32 + issuerFingerprintSubpacket signatureSubpacketType = 33 + prefCipherSuitesSubpacket signatureSubpacketType = 39 +) + +// parseSignatureSubpacket parses a single subpacket. len(subpacket) is >= 1. +func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (rest []byte, err error) { + // RFC 4880, section 5.2.3.1 + var ( + length uint32 + packetType signatureSubpacketType + isCritical bool + ) + if len(subpacket) == 0 { + err = errors.StructuralError("zero length signature subpacket") + return + } + switch { + case subpacket[0] < 192: + length = uint32(subpacket[0]) + subpacket = subpacket[1:] + case subpacket[0] < 255: + if len(subpacket) < 2 { + goto Truncated + } + length = uint32(subpacket[0]-192)<<8 + uint32(subpacket[1]) + 192 + subpacket = subpacket[2:] + default: + if len(subpacket) < 5 { + goto Truncated + } + length = uint32(subpacket[1])<<24 | + uint32(subpacket[2])<<16 | + uint32(subpacket[3])<<8 | + uint32(subpacket[4]) + subpacket = subpacket[5:] + } + if length > uint32(len(subpacket)) { + goto Truncated + } + rest = subpacket[length:] + subpacket = subpacket[:length] + if len(subpacket) == 0 { + err = errors.StructuralError("zero length signature subpacket") + return + } + packetType = signatureSubpacketType(subpacket[0] & 0x7f) + isCritical = subpacket[0]&0x80 == 0x80 + subpacket = subpacket[1:] + sig.rawSubpackets = append(sig.rawSubpackets, outputSubpacket{isHashed, packetType, isCritical, subpacket}) + if !isHashed && + packetType != issuerSubpacket && + packetType != issuerFingerprintSubpacket && + packetType != embeddedSignatureSubpacket { + return + } + switch packetType { + case creationTimeSubpacket: + if len(subpacket) != 4 { + err = errors.StructuralError("signature creation time not four bytes") + return + } + t := binary.BigEndian.Uint32(subpacket) + sig.CreationTime = time.Unix(int64(t), 0) + case signatureExpirationSubpacket: + // Signature expiration time, section 5.2.3.10 + if len(subpacket) != 4 { + err = errors.StructuralError("expiration subpacket with bad length") + return + } + sig.SigLifetimeSecs = new(uint32) + *sig.SigLifetimeSecs = binary.BigEndian.Uint32(subpacket) + case trustSubpacket: + if len(subpacket) != 2 { + err = errors.StructuralError("trust subpacket with bad length") + return + } + // Trust level and amount, section 5.2.3.13 + sig.TrustLevel = TrustLevel(subpacket[0]) + sig.TrustAmount = TrustAmount(subpacket[1]) + case regularExpressionSubpacket: + if len(subpacket) == 0 { + err = errors.StructuralError("regexp subpacket with bad length") + return + } + // Trust regular expression, section 5.2.3.14 + // RFC specifies the string should be null-terminated; remove a null byte from the end + if subpacket[len(subpacket)-1] != 0x00 { + err = errors.StructuralError("expected regular expression to be null-terminated") + return + } + trustRegularExpression := string(subpacket[:len(subpacket)-1]) + sig.TrustRegularExpression = &trustRegularExpression + case keyExpirationSubpacket: + // Key expiration time, section 5.2.3.6 + if len(subpacket) != 4 { + err = errors.StructuralError("key expiration subpacket with bad length") + return + } + sig.KeyLifetimeSecs = new(uint32) + *sig.KeyLifetimeSecs = binary.BigEndian.Uint32(subpacket) + case prefSymmetricAlgosSubpacket: + // Preferred symmetric algorithms, section 5.2.3.7 + sig.PreferredSymmetric = make([]byte, len(subpacket)) + copy(sig.PreferredSymmetric, subpacket) + case issuerSubpacket: + // Issuer, section 5.2.3.5 + if sig.Version > 4 { + err = errors.StructuralError("issuer subpacket found in v5 key") + return + } + if len(subpacket) != 8 { + err = errors.StructuralError("issuer subpacket with bad length") + return + } + sig.IssuerKeyId = new(uint64) + *sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket) + case notationDataSubpacket: + // Notation data, section 5.2.3.16 + if len(subpacket) < 8 { + err = errors.StructuralError("notation data subpacket with bad length") + return + } + + nameLength := uint32(subpacket[4])<<8 | uint32(subpacket[5]) + valueLength := uint32(subpacket[6])<<8 | uint32(subpacket[7]) + if len(subpacket) != int(nameLength)+int(valueLength)+8 { + err = errors.StructuralError("notation data subpacket with bad length") + return + } + + notation := Notation{ + IsHumanReadable: (subpacket[0] & 0x80) == 0x80, + Name: string(subpacket[8:(nameLength + 8)]), + Value: subpacket[(nameLength + 8):(valueLength + nameLength + 8)], + IsCritical: isCritical, + } + + sig.Notations = append(sig.Notations, ¬ation) + case prefHashAlgosSubpacket: + // Preferred hash algorithms, section 5.2.3.8 + sig.PreferredHash = make([]byte, len(subpacket)) + copy(sig.PreferredHash, subpacket) + case prefCompressionSubpacket: + // Preferred compression algorithms, section 5.2.3.9 + sig.PreferredCompression = make([]byte, len(subpacket)) + copy(sig.PreferredCompression, subpacket) + case primaryUserIdSubpacket: + // Primary User ID, section 5.2.3.19 + if len(subpacket) != 1 { + err = errors.StructuralError("primary user id subpacket with bad length") + return + } + sig.IsPrimaryId = new(bool) + if subpacket[0] > 0 { + *sig.IsPrimaryId = true + } + case keyFlagsSubpacket: + // Key flags, section 5.2.3.21 + if len(subpacket) == 0 { + err = errors.StructuralError("empty key flags subpacket") + return + } + sig.FlagsValid = true + if subpacket[0]&KeyFlagCertify != 0 { + sig.FlagCertify = true + } + if subpacket[0]&KeyFlagSign != 0 { + sig.FlagSign = true + } + if subpacket[0]&KeyFlagEncryptCommunications != 0 { + sig.FlagEncryptCommunications = true + } + if subpacket[0]&KeyFlagEncryptStorage != 0 { + sig.FlagEncryptStorage = true + } + if subpacket[0]&KeyFlagSplitKey != 0 { + sig.FlagSplitKey = true + } + if subpacket[0]&KeyFlagAuthenticate != 0 { + sig.FlagAuthenticate = true + } + if subpacket[0]&KeyFlagGroupKey != 0 { + sig.FlagGroupKey = true + } + case signerUserIdSubpacket: + userId := string(subpacket) + sig.SignerUserId = &userId + case reasonForRevocationSubpacket: + // Reason For Revocation, section 5.2.3.23 + if len(subpacket) == 0 { + err = errors.StructuralError("empty revocation reason subpacket") + return + } + sig.RevocationReason = new(ReasonForRevocation) + *sig.RevocationReason = ReasonForRevocation(subpacket[0]) + sig.RevocationReasonText = string(subpacket[1:]) + case featuresSubpacket: + // Features subpacket, section 5.2.3.24 specifies a very general + // mechanism for OpenPGP implementations to signal support for new + // features. + if len(subpacket) > 0 { + if subpacket[0]&0x01 != 0 { + sig.SEIPDv1 = true + } + // 0x02 and 0x04 are reserved + if subpacket[0]&0x08 != 0 { + sig.SEIPDv2 = true + } + } + case embeddedSignatureSubpacket: + // Only usage is in signatures that cross-certify + // signing subkeys. section 5.2.3.26 describes the + // format, with its usage described in section 11.1 + if sig.EmbeddedSignature != nil { + err = errors.StructuralError("Cannot have multiple embedded signatures") + return + } + sig.EmbeddedSignature = new(Signature) + // Embedded signatures are required to be v4 signatures see + // section 12.1. However, we only parse v4 signatures in this + // file anyway. + if err := sig.EmbeddedSignature.parse(bytes.NewBuffer(subpacket)); err != nil { + return nil, err + } + if sigType := sig.EmbeddedSignature.SigType; sigType != SigTypePrimaryKeyBinding { + return nil, errors.StructuralError("cross-signature has unexpected type " + strconv.Itoa(int(sigType))) + } + case policyUriSubpacket: + // Policy URI, section 5.2.3.20 + sig.PolicyURI = string(subpacket) + case issuerFingerprintSubpacket: + if len(subpacket) == 0 { + err = errors.StructuralError("empty issuer fingerprint subpacket") + return + } + v, l := subpacket[0], len(subpacket[1:]) + if v == 5 && l != 32 || v != 5 && l != 20 { + return nil, errors.StructuralError("bad fingerprint length") + } + sig.IssuerFingerprint = make([]byte, l) + copy(sig.IssuerFingerprint, subpacket[1:]) + sig.IssuerKeyId = new(uint64) + if v == 5 { + *sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket[1:9]) + } else { + *sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket[13:21]) + } + case prefCipherSuitesSubpacket: + // Preferred AEAD cipher suites + // See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#name-preferred-aead-ciphersuites + if len(subpacket)%2 != 0 { + err = errors.StructuralError("invalid aead cipher suite length") + return + } + + sig.PreferredCipherSuites = make([][2]byte, len(subpacket)/2) + + for i := 0; i < len(subpacket)/2; i++ { + sig.PreferredCipherSuites[i] = [2]uint8{subpacket[2*i], subpacket[2*i+1]} + } + default: + if isCritical { + err = errors.UnsupportedError("unknown critical signature subpacket type " + strconv.Itoa(int(packetType))) + return + } + } + return + +Truncated: + err = errors.StructuralError("signature subpacket truncated") + return +} + +// subpacketLengthLength returns the length, in bytes, of an encoded length value. +func subpacketLengthLength(length int) int { + if length < 192 { + return 1 + } + if length < 16320 { + return 2 + } + return 5 +} + +func (sig *Signature) CheckKeyIdOrFingerprint(pk *PublicKey) bool { + if sig.IssuerFingerprint != nil && len(sig.IssuerFingerprint) >= 20 { + return bytes.Equal(sig.IssuerFingerprint, pk.Fingerprint) + } + return sig.IssuerKeyId != nil && *sig.IssuerKeyId == pk.KeyId +} + +// serializeSubpacketLength marshals the given length into to. +func serializeSubpacketLength(to []byte, length int) int { + // RFC 4880, Section 4.2.2. + if length < 192 { + to[0] = byte(length) + return 1 + } + if length < 16320 { + length -= 192 + to[0] = byte((length >> 8) + 192) + to[1] = byte(length) + return 2 + } + to[0] = 255 + to[1] = byte(length >> 24) + to[2] = byte(length >> 16) + to[3] = byte(length >> 8) + to[4] = byte(length) + return 5 +} + +// subpacketsLength returns the serialized length, in bytes, of the given +// subpackets. +func subpacketsLength(subpackets []outputSubpacket, hashed bool) (length int) { + for _, subpacket := range subpackets { + if subpacket.hashed == hashed { + length += subpacketLengthLength(len(subpacket.contents) + 1) + length += 1 // type byte + length += len(subpacket.contents) + } + } + return +} + +// serializeSubpackets marshals the given subpackets into to. +func serializeSubpackets(to []byte, subpackets []outputSubpacket, hashed bool) { + for _, subpacket := range subpackets { + if subpacket.hashed == hashed { + n := serializeSubpacketLength(to, len(subpacket.contents)+1) + to[n] = byte(subpacket.subpacketType) + if subpacket.isCritical { + to[n] |= 0x80 + } + to = to[1+n:] + n = copy(to, subpacket.contents) + to = to[n:] + } + } + return +} + +// SigExpired returns whether sig is a signature that has expired or is created +// in the future. +func (sig *Signature) SigExpired(currentTime time.Time) bool { + if sig.CreationTime.After(currentTime) { + return true + } + if sig.SigLifetimeSecs == nil || *sig.SigLifetimeSecs == 0 { + return false + } + expiry := sig.CreationTime.Add(time.Duration(*sig.SigLifetimeSecs) * time.Second) + return currentTime.After(expiry) +} + +// buildHashSuffix constructs the HashSuffix member of sig in preparation for signing. +func (sig *Signature) buildHashSuffix(hashedSubpackets []byte) (err error) { + var hashId byte + var ok bool + + if sig.Version < 5 { + hashId, ok = algorithm.HashToHashIdWithSha1(sig.Hash) + } else { + hashId, ok = algorithm.HashToHashId(sig.Hash) + } + + if !ok { + sig.HashSuffix = nil + return errors.InvalidArgumentError("hash cannot be represented in OpenPGP: " + strconv.Itoa(int(sig.Hash))) + } + + hashedFields := bytes.NewBuffer([]byte{ + uint8(sig.Version), + uint8(sig.SigType), + uint8(sig.PubKeyAlgo), + uint8(hashId), + uint8(len(hashedSubpackets) >> 8), + uint8(len(hashedSubpackets)), + }) + hashedFields.Write(hashedSubpackets) + + var l uint64 = uint64(6 + len(hashedSubpackets)) + if sig.Version == 5 { + hashedFields.Write([]byte{0x05, 0xff}) + hashedFields.Write([]byte{ + uint8(l >> 56), uint8(l >> 48), uint8(l >> 40), uint8(l >> 32), + uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l), + }) + } else { + hashedFields.Write([]byte{0x04, 0xff}) + hashedFields.Write([]byte{ + uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l), + }) + } + sig.HashSuffix = make([]byte, hashedFields.Len()) + copy(sig.HashSuffix, hashedFields.Bytes()) + return +} + +func (sig *Signature) signPrepareHash(h hash.Hash) (digest []byte, err error) { + hashedSubpacketsLen := subpacketsLength(sig.outSubpackets, true) + hashedSubpackets := make([]byte, hashedSubpacketsLen) + serializeSubpackets(hashedSubpackets, sig.outSubpackets, true) + err = sig.buildHashSuffix(hashedSubpackets) + if err != nil { + return + } + if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) { + sig.AddMetadataToHashSuffix() + } + + h.Write(sig.HashSuffix) + digest = h.Sum(nil) + copy(sig.HashTag[:], digest) + return +} + +// Sign signs a message with a private key. The hash, h, must contain +// the hash of the message to be signed and will be mutated by this function. +// On success, the signature is stored in sig. Call Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err error) { + if priv.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + sig.Version = priv.PublicKey.Version + sig.IssuerFingerprint = priv.PublicKey.Fingerprint + sig.outSubpackets, err = sig.buildSubpackets(priv.PublicKey) + if err != nil { + return err + } + digest, err := sig.signPrepareHash(h) + if err != nil { + return + } + switch priv.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly: + // supports both *rsa.PrivateKey and crypto.Signer + sigdata, err := priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash) + if err == nil { + sig.RSASignature = encoding.NewMPI(sigdata) + } + case PubKeyAlgoDSA: + dsaPriv := priv.PrivateKey.(*dsa.PrivateKey) + + // Need to truncate hashBytes to match FIPS 186-3 section 4.6. + subgroupSize := (dsaPriv.Q.BitLen() + 7) / 8 + if len(digest) > subgroupSize { + digest = digest[:subgroupSize] + } + r, s, err := dsa.Sign(config.Random(), dsaPriv, digest) + if err == nil { + sig.DSASigR = new(encoding.MPI).SetBig(r) + sig.DSASigS = new(encoding.MPI).SetBig(s) + } + case PubKeyAlgoECDSA: + sk := priv.PrivateKey.(*ecdsa.PrivateKey) + r, s, err := ecdsa.Sign(config.Random(), sk, digest) + + if err == nil { + sig.ECDSASigR = new(encoding.MPI).SetBig(r) + sig.ECDSASigS = new(encoding.MPI).SetBig(s) + } + case PubKeyAlgoEdDSA: + sk := priv.PrivateKey.(*eddsa.PrivateKey) + r, s, err := eddsa.Sign(sk, digest) + if err == nil { + sig.EdDSASigR = encoding.NewMPI(r) + sig.EdDSASigS = encoding.NewMPI(s) + } + default: + err = errors.UnsupportedError("public key algorithm: " + strconv.Itoa(int(sig.PubKeyAlgo))) + } + + return +} + +// SignUserId computes a signature from priv, asserting that pub is a valid +// key for the identity id. On success, the signature is stored in sig. Call +// Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) SignUserId(id string, pub *PublicKey, priv *PrivateKey, config *Config) error { + if priv.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + h, err := userIdSignatureHash(id, pub, sig.Hash) + if err != nil { + return err + } + return sig.Sign(h, priv, config) +} + +// CrossSignKey computes a signature from signingKey on pub hashed using hashKey. On success, +// the signature is stored in sig. Call Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) CrossSignKey(pub *PublicKey, hashKey *PublicKey, signingKey *PrivateKey, + config *Config) error { + h, err := keySignatureHash(hashKey, pub, sig.Hash) + if err != nil { + return err + } + return sig.Sign(h, signingKey, config) +} + +// SignKey computes a signature from priv, asserting that pub is a subkey. On +// success, the signature is stored in sig. Call Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) SignKey(pub *PublicKey, priv *PrivateKey, config *Config) error { + if priv.Dummy() { + return errors.ErrDummyPrivateKey("dummy key found") + } + h, err := keySignatureHash(&priv.PublicKey, pub, sig.Hash) + if err != nil { + return err + } + return sig.Sign(h, priv, config) +} + +// RevokeKey computes a revocation signature of pub using priv. On success, the signature is +// stored in sig. Call Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) RevokeKey(pub *PublicKey, priv *PrivateKey, config *Config) error { + h, err := keyRevocationHash(pub, sig.Hash) + if err != nil { + return err + } + return sig.Sign(h, priv, config) +} + +// RevokeSubkey computes a subkey revocation signature of pub using priv. +// On success, the signature is stored in sig. Call Serialize to write it out. +// If config is nil, sensible defaults will be used. +func (sig *Signature) RevokeSubkey(pub *PublicKey, priv *PrivateKey, config *Config) error { + // Identical to a subkey binding signature + return sig.SignKey(pub, priv, config) +} + +// Serialize marshals sig to w. Sign, SignUserId or SignKey must have been +// called first. +func (sig *Signature) Serialize(w io.Writer) (err error) { + if len(sig.outSubpackets) == 0 { + sig.outSubpackets = sig.rawSubpackets + } + if sig.RSASignature == nil && sig.DSASigR == nil && sig.ECDSASigR == nil && sig.EdDSASigR == nil { + return errors.InvalidArgumentError("Signature: need to call Sign, SignUserId or SignKey before Serialize") + } + + sigLength := 0 + switch sig.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly: + sigLength = int(sig.RSASignature.EncodedLength()) + case PubKeyAlgoDSA: + sigLength = int(sig.DSASigR.EncodedLength()) + sigLength += int(sig.DSASigS.EncodedLength()) + case PubKeyAlgoECDSA: + sigLength = int(sig.ECDSASigR.EncodedLength()) + sigLength += int(sig.ECDSASigS.EncodedLength()) + case PubKeyAlgoEdDSA: + sigLength = int(sig.EdDSASigR.EncodedLength()) + sigLength += int(sig.EdDSASigS.EncodedLength()) + default: + panic("impossible") + } + + unhashedSubpacketsLen := subpacketsLength(sig.outSubpackets, false) + length := len(sig.HashSuffix) - 6 /* trailer not included */ + + 2 /* length of unhashed subpackets */ + unhashedSubpacketsLen + + 2 /* hash tag */ + sigLength + if sig.Version == 5 { + length -= 4 // eight-octet instead of four-octet big endian + } + err = serializeHeader(w, packetTypeSignature, length) + if err != nil { + return + } + err = sig.serializeBody(w) + if err != nil { + return err + } + return +} + +func (sig *Signature) serializeBody(w io.Writer) (err error) { + hashedSubpacketsLen := uint16(uint16(sig.HashSuffix[4])<<8) | uint16(sig.HashSuffix[5]) + fields := sig.HashSuffix[:6+hashedSubpacketsLen] + _, err = w.Write(fields) + if err != nil { + return + } + + unhashedSubpacketsLen := subpacketsLength(sig.outSubpackets, false) + unhashedSubpackets := make([]byte, 2+unhashedSubpacketsLen) + unhashedSubpackets[0] = byte(unhashedSubpacketsLen >> 8) + unhashedSubpackets[1] = byte(unhashedSubpacketsLen) + serializeSubpackets(unhashedSubpackets[2:], sig.outSubpackets, false) + + _, err = w.Write(unhashedSubpackets) + if err != nil { + return + } + _, err = w.Write(sig.HashTag[:]) + if err != nil { + return + } + + switch sig.PubKeyAlgo { + case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly: + _, err = w.Write(sig.RSASignature.EncodedBytes()) + case PubKeyAlgoDSA: + if _, err = w.Write(sig.DSASigR.EncodedBytes()); err != nil { + return + } + _, err = w.Write(sig.DSASigS.EncodedBytes()) + case PubKeyAlgoECDSA: + if _, err = w.Write(sig.ECDSASigR.EncodedBytes()); err != nil { + return + } + _, err = w.Write(sig.ECDSASigS.EncodedBytes()) + case PubKeyAlgoEdDSA: + if _, err = w.Write(sig.EdDSASigR.EncodedBytes()); err != nil { + return + } + _, err = w.Write(sig.EdDSASigS.EncodedBytes()) + default: + panic("impossible") + } + return +} + +// outputSubpacket represents a subpacket to be marshaled. +type outputSubpacket struct { + hashed bool // true if this subpacket is in the hashed area. + subpacketType signatureSubpacketType + isCritical bool + contents []byte +} + +func (sig *Signature) buildSubpackets(issuer PublicKey) (subpackets []outputSubpacket, err error) { + creationTime := make([]byte, 4) + binary.BigEndian.PutUint32(creationTime, uint32(sig.CreationTime.Unix())) + subpackets = append(subpackets, outputSubpacket{true, creationTimeSubpacket, false, creationTime}) + + if sig.IssuerKeyId != nil && sig.Version == 4 { + keyId := make([]byte, 8) + binary.BigEndian.PutUint64(keyId, *sig.IssuerKeyId) + subpackets = append(subpackets, outputSubpacket{true, issuerSubpacket, false, keyId}) + } + if sig.IssuerFingerprint != nil { + contents := append([]uint8{uint8(issuer.Version)}, sig.IssuerFingerprint...) + subpackets = append(subpackets, outputSubpacket{true, issuerFingerprintSubpacket, sig.Version == 5, contents}) + } + if sig.SignerUserId != nil { + subpackets = append(subpackets, outputSubpacket{true, signerUserIdSubpacket, false, []byte(*sig.SignerUserId)}) + } + if sig.SigLifetimeSecs != nil && *sig.SigLifetimeSecs != 0 { + sigLifetime := make([]byte, 4) + binary.BigEndian.PutUint32(sigLifetime, *sig.SigLifetimeSecs) + subpackets = append(subpackets, outputSubpacket{true, signatureExpirationSubpacket, true, sigLifetime}) + } + + // Key flags may only appear in self-signatures or certification signatures. + + if sig.FlagsValid { + var flags byte + if sig.FlagCertify { + flags |= KeyFlagCertify + } + if sig.FlagSign { + flags |= KeyFlagSign + } + if sig.FlagEncryptCommunications { + flags |= KeyFlagEncryptCommunications + } + if sig.FlagEncryptStorage { + flags |= KeyFlagEncryptStorage + } + if sig.FlagSplitKey { + flags |= KeyFlagSplitKey + } + if sig.FlagAuthenticate { + flags |= KeyFlagAuthenticate + } + if sig.FlagGroupKey { + flags |= KeyFlagGroupKey + } + subpackets = append(subpackets, outputSubpacket{true, keyFlagsSubpacket, false, []byte{flags}}) + } + + for _, notation := range sig.Notations { + subpackets = append( + subpackets, + outputSubpacket{ + true, + notationDataSubpacket, + notation.IsCritical, + notation.getData(), + }) + } + + // The following subpackets may only appear in self-signatures. + + var features = byte(0x00) + if sig.SEIPDv1 { + features |= 0x01 + } + if sig.SEIPDv2 { + features |= 0x08 + } + + if features != 0x00 { + subpackets = append(subpackets, outputSubpacket{true, featuresSubpacket, false, []byte{features}}) + } + + if sig.TrustLevel != 0 { + subpackets = append(subpackets, outputSubpacket{true, trustSubpacket, true, []byte{byte(sig.TrustLevel), byte(sig.TrustAmount)}}) + } + + if sig.TrustRegularExpression != nil { + // RFC specifies the string should be null-terminated; add a null byte to the end + subpackets = append(subpackets, outputSubpacket{true, regularExpressionSubpacket, true, []byte(*sig.TrustRegularExpression + "\000")}) + } + + if sig.KeyLifetimeSecs != nil && *sig.KeyLifetimeSecs != 0 { + keyLifetime := make([]byte, 4) + binary.BigEndian.PutUint32(keyLifetime, *sig.KeyLifetimeSecs) + subpackets = append(subpackets, outputSubpacket{true, keyExpirationSubpacket, true, keyLifetime}) + } + + if sig.IsPrimaryId != nil && *sig.IsPrimaryId { + subpackets = append(subpackets, outputSubpacket{true, primaryUserIdSubpacket, false, []byte{1}}) + } + + if len(sig.PreferredSymmetric) > 0 { + subpackets = append(subpackets, outputSubpacket{true, prefSymmetricAlgosSubpacket, false, sig.PreferredSymmetric}) + } + + if len(sig.PreferredHash) > 0 { + subpackets = append(subpackets, outputSubpacket{true, prefHashAlgosSubpacket, false, sig.PreferredHash}) + } + + if len(sig.PreferredCompression) > 0 { + subpackets = append(subpackets, outputSubpacket{true, prefCompressionSubpacket, false, sig.PreferredCompression}) + } + + if len(sig.PolicyURI) > 0 { + subpackets = append(subpackets, outputSubpacket{true, policyUriSubpacket, false, []uint8(sig.PolicyURI)}) + } + + if len(sig.PreferredCipherSuites) > 0 { + serialized := make([]byte, len(sig.PreferredCipherSuites)*2) + for i, cipherSuite := range sig.PreferredCipherSuites { + serialized[2*i] = cipherSuite[0] + serialized[2*i+1] = cipherSuite[1] + } + subpackets = append(subpackets, outputSubpacket{true, prefCipherSuitesSubpacket, false, serialized}) + } + + // Revocation reason appears only in revocation signatures and is serialized as per section 5.2.3.23. + if sig.RevocationReason != nil { + subpackets = append(subpackets, outputSubpacket{true, reasonForRevocationSubpacket, true, + append([]uint8{uint8(*sig.RevocationReason)}, []uint8(sig.RevocationReasonText)...)}) + } + + // EmbeddedSignature appears only in subkeys capable of signing and is serialized as per section 5.2.3.26. + if sig.EmbeddedSignature != nil { + var buf bytes.Buffer + err = sig.EmbeddedSignature.serializeBody(&buf) + if err != nil { + return + } + subpackets = append(subpackets, outputSubpacket{true, embeddedSignatureSubpacket, true, buf.Bytes()}) + } + + return +} + +// AddMetadataToHashSuffix modifies the current hash suffix to include metadata +// (format, filename, and time). Version 5 keys protect this data including it +// in the hash computation. See section 5.2.4. +func (sig *Signature) AddMetadataToHashSuffix() { + if sig == nil || sig.Version != 5 { + return + } + if sig.SigType != 0x00 && sig.SigType != 0x01 { + return + } + lit := sig.Metadata + if lit == nil { + // This will translate into six 0x00 bytes. + lit = &LiteralData{} + } + + // Extract the current byte count + n := sig.HashSuffix[len(sig.HashSuffix)-8:] + l := uint64( + uint64(n[0])<<56 | uint64(n[1])<<48 | uint64(n[2])<<40 | uint64(n[3])<<32 | + uint64(n[4])<<24 | uint64(n[5])<<16 | uint64(n[6])<<8 | uint64(n[7])) + + suffix := bytes.NewBuffer(nil) + suffix.Write(sig.HashSuffix[:l]) + + // Add the metadata + var buf [4]byte + buf[0] = lit.Format + fileName := lit.FileName + if len(lit.FileName) > 255 { + fileName = fileName[:255] + } + buf[1] = byte(len(fileName)) + suffix.Write(buf[:2]) + suffix.Write([]byte(lit.FileName)) + binary.BigEndian.PutUint32(buf[:], lit.Time) + suffix.Write(buf[:]) + + // Update the counter and restore trailing bytes + l = uint64(suffix.Len()) + suffix.Write([]byte{0x05, 0xff}) + suffix.Write([]byte{ + uint8(l >> 56), uint8(l >> 48), uint8(l >> 40), uint8(l >> 32), + uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l), + }) + sig.HashSuffix = suffix.Bytes() +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go new file mode 100644 index 00000000..a8abf2ff --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go @@ -0,0 +1,303 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "bytes" + "crypto/cipher" + "crypto/sha256" + "io" + "strconv" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/s2k" + "golang.org/x/crypto/hkdf" +) + +// This is the largest session key that we'll support. Since at most 256-bit cipher +// is supported in OpenPGP, this is large enough to contain also the auth tag. +const maxSessionKeySizeInBytes = 64 + +// SymmetricKeyEncrypted represents a passphrase protected session key. See RFC +// 4880, section 5.3. +type SymmetricKeyEncrypted struct { + Version int + CipherFunc CipherFunction + Mode AEADMode + s2k func(out, in []byte) + iv []byte + encryptedKey []byte // Contains also the authentication tag for AEAD +} + +// parse parses an SymmetricKeyEncrypted packet as specified in +// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#name-symmetric-key-encrypted-ses +func (ske *SymmetricKeyEncrypted) parse(r io.Reader) error { + var buf [1]byte + + // Version + if _, err := readFull(r, buf[:]); err != nil { + return err + } + ske.Version = int(buf[0]) + if ske.Version != 4 && ske.Version != 5 { + return errors.UnsupportedError("unknown SymmetricKeyEncrypted version") + } + + if ske.Version == 5 { + // Scalar octet count + if _, err := readFull(r, buf[:]); err != nil { + return err + } + } + + // Cipher function + if _, err := readFull(r, buf[:]); err != nil { + return err + } + ske.CipherFunc = CipherFunction(buf[0]) + if !ske.CipherFunc.IsSupported() { + return errors.UnsupportedError("unknown cipher: " + strconv.Itoa(int(buf[0]))) + } + + if ske.Version == 5 { + // AEAD mode + if _, err := readFull(r, buf[:]); err != nil { + return errors.StructuralError("cannot read AEAD octet from packet") + } + ske.Mode = AEADMode(buf[0]) + + // Scalar octet count + if _, err := readFull(r, buf[:]); err != nil { + return err + } + } + + var err error + if ske.s2k, err = s2k.Parse(r); err != nil { + if _, ok := err.(errors.ErrDummyPrivateKey); ok { + return errors.UnsupportedError("missing key GNU extension in session key") + } + return err + } + + if ske.Version == 5 { + // AEAD IV + iv := make([]byte, ske.Mode.IvLength()) + _, err := readFull(r, iv) + if err != nil { + return errors.StructuralError("cannot read AEAD IV") + } + + ske.iv = iv + } + + encryptedKey := make([]byte, maxSessionKeySizeInBytes) + // The session key may follow. We just have to try and read to find + // out. If it exists then we limit it to maxSessionKeySizeInBytes. + n, err := readFull(r, encryptedKey) + if err != nil && err != io.ErrUnexpectedEOF { + return err + } + + if n != 0 { + if n == maxSessionKeySizeInBytes { + return errors.UnsupportedError("oversized encrypted session key") + } + ske.encryptedKey = encryptedKey[:n] + } + return nil +} + +// Decrypt attempts to decrypt an encrypted session key and returns the key and +// the cipher to use when decrypting a subsequent Symmetrically Encrypted Data +// packet. +func (ske *SymmetricKeyEncrypted) Decrypt(passphrase []byte) ([]byte, CipherFunction, error) { + key := make([]byte, ske.CipherFunc.KeySize()) + ske.s2k(key, passphrase) + if len(ske.encryptedKey) == 0 { + return key, ske.CipherFunc, nil + } + switch ske.Version { + case 4: + plaintextKey, cipherFunc, err := ske.decryptV4(key) + return plaintextKey, cipherFunc, err + case 5: + plaintextKey, err := ske.decryptV5(key) + return plaintextKey, CipherFunction(0), err + } + err := errors.UnsupportedError("unknown SymmetricKeyEncrypted version") + return nil, CipherFunction(0), err +} + +func (ske *SymmetricKeyEncrypted) decryptV4(key []byte) ([]byte, CipherFunction, error) { + // the IV is all zeros + iv := make([]byte, ske.CipherFunc.blockSize()) + c := cipher.NewCFBDecrypter(ske.CipherFunc.new(key), iv) + plaintextKey := make([]byte, len(ske.encryptedKey)) + c.XORKeyStream(plaintextKey, ske.encryptedKey) + cipherFunc := CipherFunction(plaintextKey[0]) + if cipherFunc.blockSize() == 0 { + return nil, ske.CipherFunc, errors.UnsupportedError( + "unknown cipher: " + strconv.Itoa(int(cipherFunc))) + } + plaintextKey = plaintextKey[1:] + if len(plaintextKey) != cipherFunc.KeySize() { + return nil, cipherFunc, errors.StructuralError( + "length of decrypted key not equal to cipher keysize") + } + return plaintextKey, cipherFunc, nil +} + +func (ske *SymmetricKeyEncrypted) decryptV5(key []byte) ([]byte, error) { + adata := []byte{0xc3, byte(5), byte(ske.CipherFunc), byte(ske.Mode)} + aead := getEncryptedKeyAeadInstance(ske.CipherFunc, ske.Mode, key, adata) + + plaintextKey, err := aead.Open(nil, ske.iv, ske.encryptedKey, adata) + if err != nil { + return nil, err + } + return plaintextKey, nil +} + +// SerializeSymmetricKeyEncrypted serializes a symmetric key packet to w. +// The packet contains a random session key, encrypted by a key derived from +// the given passphrase. The session key is returned and must be passed to +// SerializeSymmetricallyEncrypted. +// If config is nil, sensible defaults will be used. +func SerializeSymmetricKeyEncrypted(w io.Writer, passphrase []byte, config *Config) (key []byte, err error) { + cipherFunc := config.Cipher() + + sessionKey := make([]byte, cipherFunc.KeySize()) + _, err = io.ReadFull(config.Random(), sessionKey) + if err != nil { + return + } + + err = SerializeSymmetricKeyEncryptedReuseKey(w, sessionKey, passphrase, config) + if err != nil { + return + } + + key = sessionKey + return +} + +// SerializeSymmetricKeyEncryptedReuseKey serializes a symmetric key packet to w. +// The packet contains the given session key, encrypted by a key derived from +// the given passphrase. The returned session key must be passed to +// SerializeSymmetricallyEncrypted. +// If config is nil, sensible defaults will be used. +func SerializeSymmetricKeyEncryptedReuseKey(w io.Writer, sessionKey []byte, passphrase []byte, config *Config) (err error) { + var version int + if config.AEAD() != nil { + version = 5 + } else { + version = 4 + } + cipherFunc := config.Cipher() + // cipherFunc must be AES + if !cipherFunc.IsSupported() || cipherFunc < CipherAES128 || cipherFunc > CipherAES256 { + return errors.UnsupportedError("unsupported cipher: " + strconv.Itoa(int(cipherFunc))) + } + + keySize := cipherFunc.KeySize() + s2kBuf := new(bytes.Buffer) + keyEncryptingKey := make([]byte, keySize) + // s2k.Serialize salts and stretches the passphrase, and writes the + // resulting key to keyEncryptingKey and the s2k descriptor to s2kBuf. + err = s2k.Serialize(s2kBuf, keyEncryptingKey, config.Random(), passphrase, config.S2K()) + if err != nil { + return + } + s2kBytes := s2kBuf.Bytes() + + var packetLength int + switch version { + case 4: + packetLength = 2 /* header */ + len(s2kBytes) + 1 /* cipher type */ + keySize + case 5: + ivLen := config.AEAD().Mode().IvLength() + tagLen := config.AEAD().Mode().TagLength() + packetLength = 5 + len(s2kBytes) + ivLen + keySize + tagLen + } + err = serializeHeader(w, packetTypeSymmetricKeyEncrypted, packetLength) + if err != nil { + return + } + + // Symmetric Key Encrypted Version + buf := []byte{byte(version)} + + if version == 5 { + // Scalar octet count + buf = append(buf, byte(3+len(s2kBytes)+config.AEAD().Mode().IvLength())) + } + + // Cipher function + buf = append(buf, byte(cipherFunc)) + + if version == 5 { + // AEAD mode + buf = append(buf, byte(config.AEAD().Mode())) + + // Scalar octet count + buf = append(buf, byte(len(s2kBytes))) + } + _, err = w.Write(buf) + if err != nil { + return + } + _, err = w.Write(s2kBytes) + if err != nil { + return + } + + switch version { + case 4: + iv := make([]byte, cipherFunc.blockSize()) + c := cipher.NewCFBEncrypter(cipherFunc.new(keyEncryptingKey), iv) + encryptedCipherAndKey := make([]byte, keySize+1) + c.XORKeyStream(encryptedCipherAndKey, buf[1:]) + c.XORKeyStream(encryptedCipherAndKey[1:], sessionKey) + _, err = w.Write(encryptedCipherAndKey) + if err != nil { + return + } + case 5: + mode := config.AEAD().Mode() + adata := []byte{0xc3, byte(5), byte(cipherFunc), byte(mode)} + aead := getEncryptedKeyAeadInstance(cipherFunc, mode, keyEncryptingKey, adata) + + // Sample iv using random reader + iv := make([]byte, config.AEAD().Mode().IvLength()) + _, err = io.ReadFull(config.Random(), iv) + if err != nil { + return + } + // Seal and write (encryptedData includes auth. tag) + + encryptedData := aead.Seal(nil, iv, sessionKey, adata) + _, err = w.Write(iv) + if err != nil { + return + } + _, err = w.Write(encryptedData) + if err != nil { + return + } + } + + return +} + +func getEncryptedKeyAeadInstance(c CipherFunction, mode AEADMode, inputKey, associatedData []byte) (aead cipher.AEAD) { + hkdfReader := hkdf.New(sha256.New, inputKey, []byte{}, associatedData) + + encryptionKey := make([]byte, c.KeySize()) + _, _ = readFull(hkdfReader, encryptionKey) + + blockCipher := c.new(encryptionKey) + return mode.new(blockCipher) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go new file mode 100644 index 00000000..609e9fc1 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go @@ -0,0 +1,90 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "io" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +const aeadSaltSize = 32 + +// SymmetricallyEncrypted represents a symmetrically encrypted byte string. The +// encrypted Contents will consist of more OpenPGP packets. See RFC 4880, +// sections 5.7 and 5.13. +type SymmetricallyEncrypted struct { + Version int + Contents io.Reader // contains tag for version 2 + IntegrityProtected bool // If true it is type 18 (with MDC or AEAD). False is packet type 9 + + // Specific to version 1 + prefix []byte + + // Specific to version 2 + cipher CipherFunction + mode AEADMode + chunkSizeByte byte + salt [aeadSaltSize]byte +} + +const ( + symmetricallyEncryptedVersionMdc = 1 + symmetricallyEncryptedVersionAead = 2 +) + +func (se *SymmetricallyEncrypted) parse(r io.Reader) error { + if se.IntegrityProtected { + // See RFC 4880, section 5.13. + var buf [1]byte + _, err := readFull(r, buf[:]) + if err != nil { + return err + } + + switch buf[0] { + case symmetricallyEncryptedVersionMdc: + se.Version = symmetricallyEncryptedVersionMdc + case symmetricallyEncryptedVersionAead: + se.Version = symmetricallyEncryptedVersionAead + if err := se.parseAead(r); err != nil { + return err + } + default: + return errors.UnsupportedError("unknown SymmetricallyEncrypted version") + } + } + se.Contents = r + return nil +} + +// Decrypt returns a ReadCloser, from which the decrypted Contents of the +// packet can be read. An incorrect key will only be detected after trying +// to decrypt the entire data. +func (se *SymmetricallyEncrypted) Decrypt(c CipherFunction, key []byte) (io.ReadCloser, error) { + if se.Version == symmetricallyEncryptedVersionAead { + return se.decryptAead(key) + } + + return se.decryptMdc(c, key) +} + +// SerializeSymmetricallyEncrypted serializes a symmetrically encrypted packet +// to w and returns a WriteCloser to which the to-be-encrypted packets can be +// written. +// If config is nil, sensible defaults will be used. +func SerializeSymmetricallyEncrypted(w io.Writer, c CipherFunction, aeadSupported bool, cipherSuite CipherSuite, key []byte, config *Config) (Contents io.WriteCloser, err error) { + writeCloser := noOpCloser{w} + ciphertext, err := serializeStreamHeader(writeCloser, packetTypeSymmetricallyEncryptedIntegrityProtected) + if err != nil { + return + } + + if aeadSupported { + return serializeSymmetricallyEncryptedAead(ciphertext, cipherSuite, config.AEADConfig.ChunkSizeByte(), config.Random(), key) + } + + return serializeSymmetricallyEncryptedMdc(ciphertext, c, key, config) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go new file mode 100644 index 00000000..969c4223 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go @@ -0,0 +1,155 @@ +// Copyright 2023 Proton AG. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto/cipher" + "crypto/sha256" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "golang.org/x/crypto/hkdf" + "io" +) + +// parseAead parses a V2 SEIPD packet (AEAD) as specified in +// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2 +func (se *SymmetricallyEncrypted) parseAead(r io.Reader) error { + headerData := make([]byte, 3) + if n, err := io.ReadFull(r, headerData); n < 3 { + return errors.StructuralError("could not read aead header: " + err.Error()) + } + + // Cipher + se.cipher = CipherFunction(headerData[0]) + // cipherFunc must have block size 16 to use AEAD + if se.cipher.blockSize() != 16 { + return errors.UnsupportedError("invalid aead cipher: " + string(se.cipher)) + } + + // Mode + se.mode = AEADMode(headerData[1]) + if se.mode.TagLength() == 0 { + return errors.UnsupportedError("unknown aead mode: " + string(se.mode)) + } + + // Chunk size + se.chunkSizeByte = headerData[2] + if se.chunkSizeByte > 16 { + return errors.UnsupportedError("invalid aead chunk size byte: " + string(se.chunkSizeByte)) + } + + // Salt + if n, err := io.ReadFull(r, se.salt[:]); n < aeadSaltSize { + return errors.StructuralError("could not read aead salt: " + err.Error()) + } + + return nil +} + +// associatedData for chunks: tag, version, cipher, mode, chunk size byte +func (se *SymmetricallyEncrypted) associatedData() []byte { + return []byte{ + 0xD2, + symmetricallyEncryptedVersionAead, + byte(se.cipher), + byte(se.mode), + se.chunkSizeByte, + } +} + +// decryptAead decrypts a V2 SEIPD packet (AEAD) as specified in +// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2 +func (se *SymmetricallyEncrypted) decryptAead(inputKey []byte) (io.ReadCloser, error) { + aead, nonce := getSymmetricallyEncryptedAeadInstance(se.cipher, se.mode, inputKey, se.salt[:], se.associatedData()) + + // Carry the first tagLen bytes + tagLen := se.mode.TagLength() + peekedBytes := make([]byte, tagLen) + n, err := io.ReadFull(se.Contents, peekedBytes) + if n < tagLen || (err != nil && err != io.EOF) { + return nil, errors.StructuralError("not enough data to decrypt:" + err.Error()) + } + + return &aeadDecrypter{ + aeadCrypter: aeadCrypter{ + aead: aead, + chunkSize: decodeAEADChunkSize(se.chunkSizeByte), + initialNonce: nonce, + associatedData: se.associatedData(), + chunkIndex: make([]byte, 8), + packetTag: packetTypeSymmetricallyEncryptedIntegrityProtected, + }, + reader: se.Contents, + peekedBytes: peekedBytes, + }, nil +} + +// serializeSymmetricallyEncryptedAead encrypts to a writer a V2 SEIPD packet (AEAD) as specified in +// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2 +func serializeSymmetricallyEncryptedAead(ciphertext io.WriteCloser, cipherSuite CipherSuite, chunkSizeByte byte, rand io.Reader, inputKey []byte) (Contents io.WriteCloser, err error) { + // cipherFunc must have block size 16 to use AEAD + if cipherSuite.Cipher.blockSize() != 16 { + return nil, errors.InvalidArgumentError("invalid aead cipher function") + } + + if cipherSuite.Cipher.KeySize() != len(inputKey) { + return nil, errors.InvalidArgumentError("error in aead serialization: bad key length") + } + + // Data for en/decryption: tag, version, cipher, aead mode, chunk size + prefix := []byte{ + 0xD2, + symmetricallyEncryptedVersionAead, + byte(cipherSuite.Cipher), + byte(cipherSuite.Mode), + chunkSizeByte, + } + + // Write header (that correspond to prefix except first byte) + n, err := ciphertext.Write(prefix[1:]) + if err != nil || n < 4 { + return nil, err + } + + // Random salt + salt := make([]byte, aeadSaltSize) + if _, err := rand.Read(salt); err != nil { + return nil, err + } + + if _, err := ciphertext.Write(salt); err != nil { + return nil, err + } + + aead, nonce := getSymmetricallyEncryptedAeadInstance(cipherSuite.Cipher, cipherSuite.Mode, inputKey, salt, prefix) + + return &aeadEncrypter{ + aeadCrypter: aeadCrypter{ + aead: aead, + chunkSize: decodeAEADChunkSize(chunkSizeByte), + associatedData: prefix, + chunkIndex: make([]byte, 8), + initialNonce: nonce, + packetTag: packetTypeSymmetricallyEncryptedIntegrityProtected, + }, + writer: ciphertext, + }, nil +} + +func getSymmetricallyEncryptedAeadInstance(c CipherFunction, mode AEADMode, inputKey, salt, associatedData []byte) (aead cipher.AEAD, nonce []byte) { + hkdfReader := hkdf.New(sha256.New, inputKey, salt, associatedData) + + encryptionKey := make([]byte, c.KeySize()) + _, _ = readFull(hkdfReader, encryptionKey) + + // Last 64 bits of nonce are the counter + nonce = make([]byte, mode.IvLength()-8) + + _, _ = readFull(hkdfReader, nonce) + + blockCipher := c.new(encryptionKey) + aead = mode.new(blockCipher) + + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_mdc.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_mdc.go new file mode 100644 index 00000000..fa26bebe --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_mdc.go @@ -0,0 +1,256 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "crypto/cipher" + "crypto/sha1" + "crypto/subtle" + "hash" + "io" + "strconv" + + "github.com/ProtonMail/go-crypto/openpgp/errors" +) + +// seMdcReader wraps an io.Reader with a no-op Close method. +type seMdcReader struct { + in io.Reader +} + +func (ser seMdcReader) Read(buf []byte) (int, error) { + return ser.in.Read(buf) +} + +func (ser seMdcReader) Close() error { + return nil +} + +func (se *SymmetricallyEncrypted) decryptMdc(c CipherFunction, key []byte) (io.ReadCloser, error) { + if !c.IsSupported() { + return nil, errors.UnsupportedError("unsupported cipher: " + strconv.Itoa(int(c))) + } + + if len(key) != c.KeySize() { + return nil, errors.InvalidArgumentError("SymmetricallyEncrypted: incorrect key length") + } + + if se.prefix == nil { + se.prefix = make([]byte, c.blockSize()+2) + _, err := readFull(se.Contents, se.prefix) + if err != nil { + return nil, err + } + } else if len(se.prefix) != c.blockSize()+2 { + return nil, errors.InvalidArgumentError("can't try ciphers with different block lengths") + } + + ocfbResync := OCFBResync + if se.IntegrityProtected { + // MDC packets use a different form of OCFB mode. + ocfbResync = OCFBNoResync + } + + s := NewOCFBDecrypter(c.new(key), se.prefix, ocfbResync) + + plaintext := cipher.StreamReader{S: s, R: se.Contents} + + if se.IntegrityProtected { + // IntegrityProtected packets have an embedded hash that we need to check. + h := sha1.New() + h.Write(se.prefix) + return &seMDCReader{in: plaintext, h: h}, nil + } + + // Otherwise, we just need to wrap plaintext so that it's a valid ReadCloser. + return seMdcReader{plaintext}, nil +} + +const mdcTrailerSize = 1 /* tag byte */ + 1 /* length byte */ + sha1.Size + +// An seMDCReader wraps an io.Reader, maintains a running hash and keeps hold +// of the most recent 22 bytes (mdcTrailerSize). Upon EOF, those bytes form an +// MDC packet containing a hash of the previous Contents which is checked +// against the running hash. See RFC 4880, section 5.13. +type seMDCReader struct { + in io.Reader + h hash.Hash + trailer [mdcTrailerSize]byte + scratch [mdcTrailerSize]byte + trailerUsed int + error bool + eof bool +} + +func (ser *seMDCReader) Read(buf []byte) (n int, err error) { + if ser.error { + err = io.ErrUnexpectedEOF + return + } + if ser.eof { + err = io.EOF + return + } + + // If we haven't yet filled the trailer buffer then we must do that + // first. + for ser.trailerUsed < mdcTrailerSize { + n, err = ser.in.Read(ser.trailer[ser.trailerUsed:]) + ser.trailerUsed += n + if err == io.EOF { + if ser.trailerUsed != mdcTrailerSize { + n = 0 + err = io.ErrUnexpectedEOF + ser.error = true + return + } + ser.eof = true + n = 0 + return + } + + if err != nil { + n = 0 + return + } + } + + // If it's a short read then we read into a temporary buffer and shift + // the data into the caller's buffer. + if len(buf) <= mdcTrailerSize { + n, err = readFull(ser.in, ser.scratch[:len(buf)]) + copy(buf, ser.trailer[:n]) + ser.h.Write(buf[:n]) + copy(ser.trailer[:], ser.trailer[n:]) + copy(ser.trailer[mdcTrailerSize-n:], ser.scratch[:]) + if n < len(buf) { + ser.eof = true + err = io.EOF + } + return + } + + n, err = ser.in.Read(buf[mdcTrailerSize:]) + copy(buf, ser.trailer[:]) + ser.h.Write(buf[:n]) + copy(ser.trailer[:], buf[n:]) + + if err == io.EOF { + ser.eof = true + } + return +} + +// This is a new-format packet tag byte for a type 19 (Integrity Protected) packet. +const mdcPacketTagByte = byte(0x80) | 0x40 | 19 + +func (ser *seMDCReader) Close() error { + if ser.error { + return errors.ErrMDCMissing + } + + for !ser.eof { + // We haven't seen EOF so we need to read to the end + var buf [1024]byte + _, err := ser.Read(buf[:]) + if err == io.EOF { + break + } + if err != nil { + return errors.ErrMDCMissing + } + } + + ser.h.Write(ser.trailer[:2]) + + final := ser.h.Sum(nil) + if subtle.ConstantTimeCompare(final, ser.trailer[2:]) != 1 { + return errors.ErrMDCHashMismatch + } + // The hash already includes the MDC header, but we still check its value + // to confirm encryption correctness + if ser.trailer[0] != mdcPacketTagByte || ser.trailer[1] != sha1.Size { + return errors.ErrMDCMissing + } + return nil +} + +// An seMDCWriter writes through to an io.WriteCloser while maintains a running +// hash of the data written. On close, it emits an MDC packet containing the +// running hash. +type seMDCWriter struct { + w io.WriteCloser + h hash.Hash +} + +func (w *seMDCWriter) Write(buf []byte) (n int, err error) { + w.h.Write(buf) + return w.w.Write(buf) +} + +func (w *seMDCWriter) Close() (err error) { + var buf [mdcTrailerSize]byte + + buf[0] = mdcPacketTagByte + buf[1] = sha1.Size + w.h.Write(buf[:2]) + digest := w.h.Sum(nil) + copy(buf[2:], digest) + + _, err = w.w.Write(buf[:]) + if err != nil { + return + } + return w.w.Close() +} + +// noOpCloser is like an ioutil.NopCloser, but for an io.Writer. +type noOpCloser struct { + w io.Writer +} + +func (c noOpCloser) Write(data []byte) (n int, err error) { + return c.w.Write(data) +} + +func (c noOpCloser) Close() error { + return nil +} + +func serializeSymmetricallyEncryptedMdc(ciphertext io.WriteCloser, c CipherFunction, key []byte, config *Config) (Contents io.WriteCloser, err error) { + // Disallow old cipher suites + if !c.IsSupported() || c < CipherAES128 { + return nil, errors.InvalidArgumentError("invalid mdc cipher function") + } + + if c.KeySize() != len(key) { + return nil, errors.InvalidArgumentError("error in mdc serialization: bad key length") + } + + _, err = ciphertext.Write([]byte{symmetricallyEncryptedVersionMdc}) + if err != nil { + return + } + + block := c.new(key) + blockSize := block.BlockSize() + iv := make([]byte, blockSize) + _, err = config.Random().Read(iv) + if err != nil { + return + } + s, prefix := NewOCFBEncrypter(block, iv, OCFBNoResync) + _, err = ciphertext.Write(prefix) + if err != nil { + return + } + plaintext := cipher.StreamWriter{S: s, W: ciphertext} + + h := sha1.New() + h.Write(iv) + h.Write(iv[blockSize-2:]) + Contents = &seMDCWriter{w: plaintext, h: h} + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userattribute.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userattribute.go new file mode 100644 index 00000000..88ec72c6 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userattribute.go @@ -0,0 +1,101 @@ +// Copyright 2013 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "bytes" + "image" + "image/jpeg" + "io" + "io/ioutil" +) + +const UserAttrImageSubpacket = 1 + +// UserAttribute is capable of storing other types of data about a user +// beyond name, email and a text comment. In practice, user attributes are typically used +// to store a signed thumbnail photo JPEG image of the user. +// See RFC 4880, section 5.12. +type UserAttribute struct { + Contents []*OpaqueSubpacket +} + +// NewUserAttributePhoto creates a user attribute packet +// containing the given images. +func NewUserAttributePhoto(photos ...image.Image) (uat *UserAttribute, err error) { + uat = new(UserAttribute) + for _, photo := range photos { + var buf bytes.Buffer + // RFC 4880, Section 5.12.1. + data := []byte{ + 0x10, 0x00, // Little-endian image header length (16 bytes) + 0x01, // Image header version 1 + 0x01, // JPEG + 0, 0, 0, 0, // 12 reserved octets, must be all zero. + 0, 0, 0, 0, + 0, 0, 0, 0} + if _, err = buf.Write(data); err != nil { + return + } + if err = jpeg.Encode(&buf, photo, nil); err != nil { + return + } + + lengthBuf := make([]byte, 5) + n := serializeSubpacketLength(lengthBuf, len(buf.Bytes())+1) + lengthBuf = lengthBuf[:n] + + uat.Contents = append(uat.Contents, &OpaqueSubpacket{ + SubType: UserAttrImageSubpacket, + EncodedLength: lengthBuf, + Contents: buf.Bytes(), + }) + } + return +} + +// NewUserAttribute creates a new user attribute packet containing the given subpackets. +func NewUserAttribute(contents ...*OpaqueSubpacket) *UserAttribute { + return &UserAttribute{Contents: contents} +} + +func (uat *UserAttribute) parse(r io.Reader) (err error) { + // RFC 4880, section 5.13 + b, err := ioutil.ReadAll(r) + if err != nil { + return + } + uat.Contents, err = OpaqueSubpackets(b) + return +} + +// Serialize marshals the user attribute to w in the form of an OpenPGP packet, including +// header. +func (uat *UserAttribute) Serialize(w io.Writer) (err error) { + var buf bytes.Buffer + for _, sp := range uat.Contents { + err = sp.Serialize(&buf) + if err != nil { + return err + } + } + if err = serializeHeader(w, packetTypeUserAttribute, buf.Len()); err != nil { + return err + } + _, err = w.Write(buf.Bytes()) + return +} + +// ImageData returns zero or more byte slices, each containing +// JPEG File Interchange Format (JFIF), for each photo in the +// user attribute packet. +func (uat *UserAttribute) ImageData() (imageData [][]byte) { + for _, sp := range uat.Contents { + if sp.SubType == UserAttrImageSubpacket && len(sp.Contents) > 16 { + imageData = append(imageData, sp.Contents[16:]) + } + } + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userid.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userid.go new file mode 100644 index 00000000..614fbafd --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userid.go @@ -0,0 +1,167 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package packet + +import ( + "io" + "io/ioutil" + "strings" +) + +// UserId contains text that is intended to represent the name and email +// address of the key holder. See RFC 4880, section 5.11. By convention, this +// takes the form "Full Name (Comment) " +type UserId struct { + Id string // By convention, this takes the form "Full Name (Comment) " which is split out in the fields below. + + Name, Comment, Email string +} + +func hasInvalidCharacters(s string) bool { + for _, c := range s { + switch c { + case '(', ')', '<', '>', 0: + return true + } + } + return false +} + +// NewUserId returns a UserId or nil if any of the arguments contain invalid +// characters. The invalid characters are '\x00', '(', ')', '<' and '>' +func NewUserId(name, comment, email string) *UserId { + // RFC 4880 doesn't deal with the structure of userid strings; the + // name, comment and email form is just a convention. However, there's + // no convention about escaping the metacharacters and GPG just refuses + // to create user ids where, say, the name contains a '('. We mirror + // this behaviour. + + if hasInvalidCharacters(name) || hasInvalidCharacters(comment) || hasInvalidCharacters(email) { + return nil + } + + uid := new(UserId) + uid.Name, uid.Comment, uid.Email = name, comment, email + uid.Id = name + if len(comment) > 0 { + if len(uid.Id) > 0 { + uid.Id += " " + } + uid.Id += "(" + uid.Id += comment + uid.Id += ")" + } + if len(email) > 0 { + if len(uid.Id) > 0 { + uid.Id += " " + } + uid.Id += "<" + uid.Id += email + uid.Id += ">" + } + return uid +} + +func (uid *UserId) parse(r io.Reader) (err error) { + // RFC 4880, section 5.11 + b, err := ioutil.ReadAll(r) + if err != nil { + return + } + uid.Id = string(b) + uid.Name, uid.Comment, uid.Email = parseUserId(uid.Id) + return +} + +// Serialize marshals uid to w in the form of an OpenPGP packet, including +// header. +func (uid *UserId) Serialize(w io.Writer) error { + err := serializeHeader(w, packetTypeUserId, len(uid.Id)) + if err != nil { + return err + } + _, err = w.Write([]byte(uid.Id)) + return err +} + +// parseUserId extracts the name, comment and email from a user id string that +// is formatted as "Full Name (Comment) ". +func parseUserId(id string) (name, comment, email string) { + var n, c, e struct { + start, end int + } + var state int + + for offset, rune := range id { + switch state { + case 0: + // Entering name + n.start = offset + state = 1 + fallthrough + case 1: + // In name + if rune == '(' { + state = 2 + n.end = offset + } else if rune == '<' { + state = 5 + n.end = offset + } + case 2: + // Entering comment + c.start = offset + state = 3 + fallthrough + case 3: + // In comment + if rune == ')' { + state = 4 + c.end = offset + } + case 4: + // Between comment and email + if rune == '<' { + state = 5 + } + case 5: + // Entering email + e.start = offset + state = 6 + fallthrough + case 6: + // In email + if rune == '>' { + state = 7 + e.end = offset + } + default: + // After email + } + } + switch state { + case 1: + // ended in the name + n.end = len(id) + case 3: + // ended in comment + c.end = len(id) + case 6: + // ended in email + e.end = len(id) + } + + name = strings.TrimSpace(id[n.start:n.end]) + comment = strings.TrimSpace(id[c.start:c.end]) + email = strings.TrimSpace(id[e.start:e.end]) + + // RFC 2822 3.4: alternate simple form of a mailbox + if email == "" && strings.ContainsRune(name, '@') { + email = name + name = "" + } + + return +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/read.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/read.go new file mode 100644 index 00000000..8499c737 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/read.go @@ -0,0 +1,592 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package openpgp implements high level operations on OpenPGP messages. +package openpgp // import "github.com/ProtonMail/go-crypto/openpgp" + +import ( + "crypto" + _ "crypto/sha256" + _ "crypto/sha512" + "hash" + "io" + "strconv" + + "github.com/ProtonMail/go-crypto/openpgp/armor" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/packet" + _ "golang.org/x/crypto/sha3" +) + +// SignatureType is the armor type for a PGP signature. +var SignatureType = "PGP SIGNATURE" + +// readArmored reads an armored block with the given type. +func readArmored(r io.Reader, expectedType string) (body io.Reader, err error) { + block, err := armor.Decode(r) + if err != nil { + return + } + + if block.Type != expectedType { + return nil, errors.InvalidArgumentError("expected '" + expectedType + "', got: " + block.Type) + } + + return block.Body, nil +} + +// MessageDetails contains the result of parsing an OpenPGP encrypted and/or +// signed message. +type MessageDetails struct { + IsEncrypted bool // true if the message was encrypted. + EncryptedToKeyIds []uint64 // the list of recipient key ids. + IsSymmetricallyEncrypted bool // true if a passphrase could have decrypted the message. + DecryptedWith Key // the private key used to decrypt the message, if any. + IsSigned bool // true if the message is signed. + SignedByKeyId uint64 // the key id of the signer, if any. + SignedBy *Key // the key of the signer, if available. + LiteralData *packet.LiteralData // the metadata of the contents + UnverifiedBody io.Reader // the contents of the message. + + // If IsSigned is true and SignedBy is non-zero then the signature will + // be verified as UnverifiedBody is read. The signature cannot be + // checked until the whole of UnverifiedBody is read so UnverifiedBody + // must be consumed until EOF before the data can be trusted. Even if a + // message isn't signed (or the signer is unknown) the data may contain + // an authentication code that is only checked once UnverifiedBody has + // been consumed. Once EOF has been seen, the following fields are + // valid. (An authentication code failure is reported as a + // SignatureError error when reading from UnverifiedBody.) + Signature *packet.Signature // the signature packet itself. + SignatureError error // nil if the signature is good. + UnverifiedSignatures []*packet.Signature // all other unverified signature packets. + + decrypted io.ReadCloser +} + +// A PromptFunction is used as a callback by functions that may need to decrypt +// a private key, or prompt for a passphrase. It is called with a list of +// acceptable, encrypted private keys and a boolean that indicates whether a +// passphrase is usable. It should either decrypt a private key or return a +// passphrase to try. If the decrypted private key or given passphrase isn't +// correct, the function will be called again, forever. Any error returned will +// be passed up. +type PromptFunction func(keys []Key, symmetric bool) ([]byte, error) + +// A keyEnvelopePair is used to store a private key with the envelope that +// contains a symmetric key, encrypted with that key. +type keyEnvelopePair struct { + key Key + encryptedKey *packet.EncryptedKey +} + +// ReadMessage parses an OpenPGP message that may be signed and/or encrypted. +// The given KeyRing should contain both public keys (for signature +// verification) and, possibly encrypted, private keys for decrypting. +// If config is nil, sensible defaults will be used. +func ReadMessage(r io.Reader, keyring KeyRing, prompt PromptFunction, config *packet.Config) (md *MessageDetails, err error) { + var p packet.Packet + + var symKeys []*packet.SymmetricKeyEncrypted + var pubKeys []keyEnvelopePair + // Integrity protected encrypted packet: SymmetricallyEncrypted or AEADEncrypted + var edp packet.EncryptedDataPacket + + packets := packet.NewReader(r) + md = new(MessageDetails) + md.IsEncrypted = true + + // The message, if encrypted, starts with a number of packets + // containing an encrypted decryption key. The decryption key is either + // encrypted to a public key, or with a passphrase. This loop + // collects these packets. +ParsePackets: + for { + p, err = packets.Next() + if err != nil { + return nil, err + } + switch p := p.(type) { + case *packet.SymmetricKeyEncrypted: + // This packet contains the decryption key encrypted with a passphrase. + md.IsSymmetricallyEncrypted = true + symKeys = append(symKeys, p) + case *packet.EncryptedKey: + // This packet contains the decryption key encrypted to a public key. + md.EncryptedToKeyIds = append(md.EncryptedToKeyIds, p.KeyId) + switch p.Algo { + case packet.PubKeyAlgoRSA, packet.PubKeyAlgoRSAEncryptOnly, packet.PubKeyAlgoElGamal, packet.PubKeyAlgoECDH: + break + default: + continue + } + if keyring != nil { + var keys []Key + if p.KeyId == 0 { + keys = keyring.DecryptionKeys() + } else { + keys = keyring.KeysById(p.KeyId) + } + for _, k := range keys { + pubKeys = append(pubKeys, keyEnvelopePair{k, p}) + } + } + case *packet.SymmetricallyEncrypted: + if !p.IntegrityProtected && !config.AllowUnauthenticatedMessages() { + return nil, errors.UnsupportedError("message is not integrity protected") + } + edp = p + break ParsePackets + case *packet.AEADEncrypted: + edp = p + break ParsePackets + case *packet.Compressed, *packet.LiteralData, *packet.OnePassSignature: + // This message isn't encrypted. + if len(symKeys) != 0 || len(pubKeys) != 0 { + return nil, errors.StructuralError("key material not followed by encrypted message") + } + packets.Unread(p) + return readSignedMessage(packets, nil, keyring, config) + } + } + + var candidates []Key + var decrypted io.ReadCloser + + // Now that we have the list of encrypted keys we need to decrypt at + // least one of them or, if we cannot, we need to call the prompt + // function so that it can decrypt a key or give us a passphrase. +FindKey: + for { + // See if any of the keys already have a private key available + candidates = candidates[:0] + candidateFingerprints := make(map[string]bool) + + for _, pk := range pubKeys { + if pk.key.PrivateKey == nil { + continue + } + if !pk.key.PrivateKey.Encrypted { + if len(pk.encryptedKey.Key) == 0 { + errDec := pk.encryptedKey.Decrypt(pk.key.PrivateKey, config) + if errDec != nil { + continue + } + } + // Try to decrypt symmetrically encrypted + decrypted, err = edp.Decrypt(pk.encryptedKey.CipherFunc, pk.encryptedKey.Key) + if err != nil && err != errors.ErrKeyIncorrect { + return nil, err + } + if decrypted != nil { + md.DecryptedWith = pk.key + break FindKey + } + } else { + fpr := string(pk.key.PublicKey.Fingerprint[:]) + if v := candidateFingerprints[fpr]; v { + continue + } + candidates = append(candidates, pk.key) + candidateFingerprints[fpr] = true + } + } + + if len(candidates) == 0 && len(symKeys) == 0 { + return nil, errors.ErrKeyIncorrect + } + + if prompt == nil { + return nil, errors.ErrKeyIncorrect + } + + passphrase, err := prompt(candidates, len(symKeys) != 0) + if err != nil { + return nil, err + } + + // Try the symmetric passphrase first + if len(symKeys) != 0 && passphrase != nil { + for _, s := range symKeys { + key, cipherFunc, err := s.Decrypt(passphrase) + // In v4, on wrong passphrase, session key decryption is very likely to result in an invalid cipherFunc: + // only for < 5% of cases we will proceed to decrypt the data + if err == nil { + decrypted, err = edp.Decrypt(cipherFunc, key) + if err != nil { + return nil, err + } + if decrypted != nil { + break FindKey + } + } + } + } + } + + md.decrypted = decrypted + if err := packets.Push(decrypted); err != nil { + return nil, err + } + mdFinal, sensitiveParsingErr := readSignedMessage(packets, md, keyring, config) + if sensitiveParsingErr != nil { + return nil, errors.StructuralError("parsing error") + } + return mdFinal, nil +} + +// readSignedMessage reads a possibly signed message if mdin is non-zero then +// that structure is updated and returned. Otherwise a fresh MessageDetails is +// used. +func readSignedMessage(packets *packet.Reader, mdin *MessageDetails, keyring KeyRing, config *packet.Config) (md *MessageDetails, err error) { + if mdin == nil { + mdin = new(MessageDetails) + } + md = mdin + + var p packet.Packet + var h hash.Hash + var wrappedHash hash.Hash + var prevLast bool +FindLiteralData: + for { + p, err = packets.Next() + if err != nil { + return nil, err + } + switch p := p.(type) { + case *packet.Compressed: + if err := packets.Push(p.Body); err != nil { + return nil, err + } + case *packet.OnePassSignature: + if prevLast { + return nil, errors.UnsupportedError("nested signature packets") + } + + if p.IsLast { + prevLast = true + } + + h, wrappedHash, err = hashForSignature(p.Hash, p.SigType) + if err != nil { + md.SignatureError = err + } + + md.IsSigned = true + md.SignedByKeyId = p.KeyId + if keyring != nil { + keys := keyring.KeysByIdUsage(p.KeyId, packet.KeyFlagSign) + if len(keys) > 0 { + md.SignedBy = &keys[0] + } + } + case *packet.LiteralData: + md.LiteralData = p + break FindLiteralData + } + } + + if md.IsSigned && md.SignatureError == nil { + md.UnverifiedBody = &signatureCheckReader{packets, h, wrappedHash, md, config} + } else if md.decrypted != nil { + md.UnverifiedBody = checkReader{md} + } else { + md.UnverifiedBody = md.LiteralData.Body + } + + return md, nil +} + +// hashForSignature returns a pair of hashes that can be used to verify a +// signature. The signature may specify that the contents of the signed message +// should be preprocessed (i.e. to normalize line endings). Thus this function +// returns two hashes. The second should be used to hash the message itself and +// performs any needed preprocessing. +func hashForSignature(hashFunc crypto.Hash, sigType packet.SignatureType) (hash.Hash, hash.Hash, error) { + if _, ok := algorithm.HashToHashIdWithSha1(hashFunc); !ok { + return nil, nil, errors.UnsupportedError("unsupported hash function") + } + if !hashFunc.Available() { + return nil, nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashFunc))) + } + h := hashFunc.New() + + switch sigType { + case packet.SigTypeBinary: + return h, h, nil + case packet.SigTypeText: + return h, NewCanonicalTextHash(h), nil + } + + return nil, nil, errors.UnsupportedError("unsupported signature type: " + strconv.Itoa(int(sigType))) +} + +// checkReader wraps an io.Reader from a LiteralData packet. When it sees EOF +// it closes the ReadCloser from any SymmetricallyEncrypted packet to trigger +// MDC checks. +type checkReader struct { + md *MessageDetails +} + +func (cr checkReader) Read(buf []byte) (int, error) { + n, sensitiveParsingError := cr.md.LiteralData.Body.Read(buf) + if sensitiveParsingError == io.EOF { + mdcErr := cr.md.decrypted.Close() + if mdcErr != nil { + return n, mdcErr + } + return n, io.EOF + } + + if sensitiveParsingError != nil { + return n, errors.StructuralError("parsing error") + } + + return n, nil +} + +// signatureCheckReader wraps an io.Reader from a LiteralData packet and hashes +// the data as it is read. When it sees an EOF from the underlying io.Reader +// it parses and checks a trailing Signature packet and triggers any MDC checks. +type signatureCheckReader struct { + packets *packet.Reader + h, wrappedHash hash.Hash + md *MessageDetails + config *packet.Config +} + +func (scr *signatureCheckReader) Read(buf []byte) (int, error) { + n, sensitiveParsingError := scr.md.LiteralData.Body.Read(buf) + + // Hash only if required + if scr.md.SignedBy != nil { + scr.wrappedHash.Write(buf[:n]) + } + + if sensitiveParsingError == io.EOF { + var p packet.Packet + var readError error + var sig *packet.Signature + + p, readError = scr.packets.Next() + for readError == nil { + var ok bool + if sig, ok = p.(*packet.Signature); ok { + if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) { + sig.Metadata = scr.md.LiteralData + } + + // If signature KeyID matches + if scr.md.SignedBy != nil && *sig.IssuerKeyId == scr.md.SignedByKeyId { + key := scr.md.SignedBy + signatureError := key.PublicKey.VerifySignature(scr.h, sig) + if signatureError == nil { + signatureError = checkSignatureDetails(key, sig, scr.config) + } + scr.md.Signature = sig + scr.md.SignatureError = signatureError + } else { + scr.md.UnverifiedSignatures = append(scr.md.UnverifiedSignatures, sig) + } + } + + p, readError = scr.packets.Next() + } + + if scr.md.SignedBy != nil && scr.md.Signature == nil { + if scr.md.UnverifiedSignatures == nil { + scr.md.SignatureError = errors.StructuralError("LiteralData not followed by signature") + } else { + scr.md.SignatureError = errors.StructuralError("No matching signature found") + } + } + + // The SymmetricallyEncrypted packet, if any, might have an + // unsigned hash of its own. In order to check this we need to + // close that Reader. + if scr.md.decrypted != nil { + mdcErr := scr.md.decrypted.Close() + if mdcErr != nil { + return n, mdcErr + } + } + return n, io.EOF + } + + if sensitiveParsingError != nil { + return n, errors.StructuralError("parsing error") + } + + return n, nil +} + +// VerifyDetachedSignature takes a signed file and a detached signature and +// returns the signature packet and the entity the signature was signed by, +// if any, and a possible signature verification error. +// If the signer isn't known, ErrUnknownIssuer is returned. +func VerifyDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) { + var expectedHashes []crypto.Hash + return verifyDetachedSignature(keyring, signed, signature, expectedHashes, config) +} + +// VerifyDetachedSignatureAndHash performs the same actions as +// VerifyDetachedSignature and checks that the expected hash functions were used. +func VerifyDetachedSignatureAndHash(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) { + return verifyDetachedSignature(keyring, signed, signature, expectedHashes, config) +} + +// CheckDetachedSignature takes a signed file and a detached signature and +// returns the entity the signature was signed by, if any, and a possible +// signature verification error. If the signer isn't known, +// ErrUnknownIssuer is returned. +func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (signer *Entity, err error) { + var expectedHashes []crypto.Hash + return CheckDetachedSignatureAndHash(keyring, signed, signature, expectedHashes, config) +} + +// CheckDetachedSignatureAndHash performs the same actions as +// CheckDetachedSignature and checks that the expected hash functions were used. +func CheckDetachedSignatureAndHash(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (signer *Entity, err error) { + _, signer, err = verifyDetachedSignature(keyring, signed, signature, expectedHashes, config) + return +} + +func verifyDetachedSignature(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) { + var issuerKeyId uint64 + var hashFunc crypto.Hash + var sigType packet.SignatureType + var keys []Key + var p packet.Packet + + expectedHashesLen := len(expectedHashes) + packets := packet.NewReader(signature) + for { + p, err = packets.Next() + if err == io.EOF { + return nil, nil, errors.ErrUnknownIssuer + } + if err != nil { + return nil, nil, err + } + + var ok bool + sig, ok = p.(*packet.Signature) + if !ok { + return nil, nil, errors.StructuralError("non signature packet found") + } + if sig.IssuerKeyId == nil { + return nil, nil, errors.StructuralError("signature doesn't have an issuer") + } + issuerKeyId = *sig.IssuerKeyId + hashFunc = sig.Hash + sigType = sig.SigType + + for i, expectedHash := range expectedHashes { + if hashFunc == expectedHash { + break + } + if i+1 == expectedHashesLen { + return nil, nil, errors.StructuralError("hash algorithm mismatch with cleartext message headers") + } + } + + keys = keyring.KeysByIdUsage(issuerKeyId, packet.KeyFlagSign) + if len(keys) > 0 { + break + } + } + + if len(keys) == 0 { + panic("unreachable") + } + + h, wrappedHash, err := hashForSignature(hashFunc, sigType) + if err != nil { + return nil, nil, err + } + + if _, err := io.Copy(wrappedHash, signed); err != nil && err != io.EOF { + return nil, nil, err + } + + for _, key := range keys { + err = key.PublicKey.VerifySignature(h, sig) + if err == nil { + return sig, key.Entity, checkSignatureDetails(&key, sig, config) + } + } + + return nil, nil, err +} + +// CheckArmoredDetachedSignature performs the same actions as +// CheckDetachedSignature but expects the signature to be armored. +func CheckArmoredDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (signer *Entity, err error) { + body, err := readArmored(signature, SignatureType) + if err != nil { + return + } + + return CheckDetachedSignature(keyring, signed, body, config) +} + +// checkSignatureDetails returns an error if: +// - The signature (or one of the binding signatures mentioned below) +// has a unknown critical notation data subpacket +// - The primary key of the signing entity is revoked +// - The primary identity is revoked +// - The signature is expired +// - The primary key of the signing entity is expired according to the +// primary identity binding signature +// +// ... or, if the signature was signed by a subkey and: +// - The signing subkey is revoked +// - The signing subkey is expired according to the subkey binding signature +// - The signing subkey binding signature is expired +// - The signing subkey cross-signature is expired +// +// NOTE: The order of these checks is important, as the caller may choose to +// ignore ErrSignatureExpired or ErrKeyExpired errors, but should never +// ignore any other errors. +// +// TODO: Also return an error if: +// - The primary key is expired according to a direct-key signature +// - (For V5 keys only:) The direct-key signature (exists and) is expired +func checkSignatureDetails(key *Key, signature *packet.Signature, config *packet.Config) error { + now := config.Now() + primaryIdentity := key.Entity.PrimaryIdentity() + signedBySubKey := key.PublicKey != key.Entity.PrimaryKey + sigsToCheck := []*packet.Signature{signature, primaryIdentity.SelfSignature} + if signedBySubKey { + sigsToCheck = append(sigsToCheck, key.SelfSignature, key.SelfSignature.EmbeddedSignature) + } + for _, sig := range sigsToCheck { + for _, notation := range sig.Notations { + if notation.IsCritical && !config.KnownNotation(notation.Name) { + return errors.SignatureError("unknown critical notation: " + notation.Name) + } + } + } + if key.Entity.Revoked(now) || // primary key is revoked + (signedBySubKey && key.Revoked(now)) || // subkey is revoked + primaryIdentity.Revoked(now) { // primary identity is revoked + return errors.ErrKeyRevoked + } + if key.Entity.PrimaryKey.KeyExpired(primaryIdentity.SelfSignature, now) { // primary key is expired + return errors.ErrKeyExpired + } + if signedBySubKey { + if key.PublicKey.KeyExpired(key.SelfSignature, now) { // subkey is expired + return errors.ErrKeyExpired + } + } + for _, sig := range sigsToCheck { + if sig.SigExpired(now) { // any of the relevant signatures are expired + return errors.ErrSignatureExpired + } + } + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/read_write_test_data.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/read_write_test_data.go new file mode 100644 index 00000000..db6dad5c --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/read_write_test_data.go @@ -0,0 +1,274 @@ +package openpgp + +const testKey1KeyId uint64 = 0xA34D7E18C20C31BB +const testKey3KeyId uint64 = 0x338934250CCC0360 +const testKeyP256KeyId uint64 = 0xd44a2c495918513e + +const signedInput = "Signed message\nline 2\nline 3\n" +const signedTextInput = "Signed message\r\nline 2\r\nline 3\r\n" + +const recipientUnspecifiedHex = "848c0300000000000000000103ff62d4d578d03cf40c3da998dfe216c074fa6ddec5e31c197c9666ba292830d91d18716a80f699f9d897389a90e6d62d0238f5f07a5248073c0f24920e4bc4a30c2d17ee4e0cae7c3d4aaa4e8dced50e3010a80ee692175fa0385f62ecca4b56ee6e9980aa3ec51b61b077096ac9e800edaf161268593eedb6cc7027ff5cb32745d250010d407a6221ae22ef18469b444f2822478c4d190b24d36371a95cb40087cdd42d9399c3d06a53c0673349bfb607927f20d1e122bde1e2bf3aa6cae6edf489629bcaa0689539ae3b718914d88ededc3b" + +const detachedSignatureHex = "889c04000102000605024d449cd1000a0910a34d7e18c20c31bb167603ff57718d09f28a519fdc7b5a68b6a3336da04df85e38c5cd5d5bd2092fa4629848a33d85b1729402a2aab39c3ac19f9d573f773cc62c264dc924c067a79dfd8a863ae06c7c8686120760749f5fd9b1e03a64d20a7df3446ddc8f0aeadeaeba7cbaee5c1e366d65b6a0c6cc749bcb912d2f15013f812795c2e29eb7f7b77f39ce77" + +const detachedSignatureTextHex = "889c04010102000605024d449d21000a0910a34d7e18c20c31bbc8c60400a24fbef7342603a41cb1165767bd18985d015fb72fe05db42db36cfb2f1d455967f1e491194fbf6cf88146222b23bf6ffbd50d17598d976a0417d3192ff9cc0034fd00f287b02e90418bbefe609484b09231e4e7a5f3562e199bf39909ab5276c4d37382fe088f6b5c3426fc1052865da8b3ab158672d58b6264b10823dc4b39" + +const detachedSignatureDSAHex = "884604001102000605024d6c4eac000a0910338934250ccc0360f18d00a087d743d6405ed7b87755476629600b8b694a39e900a0abff8126f46faf1547c1743c37b21b4ea15b8f83" + +const detachedSignatureP256Hex = "885e0400130a0006050256e5bb00000a0910d44a2c495918513edef001009841a4f792beb0befccb35c8838a6a87d9b936beaa86db6745ddc7b045eee0cf00fd1ac1f78306b17e965935dd3f8bae4587a76587e4af231efe19cc4011a8434817" + +// The plaintext is https://www.gutenberg.org/cache/epub/1080/pg1080.txt +const modestProposalSha512 = "lbbrB1+WP3T9AaC9OQqBdOcCjgeEQadlulXsNPgVx0tyqPzDHwUugZ2gE7V0ESKAw6kAVfgkcuvfgxAAGaeHtw==" + +const testKeys1And2Hex = "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" + +const testKeys1And2PrivateHex = "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" + +const dsaElGamalTestKeysHex = "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" + +const signedMessageHex = "a3019bc0cbccc0c4b8d8b74ee2108fe16ec6d3ca490cbe362d3f8333d3f352531472538b8b13d353b97232f352158c20943157c71c16064626063656269052062e4e01987e9b6fccff4b7df3a34c534b23e679cbec3bc0f8f6e64dfb4b55fe3f8efa9ce110ddb5cd79faf1d753c51aecfa669f7e7aa043436596cccc3359cb7dd6bbe9ecaa69e5989d9e57209571edc0b2fa7f57b9b79a64ee6e99ce1371395fee92fec2796f7b15a77c386ff668ee27f6d38f0baa6c438b561657377bf6acff3c5947befd7bf4c196252f1d6e5c524d0300" + +const signedTextMessageHex = "a3019bc0cbccc8c4b8d8b74ee2108fe16ec6d36a250cbece0c178233d3f352531472538b8b13d35379b97232f352158ca0b4312f57c71c1646462606365626906a062e4e019811591798ff99bf8afee860b0d8a8c2a85c3387e3bcf0bb3b17987f2bbcfab2aa526d930cbfd3d98757184df3995c9f3e7790e36e3e9779f06089d4c64e9e47dd6202cb6e9bc73c5d11bb59fbaf89d22d8dc7cf199ddf17af96e77c5f65f9bbed56f427bd8db7af37f6c9984bf9385efaf5f184f986fb3e6adb0ecfe35bbf92d16a7aa2a344fb0bc52fb7624f0200" + +const signedEncryptedMessageHex = "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" + +const verifiedSignatureEncryptedMessageHex = "c2b304000108000605026048f6d600210910a34d7e18c20c31bb1621045fb74b1d03b1e3cb31bc2f8aa34d7e18c20c31bb9a3b0400a32ddac1af259c1b0abab0041327ea04970944401978fb647dd1cf9aba4f164e43f0d8a9389501886474bdd4a6e77f6aea945c07dfbf87743835b44cc2c39a1f9aeecfa83135abc92e18e50396f2e6a06c44e0188b0081effbfb4160d28f118d4ff73dd199a102e47cffd8c7ff2bacd83ae72b5820c021a486766dd587b5da61" + +const unverifiedSignatureEncryptedMessageHex = "c2b304000108000605026048f6d600210910a34d7e18c20c31bb1621045fb74b1d03b1e3cb31bc2f8aa34d7e18c20c31bb9a3b0400a32ddac1af259c1b0abab0041327ea04970944401978fb647dd1cf9aba4f164e43f0d8a9389501886474bdd4a6e77f6aea945c07dfbf87743835b44cc2c39a1f9aeecfa83135abc92e18e50396f2e6a06c44e0188b0081effbfb4160d28f118d4ff73dd199a102e47cffd8c7ff2bacd83ae72b5820c021a486766dd587b5da61" + +const signedEncryptedMessage2Hex = "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" + +const signatureEncryptedMessage2Hex = "c24604001102000605024dfd0166000a091033af447ccd759b09bae600a096ec5e63ecf0a403085e10f75cc3bab327663282009f51fad9df457ed8d2b70d8a73c76e0443eac0f377" + +const symmetricallyEncryptedCompressedHex = "c32e040903085a357c1a7b5614ed00cc0d1d92f428162058b3f558a0fb0980d221ebac6c97d5eda4e0fe32f6e706e94dd263012d6ca1ef8c4bbd324098225e603a10c85ebf09cbf7b5aeeb5ce46381a52edc51038b76a8454483be74e6dcd1e50d5689a8ae7eceaeefed98a0023d49b22eb1f65c2aa1ef1783bb5e1995713b0457102ec3c3075fe871267ffa4b686ad5d52000d857" + +const dsaTestKeyHex = "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" + +const dsaTestKeyPrivateHex = "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" + +const p256TestKeyHex = "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" + +const p256TestKeyPrivateHex = "94a50456e5b83813082a8648ce3d030107020304a2072cd6d21321266c758cc5b83fab0510f751cb8d91897cddb7047d8d6f185546e2107111b0a95cb8ef063c33245502af7a65f004d5919d93ee74eb71a66253fe070302f0c2bfb0b6c30f87ee1599472b8636477eab23ced13b271886a4b50ed34c9d8436af5af5b8f88921f0efba6ef8c37c459bbb88bc1c6a13bbd25c4ce9b1e97679569ee77645d469bf4b43de637f5561b424502d3235362054657374204b6579203c696e76616c6964406578616d706c652e636f6d3e8879041313080021050256e5b838021b03050b09080702061508090a0b020416020301021e01021780000a0910d44a2c495918513e54e50100dfa64f97d9b47766fc1943c6314ba3f2b2a103d71ad286dc5b1efb96a345b0c80100dbc8150b54241f559da6ef4baacea6d31902b4f4b1bdc09b34bf0502334b77549ca90456e5b83812082a8648ce3d030107020304bfe3cea9cee13486f8d518aa487fecab451f25467d2bf08e58f63e5fa525d5482133e6a79299c274b068ef0be448152ad65cf11cf764348588ca4f6a0bcf22b603010807fe0703027510012471a603cfee2968dce19f732721ddf03e966fd133b4e3c7a685b788705cbc46fb026dc94724b830c9edbaecd2fb2c662f23169516cacd1fe423f0475c364ecc10abcabcfd4bbbda1a36a1bd8861041813080009050256e5b838021b0c000a0910d44a2c495918513e4a4800ff49d589fa64024ad30be363a032e3a0e0e6f5db56ba4c73db850518bf0121b8f20100fd78e065f4c70ea5be9df319ea67e493b936fc78da834a71828043d3154af56e" + +const armoredPrivateKeyBlock = `-----BEGIN PGP PRIVATE KEY BLOCK----- +Version: GnuPG v1.4.10 (GNU/Linux) + +lQHYBE2rFNoBBADFwqWQIW/DSqcB4yCQqnAFTJ27qS5AnB46ccAdw3u4Greeu3Bp +idpoHdjULy7zSKlwR1EA873dO/k/e11Ml3dlAFUinWeejWaK2ugFP6JjiieSsrKn +vWNicdCS4HTWn0X4sjl0ZiAygw6GNhqEQ3cpLeL0g8E9hnYzJKQ0LWJa0QARAQAB +AAP/TB81EIo2VYNmTq0pK1ZXwUpxCrvAAIG3hwKjEzHcbQznsjNvPUihZ+NZQ6+X +0HCfPAdPkGDCLCb6NavcSW+iNnLTrdDnSI6+3BbIONqWWdRDYJhqZCkqmG6zqSfL +IdkJgCw94taUg5BWP/AAeQrhzjChvpMQTVKQL5mnuZbUCeMCAN5qrYMP2S9iKdnk +VANIFj7656ARKt/nf4CBzxcpHTyB8+d2CtPDKCmlJP6vL8t58Jmih+kHJMvC0dzn +gr5f5+sCAOOe5gt9e0am7AvQWhdbHVfJU0TQJx+m2OiCJAqGTB1nvtBLHdJnfdC9 +TnXXQ6ZXibqLyBies/xeY2sCKL5qtTMCAKnX9+9d/5yQxRyrQUHt1NYhaXZnJbHx +q4ytu0eWz+5i68IYUSK69jJ1NWPM0T6SkqpB3KCAIv68VFm9PxqG1KmhSrQIVGVz +dCBLZXmIuAQTAQIAIgUCTasU2gIbAwYLCQgHAwIGFQgCCQoLBBYCAwECHgECF4AA +CgkQO9o98PRieSoLhgQAkLEZex02Qt7vGhZzMwuN0R22w3VwyYyjBx+fM3JFETy1 +ut4xcLJoJfIaF5ZS38UplgakHG0FQ+b49i8dMij0aZmDqGxrew1m4kBfjXw9B/v+ +eIqpODryb6cOSwyQFH0lQkXC040pjq9YqDsO5w0WYNXYKDnzRV0p4H1pweo2VDid +AdgETasU2gEEAN46UPeWRqKHvA99arOxee38fBt2CI08iiWyI8T3J6ivtFGixSqV +bRcPxYO/qLpVe5l84Nb3X71GfVXlc9hyv7CD6tcowL59hg1E/DC5ydI8K8iEpUmK +/UnHdIY5h8/kqgGxkY/T/hgp5fRQgW1ZoZxLajVlMRZ8W4tFtT0DeA+JABEBAAEA +A/0bE1jaaZKj6ndqcw86jd+QtD1SF+Cf21CWRNeLKnUds4FRRvclzTyUMuWPkUeX +TaNNsUOFqBsf6QQ2oHUBBK4VCHffHCW4ZEX2cd6umz7mpHW6XzN4DECEzOVksXtc +lUC1j4UB91DC/RNQqwX1IV2QLSwssVotPMPqhOi0ZLNY7wIA3n7DWKInxYZZ4K+6 +rQ+POsz6brEoRHwr8x6XlHenq1Oki855pSa1yXIARoTrSJkBtn5oI+f8AzrnN0BN +oyeQAwIA/7E++3HDi5aweWrViiul9cd3rcsS0dEnksPhvS0ozCJiHsq/6GFmy7J8 +QSHZPteedBnZyNp5jR+H7cIfVN3KgwH/Skq4PsuPhDq5TKK6i8Pc1WW8MA6DXTdU +nLkX7RGmMwjC0DBf7KWAlPjFaONAX3a8ndnz//fy1q7u2l9AZwrj1qa1iJ8EGAEC +AAkFAk2rFNoCGwwACgkQO9o98PRieSo2/QP/WTzr4ioINVsvN1akKuekmEMI3LAp +BfHwatufxxP1U+3Si/6YIk7kuPB9Hs+pRqCXzbvPRrI8NHZBmc8qIGthishdCYad +AHcVnXjtxrULkQFGbGvhKURLvS9WnzD/m1K2zzwxzkPTzT9/Yf06O6Mal5AdugPL +VrM0m72/jnpKo04= +=zNCn +-----END PGP PRIVATE KEY BLOCK-----` + +const e2ePublicKey = `-----BEGIN PGP PUBLIC KEY BLOCK----- +Charset: UTF-8 + +xv8AAABSBAAAAAATCCqGSM49AwEHAgME1LRoXSpOxtHXDUdmuvzchyg6005qIBJ4 +sfaSxX7QgH9RV2ONUhC+WiayCNADq+UMzuR/vunSr4aQffXvuGnR383/AAAAFDxk +Z2lsQHlhaG9vLWluYy5jb20+wv8AAACGBBATCAA4/wAAAAWCVGvAG/8AAAACiwn/ +AAAACZC2VkQCOjdvYf8AAAAFlQgJCgv/AAAAA5YBAv8AAAACngEAAE1BAP0X8veD +24IjmI5/C6ZAfVNXxgZZFhTAACFX75jUA3oD6AEAzoSwKf1aqH6oq62qhCN/pekX ++WAsVMBhNwzLpqtCRjLO/wAAAFYEAAAAABIIKoZIzj0DAQcCAwT50ain7vXiIRv8 +B1DO3x3cE/aattZ5sHNixJzRCXi2vQIA5QmOxZ6b5jjUekNbdHG3SZi1a2Ak5mfX +fRxC/5VGAwEIB8L/AAAAZQQYEwgAGP8AAAAFglRrwBz/AAAACZC2VkQCOjdvYQAA +FJAA9isX3xtGyMLYwp2F3nXm7QEdY5bq5VUcD/RJlj792VwA/1wH0pCzVLl4Q9F9 +ex7En5r7rHR5xwX82Msc+Rq9dSyO +=7MrZ +-----END PGP PUBLIC KEY BLOCK-----` + +const dsaKeyWithSHA512 = `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` + +const unknownHashFunctionHex = `8a00000040040001990006050253863c24000a09103b4fe6acc0b21f32ffff0101010101010101010101010101010101010101010101010101010101010101010101010101` + +const rsaSignatureBadMPIlength = `8a00000040040001030006050253863c24000a09103b4fe6acc0b21f32ffff0101010101010101010101010101010101010101010101010101010101010101010101010101` + +const missingHashFunctionHex = `8a00000040040001030006050253863c24000a09103b4fe6acc0b21f32ffff0101010101010101010101010101010101010101010101010101010101010101010101010101` + +const campbellQuine = `a0b001000300fcffa0b001000d00f2ff000300fcffa0b001000d00f2ff8270a01c00000500faff8270a01c00000500faff000500faff001400ebff8270a01c00000500faff000500faff001400ebff428821c400001400ebff428821c400001400ebff428821c400001400ebff428821c400001400ebff428821c400000000ffff000000ffff000b00f4ff428821c400000000ffff000000ffff000b00f4ff0233214c40000100feff000233214c40000100feff0000` + +const keyV4forVerifyingSignedMessageV3 = `-----BEGIN PGP PUBLIC KEY BLOCK----- +Comment: GPGTools - https://gpgtools.org + +mI0EVfxoFQEEAMBIqmbDfYygcvP6Phr1wr1XI41IF7Qixqybs/foBF8qqblD9gIY +BKpXjnBOtbkcVOJ0nljd3/sQIfH4E0vQwK5/4YRQSI59eKOqd6Fx+fWQOLG+uu6z +tewpeCj9LLHvibx/Sc7VWRnrznia6ftrXxJ/wHMezSab3tnGC0YPVdGNABEBAAG0 +JEdvY3J5cHRvIFRlc3QgS2V5IDx0aGVtYXhAZ21haWwuY29tPoi5BBMBCgAjBQJV +/GgVAhsDBwsJCAcDAgEGFQgCCQoLBBYCAwECHgECF4AACgkQeXnQmhdGW9PFVAP+ +K7TU0qX5ArvIONIxh/WAweyOk884c5cE8f+3NOPOOCRGyVy0FId5A7MmD5GOQh4H +JseOZVEVCqlmngEvtHZb3U1VYtVGE5WZ+6rQhGsMcWP5qaT4soYwMBlSYxgYwQcx +YhN9qOr292f9j2Y//TTIJmZT4Oa+lMxhWdqTfX+qMgG4jQRV/GgVAQQArhFSiij1 +b+hT3dnapbEU+23Z1yTu1DfF6zsxQ4XQWEV3eR8v+8mEDDNcz8oyyF56k6UQ3rXi +UMTIwRDg4V6SbZmaFbZYCOwp/EmXJ3rfhm7z7yzXj2OFN22luuqbyVhuL7LRdB0M +pxgmjXb4tTvfgKd26x34S+QqUJ7W6uprY4sAEQEAAYifBBgBCgAJBQJV/GgVAhsM +AAoJEHl50JoXRlvT7y8D/02ckx4OMkKBZo7viyrBw0MLG92i+DC2bs35PooHR6zz +786mitjOp5z2QWNLBvxC70S0qVfCIz8jKupO1J6rq6Z8CcbLF3qjm6h1omUBf8Nd +EfXKD2/2HV6zMKVknnKzIEzauh+eCKS2CeJUSSSryap/QLVAjRnckaES/OsEWhNB +=RZia +-----END PGP PUBLIC KEY BLOCK----- +` + +const signedMessageV3 = `-----BEGIN PGP MESSAGE----- +Comment: GPGTools - https://gpgtools.org + +owGbwMvMwMVYWXlhlrhb9GXG03JJDKF/MtxDMjKLFYAoUaEktbhEITe1uDgxPVWP +q5NhKjMrWAVcC9evD8z/bF/uWNjqtk/X3y5/38XGRQHm/57rrDRYuGnTw597Xqka +uM3137/hH3Os+Jf2dc0fXOITKwJvXJvecPVs0ta+Vg7ZO1MLn8w58Xx+6L58mbka +DGHyU9yTueZE8D+QF/Tz28Y78dqtF56R1VPn9Xw4uJqrWYdd7b3vIZ1V6R4Nh05d +iT57d/OhWwA= +=hG7R +-----END PGP MESSAGE----- +` + +// https://mailarchive.ietf.org/arch/msg/openpgp/9SheW_LENE0Kxf7haNllovPyAdY/ +const v5PrivKey = `-----BEGIN PGP PRIVATE KEY BLOCK----- + +lGEFXJH05BYAAAAtCSsGAQQB2kcPAQEHQFhZlVcVVtwf+21xNQPX+ecMJJBL0MPd +fj75iux+my8QAAAAAAAiAQCHZ1SnSUmWqxEsoI6facIVZQu6mph3cBFzzTvcm5lA +Ng5ctBhlbW1hLmdvbGRtYW5AZXhhbXBsZS5uZXSIlgUTFggASCIhBRk0e8mHJGQC +X5nfPsLgAA7ZiEiS4fez6kyUAJFZVptUBQJckfTkAhsDBQsJCAcCAyICAQYVCgkI +CwIEFgIDAQIeBwIXgAAA9cAA/jiR3yMsZMeEQ40u6uzEoXa6UXeV/S3wwJAXRJy9 +M8s0AP9vuL/7AyTfFXwwzSjDnYmzS0qAhbLDQ643N+MXGBJ2BZxmBVyR9OQSAAAA +MgorBgEEAZdVAQUBAQdA+nysrzml2UCweAqtpDuncSPlvrcBWKU0yfU0YvYWWAoD +AQgHAAAAAAAiAP9OdAPppjU1WwpqjIItkxr+VPQRT8Zm/Riw7U3F6v3OiBFHiHoF +GBYIACwiIQUZNHvJhyRkAl+Z3z7C4AAO2YhIkuH3s+pMlACRWVabVAUCXJH05AIb +DAAAOSQBAP4BOOIR/sGLNMOfeb5fPs/02QMieoiSjIBnijhob2U5AQC+RtOHCHx7 +TcIYl5/Uyoi+FOvPLcNw4hOv2nwUzSSVAw== +=IiS2 +-----END PGP PRIVATE KEY BLOCK-----` + +// Generated with the above private key +const v5PrivKeyMsg = `-----BEGIN PGP MESSAGE----- +Version: OpenPGP.js v4.10.7 +Comment: https://openpgpjs.org + +xA0DAQoWGTR7yYckZAIByxF1B21zZy50eHRfbIGSdGVzdMJ3BQEWCgAGBQJf +bIGSACMiIQUZNHvJhyRkAl+Z3z7C4AAO2YhIkuH3s+pMlACRWVabVDQvAP9G +y29VPonFXqi2zKkpZrvyvZxg+n5e8Nt9wNbuxeCd3QD/TtO2s+JvjrE4Siwv +UQdl5MlBka1QSNbMq2Bz7XwNPg4= +=6lbM +-----END PGP MESSAGE-----` + +const keyWithExpiredCrossSig = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +xsDNBF2lnPIBDAC5cL9PQoQLTMuhjbYvb4Ncuuo0bfmgPRFywX53jPhoFf4Zg6mv +/seOXpgecTdOcVttfzC8ycIKrt3aQTiwOG/ctaR4Bk/t6ayNFfdUNxHWk4WCKzdz +/56fW2O0F23qIRd8UUJp5IIlN4RDdRCtdhVQIAuzvp2oVy/LaS2kxQoKvph/5pQ/ +5whqsyroEWDJoSV0yOb25B/iwk/pLUFoyhDG9bj0kIzDxrEqW+7Ba8nocQlecMF3 +X5KMN5kp2zraLv9dlBBpWW43XktjcCZgMy20SouraVma8Je/ECwUWYUiAZxLIlMv +9CurEOtxUw6N3RdOtLmYZS9uEnn5y1UkF88o8Nku890uk6BrewFzJyLAx5wRZ4F0 +qV/yq36UWQ0JB/AUGhHVPdFf6pl6eaxBwT5GXvbBUibtf8YI2og5RsgTWtXfU7eb +SGXrl5ZMpbA6mbfhd0R8aPxWfmDWiIOhBufhMCvUHh1sApMKVZnvIff9/0Dca3wb +vLIwa3T4CyshfT0AEQEAAc0hQm9iIEJhYmJhZ2UgPGJvYkBvcGVucGdwLmV4YW1w +bGU+wsEABBMBCgATBYJeO2eVAgsJAxUICgKbAQIeAQAhCRD7/MgqAV5zMBYhBNGm +bhojsYLJmA94jPv8yCoBXnMwKWUMAJ3FKZfJ2mXvh+GFqgymvK4NoKkDRPB0CbUN +aDdG7ZOizQrWXo7Da2MYIZ6eZUDqBKLdhZ5gZfVnisDfu/yeCgpENaKib1MPHpA8 +nZQjnPejbBDomNqY8HRzr5jvXNlwywBpjWGtegCKUY9xbSynjbfzIlMrWL4S+Rfl ++bOOQKRyYJWXmECmVyqY8cz2VUYmETjNcwC8VCDUxQnhtcCJ7Aej22hfYwVEPb/J +BsJBPq8WECCiGfJ9Y2y6TF+62KzG9Kfs5hqUeHhQy8V4TSi479ewwL7DH86XmIIK +chSANBS+7iyMtctjNZfmF9zYdGJFvjI/mbBR/lK66E515Inuf75XnL8hqlXuwqvG +ni+i03Aet1DzULZEIio4uIU6ioc1lGO9h7K2Xn4S7QQH1QoISNMWqXibUR0RCGjw +FsEDTt2QwJl8XXxoJCooM7BCcCQo+rMNVUHDjIwrdoQjPld3YZsUQQRcqH6bLuln +cfn5ufl8zTGWKydoj/iTz8KcjZ7w187AzQRdpZzyAQwA1jC/XGxjK6ddgrRfW9j+ +s/U00++EvIsgTs2kr3Rg0GP7FLWV0YNtR1mpl55/bEl7yAxCDTkOgPUMXcaKlnQh +6zrlt6H53mF6Bvs3inOHQvOsGtU0dqvb1vkTF0juLiJgPlM7pWv+pNQ6IA39vKoQ +sTMBv4v5vYNXP9GgKbg8inUNT17BxzZYHfw5+q63ectgDm2on1e8CIRCZ76oBVwz +dkVxoy3gjh1eENlk2D4P0uJNZzF1Q8GV67yLANGMCDICE/OkWn6daipYDzW4iJQt +YPUWP4hWhjdm+CK+hg6IQUEn2Vtvi16D2blRP8BpUNNa4fNuylWVuJV76rIHvsLZ +1pbM3LHpRgE8s6jivS3Rz3WRs0TmWCNnvHPqWizQ3VTy+r3UQVJ5AmhJDrZdZq9i +aUIuZ01PoE1+CHiJwuxPtWvVAxf2POcm1M/F1fK1J0e+lKlQuyonTXqXR22Y41wr +fP2aPk3nPSTW2DUAf3vRMZg57ZpRxLEhEMxcM4/LMR+PABEBAAHCwrIEGAEKAAkF +gl8sAVYCmwIB3QkQ+/zIKgFeczDA+qAEGQEKAAwFgl47Z5UFgwB4TOAAIQkQfC+q +Tfk8N7IWIQQd3OFfCSF87i87N2B8L6pN+Tw3st58C/0exp0X2U4LqicSHEOSqHZj +jiysdqIELHGyo5DSPv92UFPp36aqjF9OFgtNNwSa56fmAVCD4+hor/fKARRIeIjF +qdIC5Y/9a4B10NQFJa5lsvB38x/d39LI2kEoglZnqWgdJskROo3vNQF4KlIcm6FH +dn4WI8UkC5oUUcrpZVMSKoacIaxLwqnXT42nIVgYYuqrd/ZagZZjG5WlrTOd5+NI +zi/l0fWProcPHGLjmAh4Thu8i7omtVw1nQaMnq9I77ffg3cPDgXknYrLL+q8xXh/ +0mEJyIhnmPwllWCSZuLv9DrD5pOexFfdlwXhf6cLzNpW6QhXD/Tf5KrqIPr9aOv8 +9xaEEXWh0vEby2kIsI2++ft+vfdIyxYw/wKqx0awTSnuBV1rG3z1dswX4BfoY66x +Bz3KOVqlz9+mG/FTRQwrgPvR+qgLCHbuotxoGN7fzW+PI75hQG5JQAqhsC9sHjQH +UrI21/VUNwzfw3v5pYsWuFb5bdQ3ASJetICQiMy7IW8WIQTRpm4aI7GCyZgPeIz7 +/MgqAV5zMG6/C/wLpPl/9e6Hf5wmXIUwpZNQbNZvpiCcyx9sXsHXaycOQVxn3McZ +nYOUP9/mobl1tIeDQyTNbkxWjU0zzJl8XQsDZerb5098pg+x7oGIL7M1vn5s5JMl +owROourqF88JEtOBxLMxlAM7X4hB48xKQ3Hu9hS1GdnqLKki4MqRGl4l5FUwyGOM +GjyS3TzkfiDJNwQxybQiC9n57ij20ieNyLfuWCMLcNNnZUgZtnF6wCctoq/0ZIWu +a7nvuA/XC2WW9YjEJJiWdy5109pqac+qWiY11HWy/nms4gpMdxVpT0RhrKGWq4o0 +M5q3ZElOoeN70UO3OSbU5EVrG7gB1GuwF9mTHUVlV0veSTw0axkta3FGT//XfSpD +lRrCkyLzwq0M+UUHQAuYpAfobDlDdnxxOD2jm5GyTzak3GSVFfjW09QFVO6HlGp5 +01/jtzkUiS6nwoHHkfnyn0beZuR8X6KlcrzLB0VFgQFLmkSM9cSOgYhD0PTu9aHb +hW1Hj9AO8lzggBQ= +=Nt+N +-----END PGP PUBLIC KEY BLOCK----- +` + +const sigFromKeyWithExpiredCrossSig = `-----BEGIN PGP SIGNATURE----- + +wsDzBAABCgAGBYJfLAFsACEJEHwvqk35PDeyFiEEHdzhXwkhfO4vOzdgfC+qTfk8 +N7KiqwwAts4QGB7v9bABCC2qkTxJhmStC0wQMcHRcjL/qAiVnmasQWmvE9KVsdm3 +AaXd8mIx4a37/RRvr9dYrY2eE4uw72cMqPxNja2tvVXkHQvk1oEUqfkvbXs4ypKI +NyeTWjXNOTZEbg0hbm3nMy+Wv7zgB1CEvAsEboLDJlhGqPcD+X8a6CJGrBGUBUrv +KVmZr3U6vEzClz3DBLpoddCQseJRhT4YM1nKmBlZ5quh2LFgTSpajv5OsZheqt9y +EZAPbqmLhDmWRQwGzkWHKceKS7nZ/ox2WK6OS7Ob8ZGZkM64iPo6/EGj5Yc19vQN +AGiIaPEGszBBWlOpHTPhNm0LB0nMWqqaT87oNYwP8CQuuxDb6rKJ2lffCmZH27Lb +UbQZcH8J+0UhpeaiadPZxH5ATJAcenmVtVVMLVOFnm+eIlxzov9ntpgGYt8hLdXB +ITEG9mMgp3TGS9ZzSifMZ8UGtHdp9QdBg8NEVPFzDOMGxpc/Bftav7RRRuPiAER+ +7A5CBid5 +=aQkm +-----END PGP SIGNATURE----- +` + +const signedMessageWithCriticalNotation = `-----BEGIN PGP MESSAGE----- + +owGbwMvMwMH4oOW7S46CznTG09xJDDE3Wl1KUotLuDousDAwcjBYiSmyXL+48d6x +U1PSGUxcj8IUszKBVMpMaWAAAgEGZpAeh9SKxNyCnFS95PzcytRiBi5OAZjyXXzM +f8WYLqv7TXP61Sa4rqT12CI3xaN73YS2pt089f96odCKaEPnWJ3iSGmzJaW/ug10 +2Zo8Wj2k4s7t8wt4H3HtTu+y5UZfV3VOO+l//sdE/o+Lsub8FZH7/eOq7OnbNp4n +vwjE8mqJXetNMfj8r2SCyvkEnlVRYR+/mnge+ib56FdJ8uKtqSxyvgA= +=fRXs +-----END PGP MESSAGE-----` + +const criticalNotationSigner = `-----BEGIN PGP PUBLIC KEY BLOCK----- + +mI0EUmEvTgEEANyWtQQMOybQ9JltDqmaX0WnNPJeLILIM36sw6zL0nfTQ5zXSS3+ +fIF6P29lJFxpblWk02PSID5zX/DYU9/zjM2xPO8Oa4xo0cVTOTLj++Ri5mtr//f5 +GLsIXxFrBJhD/ghFsL3Op0GXOeLJ9A5bsOn8th7x6JucNKuaRB6bQbSPABEBAAG0 +JFRlc3QgTWNUZXN0aW5ndG9uIDx0ZXN0QGV4YW1wbGUuY29tPoi5BBMBAgAjBQJS +YS9OAhsvBwsJCAcDAgEGFQgCCQoLBBYCAwECHgECF4AACgkQSmNhOk1uQJQwDAP6 +AgrTyqkRlJVqz2pb46TfbDM2TDF7o9CBnBzIGoxBhlRwpqALz7z2kxBDmwpQa+ki +Bq3jZN/UosY9y8bhwMAlnrDY9jP1gdCo+H0sD48CdXybblNwaYpwqC8VSpDdTndf +9j2wE/weihGp/DAdy/2kyBCaiOY1sjhUfJ1GogF49rC4jQRSYS9OAQQA6R/PtBFa +JaT4jq10yqASk4sqwVMsc6HcifM5lSdxzExFP74naUMMyEsKHP53QxTF0Grqusag +Qg/ZtgT0CN1HUM152y7ACOdp1giKjpMzOTQClqCoclyvWOFB+L/SwGEIJf7LSCEr +woBuJifJc8xAVr0XX0JthoW+uP91eTQ3XpsAEQEAAYkBPQQYAQIACQUCUmEvTgIb +LgCoCRBKY2E6TW5AlJ0gBBkBAgAGBQJSYS9OAAoJEOCE90RsICyXuqIEANmmiRCA +SF7YK7PvFkieJNwzeK0V3F2lGX+uu6Y3Q/Zxdtwc4xR+me/CSBmsURyXTO29OWhP +GLszPH9zSJU9BdDi6v0yNprmFPX/1Ng0Abn/sCkwetvjxC1YIvTLFwtUL/7v6NS2 +bZpsUxRTg9+cSrMWWSNjiY9qUKajm1tuzPDZXAUEAMNmAN3xXN/Kjyvj2OK2ck0X +W748sl/tc3qiKPMJ+0AkMF7Pjhmh9nxqE9+QCEl7qinFqqBLjuzgUhBU4QlwX1GD +AtNTq6ihLMD5v1d82ZC7tNatdlDMGWnIdvEMCv2GZcuIqDQ9rXWs49e7tq1NncLY +hz3tYjKhoFTKEIq3y3Pp +=h/aX +-----END PGP PUBLIC KEY BLOCK-----` diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k.go new file mode 100644 index 00000000..a4369596 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k.go @@ -0,0 +1,407 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package s2k implements the various OpenPGP string-to-key transforms as +// specified in RFC 4800 section 3.7.1, and Argon2 specified in +// draft-ietf-openpgp-crypto-refresh-08 section 3.7.1.4. +package s2k // import "github.com/ProtonMail/go-crypto/openpgp/s2k" + +import ( + "crypto" + "hash" + "io" + "strconv" + + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "golang.org/x/crypto/argon2" +) + +type Mode uint8 + +// Defines the default S2KMode constants +// +// 0 (simple), 1(salted), 3(iterated), 4(argon2) +const ( + SimpleS2K Mode = 0 + SaltedS2K Mode = 1 + IteratedSaltedS2K Mode = 3 + Argon2S2K Mode = 4 + GnuS2K Mode = 101 +) + +const Argon2SaltSize int = 16 + +// Params contains all the parameters of the s2k packet +type Params struct { + // mode is the mode of s2k function. + // It can be 0 (simple), 1(salted), 3(iterated) + // 2(reserved) 100-110(private/experimental). + mode Mode + // hashId is the ID of the hash function used in any of the modes + hashId byte + // salt is a byte array to use as a salt in hashing process or argon2 + saltBytes [Argon2SaltSize]byte + // countByte is used to determine how many rounds of hashing are to + // be performed in s2k mode 3. See RFC 4880 Section 3.7.1.3. + countByte byte + // passes is a parameter in Argon2 to determine the number of iterations + // See RFC the crypto refresh Section 3.7.1.4. + passes byte + // parallelism is a parameter in Argon2 to determine the degree of paralellism + // See RFC the crypto refresh Section 3.7.1.4. + parallelism byte + // memoryExp is a parameter in Argon2 to determine the memory usage + // i.e., 2 ** memoryExp kibibytes + // See RFC the crypto refresh Section 3.7.1.4. + memoryExp byte +} + +// encodeCount converts an iterative "count" in the range 1024 to +// 65011712, inclusive, to an encoded count. The return value is the +// octet that is actually stored in the GPG file. encodeCount panics +// if i is not in the above range (encodedCount above takes care to +// pass i in the correct range). See RFC 4880 Section 3.7.7.1. +func encodeCount(i int) uint8 { + if i < 65536 || i > 65011712 { + panic("count arg i outside the required range") + } + + for encoded := 96; encoded < 256; encoded++ { + count := decodeCount(uint8(encoded)) + if count >= i { + return uint8(encoded) + } + } + + return 255 +} + +// decodeCount returns the s2k mode 3 iterative "count" corresponding to +// the encoded octet c. +func decodeCount(c uint8) int { + return (16 + int(c&15)) << (uint32(c>>4) + 6) +} + +// encodeMemory converts the Argon2 "memory" in the range parallelism*8 to +// 2**31, inclusive, to an encoded memory. The return value is the +// octet that is actually stored in the GPG file. encodeMemory panics +// if is not in the above range +// See OpenPGP crypto refresh Section 3.7.1.4. +func encodeMemory(memory uint32, parallelism uint8) uint8 { + if memory < (8 * uint32(parallelism)) || memory > uint32(2147483648) { + panic("Memory argument memory is outside the required range") + } + + for exp := 3; exp < 31; exp++ { + compare := decodeMemory(uint8(exp)) + if compare >= memory { + return uint8(exp) + } + } + + return 31 +} + +// decodeMemory computes the decoded memory in kibibytes as 2**memoryExponent +func decodeMemory(memoryExponent uint8) uint32 { + return uint32(1) << memoryExponent +} + +// Simple writes to out the result of computing the Simple S2K function (RFC +// 4880, section 3.7.1.1) using the given hash and input passphrase. +func Simple(out []byte, h hash.Hash, in []byte) { + Salted(out, h, in, nil) +} + +var zero [1]byte + +// Salted writes to out the result of computing the Salted S2K function (RFC +// 4880, section 3.7.1.2) using the given hash, input passphrase and salt. +func Salted(out []byte, h hash.Hash, in []byte, salt []byte) { + done := 0 + var digest []byte + + for i := 0; done < len(out); i++ { + h.Reset() + for j := 0; j < i; j++ { + h.Write(zero[:]) + } + h.Write(salt) + h.Write(in) + digest = h.Sum(digest[:0]) + n := copy(out[done:], digest) + done += n + } +} + +// Iterated writes to out the result of computing the Iterated and Salted S2K +// function (RFC 4880, section 3.7.1.3) using the given hash, input passphrase, +// salt and iteration count. +func Iterated(out []byte, h hash.Hash, in []byte, salt []byte, count int) { + combined := make([]byte, len(in)+len(salt)) + copy(combined, salt) + copy(combined[len(salt):], in) + + if count < len(combined) { + count = len(combined) + } + + done := 0 + var digest []byte + for i := 0; done < len(out); i++ { + h.Reset() + for j := 0; j < i; j++ { + h.Write(zero[:]) + } + written := 0 + for written < count { + if written+len(combined) > count { + todo := count - written + h.Write(combined[:todo]) + written = count + } else { + h.Write(combined) + written += len(combined) + } + } + digest = h.Sum(digest[:0]) + n := copy(out[done:], digest) + done += n + } +} + +// Argon2 writes to out the key derived from the password (in) with the Argon2 +// function (the crypto refresh, section 3.7.1.4) +func Argon2(out []byte, in []byte, salt []byte, passes uint8, paralellism uint8, memoryExp uint8) { + key := argon2.IDKey(in, salt, uint32(passes), decodeMemory(memoryExp), paralellism, uint32(len(out))) + copy(out[:], key) +} + +// Generate generates valid parameters from given configuration. +// It will enforce the Iterated and Salted or Argon2 S2K method. +func Generate(rand io.Reader, c *Config) (*Params, error) { + var params *Params + if c != nil && c.Mode() == Argon2S2K { + // handle Argon2 case + argonConfig := c.Argon2() + params = &Params{ + mode: Argon2S2K, + passes: argonConfig.Passes(), + parallelism: argonConfig.Parallelism(), + memoryExp: argonConfig.EncodedMemory(), + } + } else if c != nil && c.PassphraseIsHighEntropy && c.Mode() == SaltedS2K { // Allow SaltedS2K if PassphraseIsHighEntropy + hashId, ok := algorithm.HashToHashId(c.hash()) + if !ok { + return nil, errors.UnsupportedError("no such hash") + } + + params = &Params{ + mode: SaltedS2K, + hashId: hashId, + } + } else { // Enforce IteratedSaltedS2K method otherwise + hashId, ok := algorithm.HashToHashId(c.hash()) + if !ok { + return nil, errors.UnsupportedError("no such hash") + } + if c != nil { + c.S2KMode = IteratedSaltedS2K + } + params = &Params{ + mode: IteratedSaltedS2K, + hashId: hashId, + countByte: c.EncodedCount(), + } + } + if _, err := io.ReadFull(rand, params.salt()); err != nil { + return nil, err + } + return params, nil +} + +// Parse reads a binary specification for a string-to-key transformation from r +// and returns a function which performs that transform. If the S2K is a special +// GNU extension that indicates that the private key is missing, then the error +// returned is errors.ErrDummyPrivateKey. +func Parse(r io.Reader) (f func(out, in []byte), err error) { + params, err := ParseIntoParams(r) + if err != nil { + return nil, err + } + + return params.Function() +} + +// ParseIntoParams reads a binary specification for a string-to-key +// transformation from r and returns a struct describing the s2k parameters. +func ParseIntoParams(r io.Reader) (params *Params, err error) { + var buf [Argon2SaltSize + 3]byte + + _, err = io.ReadFull(r, buf[:1]) + if err != nil { + return + } + + params = &Params{ + mode: Mode(buf[0]), + } + + switch params.mode { + case SimpleS2K: + _, err = io.ReadFull(r, buf[:1]) + if err != nil { + return nil, err + } + params.hashId = buf[0] + return params, nil + case SaltedS2K: + _, err = io.ReadFull(r, buf[:9]) + if err != nil { + return nil, err + } + params.hashId = buf[0] + copy(params.salt(), buf[1:9]) + return params, nil + case IteratedSaltedS2K: + _, err = io.ReadFull(r, buf[:10]) + if err != nil { + return nil, err + } + params.hashId = buf[0] + copy(params.salt(), buf[1:9]) + params.countByte = buf[9] + return params, nil + case Argon2S2K: + _, err = io.ReadFull(r, buf[:Argon2SaltSize+3]) + if err != nil { + return nil, err + } + copy(params.salt(), buf[:Argon2SaltSize]) + params.passes = buf[Argon2SaltSize] + params.parallelism = buf[Argon2SaltSize+1] + params.memoryExp = buf[Argon2SaltSize+2] + return params, nil + case GnuS2K: + // This is a GNU extension. See + // https://git.gnupg.org/cgi-bin/gitweb.cgi?p=gnupg.git;a=blob;f=doc/DETAILS;h=fe55ae16ab4e26d8356dc574c9e8bc935e71aef1;hb=23191d7851eae2217ecdac6484349849a24fd94a#l1109 + if _, err = io.ReadFull(r, buf[:5]); err != nil { + return nil, err + } + params.hashId = buf[0] + if buf[1] == 'G' && buf[2] == 'N' && buf[3] == 'U' && buf[4] == 1 { + return params, nil + } + return nil, errors.UnsupportedError("GNU S2K extension") + } + + return nil, errors.UnsupportedError("S2K function") +} + +func (params *Params) Dummy() bool { + return params != nil && params.mode == GnuS2K +} + +func (params *Params) salt() []byte { + switch params.mode { + case SaltedS2K, IteratedSaltedS2K: return params.saltBytes[:8] + case Argon2S2K: return params.saltBytes[:Argon2SaltSize] + default: return nil + } +} + +func (params *Params) Function() (f func(out, in []byte), err error) { + if params.Dummy() { + return nil, errors.ErrDummyPrivateKey("dummy key found") + } + var hashObj crypto.Hash + if params.mode != Argon2S2K { + var ok bool + hashObj, ok = algorithm.HashIdToHashWithSha1(params.hashId) + if !ok { + return nil, errors.UnsupportedError("hash for S2K function: " + strconv.Itoa(int(params.hashId))) + } + if !hashObj.Available() { + return nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashObj))) + } + } + + switch params.mode { + case SimpleS2K: + f := func(out, in []byte) { + Simple(out, hashObj.New(), in) + } + + return f, nil + case SaltedS2K: + f := func(out, in []byte) { + Salted(out, hashObj.New(), in, params.salt()) + } + + return f, nil + case IteratedSaltedS2K: + f := func(out, in []byte) { + Iterated(out, hashObj.New(), in, params.salt(), decodeCount(params.countByte)) + } + + return f, nil + case Argon2S2K: + f := func(out, in []byte) { + Argon2(out, in, params.salt(), params.passes, params.parallelism, params.memoryExp) + } + return f, nil + } + + return nil, errors.UnsupportedError("S2K function") +} + +func (params *Params) Serialize(w io.Writer) (err error) { + if _, err = w.Write([]byte{uint8(params.mode)}); err != nil { + return + } + if params.mode != Argon2S2K { + if _, err = w.Write([]byte{params.hashId}); err != nil { + return + } + } + if params.Dummy() { + _, err = w.Write(append([]byte("GNU"), 1)) + return + } + if params.mode > 0 { + if _, err = w.Write(params.salt()); err != nil { + return + } + if params.mode == IteratedSaltedS2K { + _, err = w.Write([]byte{params.countByte}) + } + if params.mode == Argon2S2K { + _, err = w.Write([]byte{params.passes, params.parallelism, params.memoryExp}) + } + } + return +} + +// Serialize salts and stretches the given passphrase and writes the +// resulting key into key. It also serializes an S2K descriptor to +// w. The key stretching can be configured with c, which may be +// nil. In that case, sensible defaults will be used. +func Serialize(w io.Writer, key []byte, rand io.Reader, passphrase []byte, c *Config) error { + params, err := Generate(rand, c) + if err != nil { + return err + } + err = params.Serialize(w) + if err != nil { + return err + } + + f, err := params.Function() + if err != nil { + return err + } + f(key, passphrase) + return nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_cache.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_cache.go new file mode 100644 index 00000000..25a4442d --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_cache.go @@ -0,0 +1,26 @@ +package s2k + +// Cache stores keys derived with s2k functions from one passphrase +// to avoid recomputation if multiple items are encrypted with +// the same parameters. +type Cache map[Params][]byte + +// GetOrComputeDerivedKey tries to retrieve the key +// for the given s2k parameters from the cache. +// If there is no hit, it derives the key with the s2k function from the passphrase, +// updates the cache, and returns the key. +func (c *Cache) GetOrComputeDerivedKey(passphrase []byte, params *Params, expectedKeySize int) ([]byte, error) { + key, found := (*c)[*params] + if !found || len(key) != expectedKeySize { + var err error + derivedKey := make([]byte, expectedKeySize) + s2k, err := params.Function() + if err != nil { + return nil, err + } + s2k(derivedKey, passphrase) + (*c)[*params] = key + return derivedKey, nil + } + return key, nil +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_config.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_config.go new file mode 100644 index 00000000..b40be522 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k_config.go @@ -0,0 +1,129 @@ +package s2k + +import "crypto" + +// Config collects configuration parameters for s2k key-stretching +// transformations. A nil *Config is valid and results in all default +// values. +type Config struct { + // S2K (String to Key) mode, used for key derivation in the context of secret key encryption + // and passphrase-encrypted data. Either s2k.Argon2S2K or s2k.IteratedSaltedS2K may be used. + // If the passphrase is a high-entropy key, indicated by setting PassphraseIsHighEntropy to true, + // s2k.SaltedS2K can also be used. + // Note: Argon2 is the strongest option but not all OpenPGP implementations are compatible with it + //(pending standardisation). + // 0 (simple), 1(salted), 3(iterated), 4(argon2) + // 2(reserved) 100-110(private/experimental). + S2KMode Mode + // Only relevant if S2KMode is not set to s2k.Argon2S2K. + // Hash is the default hash function to be used. If + // nil, SHA256 is used. + Hash crypto.Hash + // Argon2 parameters for S2K (String to Key). + // Only relevant if S2KMode is set to s2k.Argon2S2K. + // If nil, default parameters are used. + // For more details on the choice of parameters, see https://tools.ietf.org/html/rfc9106#section-4. + Argon2Config *Argon2Config + // Only relevant if S2KMode is set to s2k.IteratedSaltedS2K. + // Iteration count for Iterated S2K (String to Key). It + // determines the strength of the passphrase stretching when + // the said passphrase is hashed to produce a key. S2KCount + // should be between 65536 and 65011712, inclusive. If Config + // is nil or S2KCount is 0, the value 16777216 used. Not all + // values in the above range can be represented. S2KCount will + // be rounded up to the next representable value if it cannot + // be encoded exactly. When set, it is strongly encrouraged to + // use a value that is at least 65536. See RFC 4880 Section + // 3.7.1.3. + S2KCount int + // Indicates whether the passphrase passed by the application is a + // high-entropy key (e.g. it's randomly generated or derived from + // another passphrase using a strong key derivation function). + // When true, allows the S2KMode to be s2k.SaltedS2K. + // When the passphrase is not a high-entropy key, using SaltedS2K is + // insecure, and not allowed by draft-ietf-openpgp-crypto-refresh-08. + PassphraseIsHighEntropy bool +} + +// Argon2Config stores the Argon2 parameters +// A nil *Argon2Config is valid and results in all default +type Argon2Config struct { + NumberOfPasses uint8 + DegreeOfParallelism uint8 + // The memory parameter for Argon2 specifies desired memory usage in kibibytes. + // For example memory=64*1024 sets the memory cost to ~64 MB. + Memory uint32 +} + +func (c *Config) Mode() Mode { + if c == nil { + return IteratedSaltedS2K + } + return c.S2KMode +} + +func (c *Config) hash() crypto.Hash { + if c == nil || uint(c.Hash) == 0 { + return crypto.SHA256 + } + + return c.Hash +} + +func (c *Config) Argon2() *Argon2Config { + if c == nil || c.Argon2Config == nil { + return nil + } + return c.Argon2Config +} + +// EncodedCount get encoded count +func (c *Config) EncodedCount() uint8 { + if c == nil || c.S2KCount == 0 { + return 224 // The common case. Corresponding to 16777216 + } + + i := c.S2KCount + + switch { + case i < 65536: + i = 65536 + case i > 65011712: + i = 65011712 + } + + return encodeCount(i) +} + +func (c *Argon2Config) Passes() uint8 { + if c == nil || c.NumberOfPasses == 0 { + return 3 + } + return c.NumberOfPasses +} + +func (c *Argon2Config) Parallelism() uint8 { + if c == nil || c.DegreeOfParallelism == 0 { + return 4 + } + return c.DegreeOfParallelism +} + +func (c *Argon2Config) EncodedMemory() uint8 { + if c == nil || c.Memory == 0 { + return 16 // 64 MiB of RAM + } + + memory := c.Memory + lowerBound := uint32(c.Parallelism())*8 + upperBound := uint32(2147483648) + + switch { + case memory < lowerBound: + memory = lowerBound + case memory > upperBound: + memory = upperBound + } + + return encodeMemory(memory, c.Parallelism()) +} diff --git a/vendor/github.com/ProtonMail/go-crypto/openpgp/write.go b/vendor/github.com/ProtonMail/go-crypto/openpgp/write.go new file mode 100644 index 00000000..7fdd13a3 --- /dev/null +++ b/vendor/github.com/ProtonMail/go-crypto/openpgp/write.go @@ -0,0 +1,583 @@ +// Copyright 2011 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package openpgp + +import ( + "crypto" + "hash" + "io" + "strconv" + "time" + + "github.com/ProtonMail/go-crypto/openpgp/armor" + "github.com/ProtonMail/go-crypto/openpgp/errors" + "github.com/ProtonMail/go-crypto/openpgp/internal/algorithm" + "github.com/ProtonMail/go-crypto/openpgp/packet" +) + +// DetachSign signs message with the private key from signer (which must +// already have been decrypted) and writes the signature to w. +// If config is nil, sensible defaults will be used. +func DetachSign(w io.Writer, signer *Entity, message io.Reader, config *packet.Config) error { + return detachSign(w, signer, message, packet.SigTypeBinary, config) +} + +// ArmoredDetachSign signs message with the private key from signer (which +// must already have been decrypted) and writes an armored signature to w. +// If config is nil, sensible defaults will be used. +func ArmoredDetachSign(w io.Writer, signer *Entity, message io.Reader, config *packet.Config) (err error) { + return armoredDetachSign(w, signer, message, packet.SigTypeBinary, config) +} + +// DetachSignText signs message (after canonicalising the line endings) with +// the private key from signer (which must already have been decrypted) and +// writes the signature to w. +// If config is nil, sensible defaults will be used. +func DetachSignText(w io.Writer, signer *Entity, message io.Reader, config *packet.Config) error { + return detachSign(w, signer, message, packet.SigTypeText, config) +} + +// ArmoredDetachSignText signs message (after canonicalising the line endings) +// with the private key from signer (which must already have been decrypted) +// and writes an armored signature to w. +// If config is nil, sensible defaults will be used. +func ArmoredDetachSignText(w io.Writer, signer *Entity, message io.Reader, config *packet.Config) error { + return armoredDetachSign(w, signer, message, packet.SigTypeText, config) +} + +func armoredDetachSign(w io.Writer, signer *Entity, message io.Reader, sigType packet.SignatureType, config *packet.Config) (err error) { + out, err := armor.Encode(w, SignatureType, nil) + if err != nil { + return + } + err = detachSign(out, signer, message, sigType, config) + if err != nil { + return + } + return out.Close() +} + +func detachSign(w io.Writer, signer *Entity, message io.Reader, sigType packet.SignatureType, config *packet.Config) (err error) { + signingKey, ok := signer.SigningKeyById(config.Now(), config.SigningKey()) + if !ok { + return errors.InvalidArgumentError("no valid signing keys") + } + if signingKey.PrivateKey == nil { + return errors.InvalidArgumentError("signing key doesn't have a private key") + } + if signingKey.PrivateKey.Encrypted { + return errors.InvalidArgumentError("signing key is encrypted") + } + if _, ok := algorithm.HashToHashId(config.Hash()); !ok { + return errors.InvalidArgumentError("invalid hash function") + } + + sig := createSignaturePacket(signingKey.PublicKey, sigType, config) + + h, wrappedHash, err := hashForSignature(sig.Hash, sig.SigType) + if err != nil { + return + } + if _, err = io.Copy(wrappedHash, message); err != nil { + return err + } + + err = sig.Sign(h, signingKey.PrivateKey, config) + if err != nil { + return + } + + return sig.Serialize(w) +} + +// FileHints contains metadata about encrypted files. This metadata is, itself, +// encrypted. +type FileHints struct { + // IsBinary can be set to hint that the contents are binary data. + IsBinary bool + // FileName hints at the name of the file that should be written. It's + // truncated to 255 bytes if longer. It may be empty to suggest that the + // file should not be written to disk. It may be equal to "_CONSOLE" to + // suggest the data should not be written to disk. + FileName string + // ModTime contains the modification time of the file, or the zero time if not applicable. + ModTime time.Time +} + +// SymmetricallyEncrypt acts like gpg -c: it encrypts a file with a passphrase. +// The resulting WriteCloser must be closed after the contents of the file have +// been written. +// If config is nil, sensible defaults will be used. +func SymmetricallyEncrypt(ciphertext io.Writer, passphrase []byte, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) { + if hints == nil { + hints = &FileHints{} + } + + key, err := packet.SerializeSymmetricKeyEncrypted(ciphertext, passphrase, config) + if err != nil { + return + } + + var w io.WriteCloser + cipherSuite := packet.CipherSuite{ + Cipher: config.Cipher(), + Mode: config.AEAD().Mode(), + } + w, err = packet.SerializeSymmetricallyEncrypted(ciphertext, config.Cipher(), config.AEAD() != nil, cipherSuite, key, config) + if err != nil { + return + } + + literalData := w + if algo := config.Compression(); algo != packet.CompressionNone { + var compConfig *packet.CompressionConfig + if config != nil { + compConfig = config.CompressionConfig + } + literalData, err = packet.SerializeCompressed(w, algo, compConfig) + if err != nil { + return + } + } + + var epochSeconds uint32 + if !hints.ModTime.IsZero() { + epochSeconds = uint32(hints.ModTime.Unix()) + } + return packet.SerializeLiteral(literalData, hints.IsBinary, hints.FileName, epochSeconds) +} + +// intersectPreferences mutates and returns a prefix of a that contains only +// the values in the intersection of a and b. The order of a is preserved. +func intersectPreferences(a []uint8, b []uint8) (intersection []uint8) { + var j int + for _, v := range a { + for _, v2 := range b { + if v == v2 { + a[j] = v + j++ + break + } + } + } + + return a[:j] +} + +// intersectPreferences mutates and returns a prefix of a that contains only +// the values in the intersection of a and b. The order of a is preserved. +func intersectCipherSuites(a [][2]uint8, b [][2]uint8) (intersection [][2]uint8) { + var j int + for _, v := range a { + for _, v2 := range b { + if v[0] == v2[0] && v[1] == v2[1] { + a[j] = v + j++ + break + } + } + } + + return a[:j] +} + +func hashToHashId(h crypto.Hash) uint8 { + v, ok := algorithm.HashToHashId(h) + if !ok { + panic("tried to convert unknown hash") + } + return v +} + +// EncryptText encrypts a message to a number of recipients and, optionally, +// signs it. Optional information is contained in 'hints', also encrypted, that +// aids the recipients in processing the message. The resulting WriteCloser +// must be closed after the contents of the file have been written. If config +// is nil, sensible defaults will be used. The signing is done in text mode. +func EncryptText(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) { + return encrypt(ciphertext, ciphertext, to, signed, hints, packet.SigTypeText, config) +} + +// Encrypt encrypts a message to a number of recipients and, optionally, signs +// it. hints contains optional information, that is also encrypted, that aids +// the recipients in processing the message. The resulting WriteCloser must +// be closed after the contents of the file have been written. +// If config is nil, sensible defaults will be used. +func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) { + return encrypt(ciphertext, ciphertext, to, signed, hints, packet.SigTypeBinary, config) +} + +// EncryptSplit encrypts a message to a number of recipients and, optionally, signs +// it. hints contains optional information, that is also encrypted, that aids +// the recipients in processing the message. The resulting WriteCloser must +// be closed after the contents of the file have been written. +// If config is nil, sensible defaults will be used. +func EncryptSplit(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) { + return encrypt(keyWriter, dataWriter, to, signed, hints, packet.SigTypeBinary, config) +} + +// EncryptTextSplit encrypts a message to a number of recipients and, optionally, signs +// it. hints contains optional information, that is also encrypted, that aids +// the recipients in processing the message. The resulting WriteCloser must +// be closed after the contents of the file have been written. +// If config is nil, sensible defaults will be used. +func EncryptTextSplit(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) { + return encrypt(keyWriter, dataWriter, to, signed, hints, packet.SigTypeText, config) +} + +// writeAndSign writes the data as a payload package and, optionally, signs +// it. hints contains optional information, that is also encrypted, +// that aids the recipients in processing the message. The resulting +// WriteCloser must be closed after the contents of the file have been +// written. If config is nil, sensible defaults will be used. +func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entity, hints *FileHints, sigType packet.SignatureType, config *packet.Config) (plaintext io.WriteCloser, err error) { + var signer *packet.PrivateKey + if signed != nil { + signKey, ok := signed.SigningKeyById(config.Now(), config.SigningKey()) + if !ok { + return nil, errors.InvalidArgumentError("no valid signing keys") + } + signer = signKey.PrivateKey + if signer == nil { + return nil, errors.InvalidArgumentError("no private key in signing key") + } + if signer.Encrypted { + return nil, errors.InvalidArgumentError("signing key must be decrypted") + } + } + + var hash crypto.Hash + for _, hashId := range candidateHashes { + if h, ok := algorithm.HashIdToHash(hashId); ok && h.Available() { + hash = h + break + } + } + + // If the hash specified by config is a candidate, we'll use that. + if configuredHash := config.Hash(); configuredHash.Available() { + for _, hashId := range candidateHashes { + if h, ok := algorithm.HashIdToHash(hashId); ok && h == configuredHash { + hash = h + break + } + } + } + + if hash == 0 { + hashId := candidateHashes[0] + name, ok := algorithm.HashIdToString(hashId) + if !ok { + name = "#" + strconv.Itoa(int(hashId)) + } + return nil, errors.InvalidArgumentError("cannot encrypt because no candidate hash functions are compiled in. (Wanted " + name + " in this case.)") + } + + if signer != nil { + ops := &packet.OnePassSignature{ + SigType: sigType, + Hash: hash, + PubKeyAlgo: signer.PubKeyAlgo, + KeyId: signer.KeyId, + IsLast: true, + } + if err := ops.Serialize(payload); err != nil { + return nil, err + } + } + + if hints == nil { + hints = &FileHints{} + } + + w := payload + if signer != nil { + // If we need to write a signature packet after the literal + // data then we need to stop literalData from closing + // encryptedData. + w = noOpCloser{w} + + } + var epochSeconds uint32 + if !hints.ModTime.IsZero() { + epochSeconds = uint32(hints.ModTime.Unix()) + } + literalData, err := packet.SerializeLiteral(w, hints.IsBinary, hints.FileName, epochSeconds) + if err != nil { + return nil, err + } + + if signer != nil { + h, wrappedHash, err := hashForSignature(hash, sigType) + if err != nil { + return nil, err + } + metadata := &packet.LiteralData{ + Format: 't', + FileName: hints.FileName, + Time: epochSeconds, + } + if hints.IsBinary { + metadata.Format = 'b' + } + return signatureWriter{payload, literalData, hash, wrappedHash, h, signer, sigType, config, metadata}, nil + } + return literalData, nil +} + +// encrypt encrypts a message to a number of recipients and, optionally, signs +// it. hints contains optional information, that is also encrypted, that aids +// the recipients in processing the message. The resulting WriteCloser must +// be closed after the contents of the file have been written. +// If config is nil, sensible defaults will be used. +func encrypt(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, sigType packet.SignatureType, config *packet.Config) (plaintext io.WriteCloser, err error) { + if len(to) == 0 { + return nil, errors.InvalidArgumentError("no encryption recipient provided") + } + + // These are the possible ciphers that we'll use for the message. + candidateCiphers := []uint8{ + uint8(packet.CipherAES256), + uint8(packet.CipherAES128), + } + + // These are the possible hash functions that we'll use for the signature. + candidateHashes := []uint8{ + hashToHashId(crypto.SHA256), + hashToHashId(crypto.SHA384), + hashToHashId(crypto.SHA512), + hashToHashId(crypto.SHA3_256), + hashToHashId(crypto.SHA3_512), + } + + // Prefer GCM if everyone supports it + candidateCipherSuites := [][2]uint8{ + {uint8(packet.CipherAES256), uint8(packet.AEADModeGCM)}, + {uint8(packet.CipherAES256), uint8(packet.AEADModeEAX)}, + {uint8(packet.CipherAES256), uint8(packet.AEADModeOCB)}, + {uint8(packet.CipherAES128), uint8(packet.AEADModeGCM)}, + {uint8(packet.CipherAES128), uint8(packet.AEADModeEAX)}, + {uint8(packet.CipherAES128), uint8(packet.AEADModeOCB)}, + } + + candidateCompression := []uint8{ + uint8(packet.CompressionNone), + uint8(packet.CompressionZIP), + uint8(packet.CompressionZLIB), + } + + encryptKeys := make([]Key, len(to)) + + // AEAD is used only if config enables it and every key supports it + aeadSupported := config.AEAD() != nil + + for i := range to { + var ok bool + encryptKeys[i], ok = to[i].EncryptionKey(config.Now()) + if !ok { + return nil, errors.InvalidArgumentError("cannot encrypt a message to key id " + strconv.FormatUint(to[i].PrimaryKey.KeyId, 16) + " because it has no valid encryption keys") + } + + sig := to[i].PrimaryIdentity().SelfSignature + if !sig.SEIPDv2 { + aeadSupported = false + } + + candidateCiphers = intersectPreferences(candidateCiphers, sig.PreferredSymmetric) + candidateHashes = intersectPreferences(candidateHashes, sig.PreferredHash) + candidateCipherSuites = intersectCipherSuites(candidateCipherSuites, sig.PreferredCipherSuites) + candidateCompression = intersectPreferences(candidateCompression, sig.PreferredCompression) + } + + // In the event that the intersection of supported algorithms is empty we use the ones + // labelled as MUST that every implementation supports. + if len(candidateCiphers) == 0 { + // https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.3 + candidateCiphers = []uint8{uint8(packet.CipherAES128)} + } + if len(candidateHashes) == 0 { + // https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#hash-algos + candidateHashes = []uint8{hashToHashId(crypto.SHA256)} + } + if len(candidateCipherSuites) == 0 { + // https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.6 + candidateCipherSuites = [][2]uint8{{uint8(packet.CipherAES128), uint8(packet.AEADModeOCB)}} + } + + cipher := packet.CipherFunction(candidateCiphers[0]) + aeadCipherSuite := packet.CipherSuite{ + Cipher: packet.CipherFunction(candidateCipherSuites[0][0]), + Mode: packet.AEADMode(candidateCipherSuites[0][1]), + } + + // If the cipher specified by config is a candidate, we'll use that. + configuredCipher := config.Cipher() + for _, c := range candidateCiphers { + cipherFunc := packet.CipherFunction(c) + if cipherFunc == configuredCipher { + cipher = cipherFunc + break + } + } + + symKey := make([]byte, cipher.KeySize()) + if _, err := io.ReadFull(config.Random(), symKey); err != nil { + return nil, err + } + + for _, key := range encryptKeys { + if err := packet.SerializeEncryptedKey(keyWriter, key.PublicKey, cipher, symKey, config); err != nil { + return nil, err + } + } + + var payload io.WriteCloser + payload, err = packet.SerializeSymmetricallyEncrypted(dataWriter, cipher, aeadSupported, aeadCipherSuite, symKey, config) + if err != nil { + return + } + + payload, err = handleCompression(payload, candidateCompression, config) + if err != nil { + return nil, err + } + + return writeAndSign(payload, candidateHashes, signed, hints, sigType, config) +} + +// Sign signs a message. The resulting WriteCloser must be closed after the +// contents of the file have been written. hints contains optional information +// that aids the recipients in processing the message. +// If config is nil, sensible defaults will be used. +func Sign(output io.Writer, signed *Entity, hints *FileHints, config *packet.Config) (input io.WriteCloser, err error) { + if signed == nil { + return nil, errors.InvalidArgumentError("no signer provided") + } + + // These are the possible hash functions that we'll use for the signature. + candidateHashes := []uint8{ + hashToHashId(crypto.SHA256), + hashToHashId(crypto.SHA384), + hashToHashId(crypto.SHA512), + hashToHashId(crypto.SHA3_256), + hashToHashId(crypto.SHA3_512), + } + defaultHashes := candidateHashes[0:1] + preferredHashes := signed.PrimaryIdentity().SelfSignature.PreferredHash + if len(preferredHashes) == 0 { + preferredHashes = defaultHashes + } + candidateHashes = intersectPreferences(candidateHashes, preferredHashes) + if len(candidateHashes) == 0 { + return nil, errors.InvalidArgumentError("cannot sign because signing key shares no common algorithms with candidate hashes") + } + + return writeAndSign(noOpCloser{output}, candidateHashes, signed, hints, packet.SigTypeBinary, config) +} + +// signatureWriter hashes the contents of a message while passing it along to +// literalData. When closed, it closes literalData, writes a signature packet +// to encryptedData and then also closes encryptedData. +type signatureWriter struct { + encryptedData io.WriteCloser + literalData io.WriteCloser + hashType crypto.Hash + wrappedHash hash.Hash + h hash.Hash + signer *packet.PrivateKey + sigType packet.SignatureType + config *packet.Config + metadata *packet.LiteralData // V5 signatures protect document metadata +} + +func (s signatureWriter) Write(data []byte) (int, error) { + s.wrappedHash.Write(data) + switch s.sigType { + case packet.SigTypeBinary: + return s.literalData.Write(data) + case packet.SigTypeText: + flag := 0 + return writeCanonical(s.literalData, data, &flag) + } + return 0, errors.UnsupportedError("unsupported signature type: " + strconv.Itoa(int(s.sigType))) +} + +func (s signatureWriter) Close() error { + sig := createSignaturePacket(&s.signer.PublicKey, s.sigType, s.config) + sig.Hash = s.hashType + sig.Metadata = s.metadata + + if err := sig.Sign(s.h, s.signer, s.config); err != nil { + return err + } + if err := s.literalData.Close(); err != nil { + return err + } + if err := sig.Serialize(s.encryptedData); err != nil { + return err + } + return s.encryptedData.Close() +} + +func createSignaturePacket(signer *packet.PublicKey, sigType packet.SignatureType, config *packet.Config) *packet.Signature { + sigLifetimeSecs := config.SigLifetime() + return &packet.Signature{ + Version: signer.Version, + SigType: sigType, + PubKeyAlgo: signer.PubKeyAlgo, + Hash: config.Hash(), + CreationTime: config.Now(), + IssuerKeyId: &signer.KeyId, + IssuerFingerprint: signer.Fingerprint, + Notations: config.Notations(), + SigLifetimeSecs: &sigLifetimeSecs, + } +} + +// noOpCloser is like an ioutil.NopCloser, but for an io.Writer. +// TODO: we have two of these in OpenPGP packages alone. This probably needs +// to be promoted somewhere more common. +type noOpCloser struct { + w io.Writer +} + +func (c noOpCloser) Write(data []byte) (n int, err error) { + return c.w.Write(data) +} + +func (c noOpCloser) Close() error { + return nil +} + +func handleCompression(compressed io.WriteCloser, candidateCompression []uint8, config *packet.Config) (data io.WriteCloser, err error) { + data = compressed + confAlgo := config.Compression() + if confAlgo == packet.CompressionNone { + return + } + + // Set algorithm labelled as MUST as fallback + // https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.4 + finalAlgo := packet.CompressionNone + // if compression specified by config available we will use it + for _, c := range candidateCompression { + if uint8(confAlgo) == c { + finalAlgo = confAlgo + break + } + } + + if finalAlgo != packet.CompressionNone { + var compConfig *packet.CompressionConfig + if config != nil { + compConfig = config.CompressionConfig + } + data, err = packet.SerializeCompressed(compressed, finalAlgo, compConfig) + if err != nil { + return + } + } + return data, nil +} diff --git a/vendor/github.com/cloudflare/circl/LICENSE b/vendor/github.com/cloudflare/circl/LICENSE new file mode 100644 index 00000000..67edaa90 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/LICENSE @@ -0,0 +1,57 @@ +Copyright (c) 2019 Cloudflare. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Cloudflare nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +======================================================================== + +Copyright (c) 2009 The Go Authors. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Google Inc. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go new file mode 100644 index 00000000..f9057c2b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go @@ -0,0 +1,96 @@ +package x25519 + +import ( + fp "github.com/cloudflare/circl/math/fp25519" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + fp.SetOne(&w[1]) // x1 = 1 + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e, + 0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb, + 0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad, + 0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 255 + const h = 3 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 255 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [5]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve25519 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) point of order 4 on Curve25519 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (x,_,1) first point of order 8 on Curve25519 */ + 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, + 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, + 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, + 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, + }, + { /* (x,_,1) second point of order 8 on Curve25519 */ + 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, + 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, + 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, + 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, + }, + { /* (-1,_,1) a point of order 4 on the twist of Curve25519 */ + 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go new file mode 100644 index 00000000..8a3d54c5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go @@ -0,0 +1,30 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package x25519 + +import ( + fp "github.com/cloudflare/circl/math/fp25519" + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h new file mode 100644 index 00000000..8c1ae4d0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s new file mode 100644 index 00000000..b7723185 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s @@ -0,0 +1,156 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp25519 package +#include "../../math/fp25519/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve25519 +#define CTE_A24 121666 + +#define Size 32 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R13, FLAGS +// Instr: x86_64, cmov +#define multiplyA24Leg(z,x) \ + MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \ + MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \ + MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \ + MOVL $CTE_A24, AX; MULQ 24+x; \ + ADDQ R12, R9; \ + ADCQ R13, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R12, FLAGS +// Instr: x86_64, cmov, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R10; \ + MULXQ 8+x, R9, R11; ADDQ R10, R9; \ + MULXQ 16+x, R10, AX; ADCQ R11, R10; \ + MULXQ 24+x, R11, R12; ADCQ AX, R11; \ + ;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \ + MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ DX, R12; \ + ADDQ R12, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, R12; \ + CMOVQCS DX, R12; \ + ADDQ R12, R8; MOVQ R8, 0+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp255.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + + +// func ladderStepAmd64(w *[5]fp255.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(w *[5]fp255.Elt, b uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// w = (mu,x1,z1,x2,z2) are five fp.Elt, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp255.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go new file mode 100644 index 00000000..dae67ea3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go @@ -0,0 +1,85 @@ +package x25519 + +import ( + "encoding/binary" + "math/bits" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +func doubleGeneric(x, z *fp.Elt) { + t0, t1 := &fp.Elt{}, &fp.Elt{} + fp.AddSub(x, z) + fp.Sqr(x, x) + fp.Sqr(z, z) + fp.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z) + fp.Mul(x, x, z) + fp.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp.Cswap(x1, x2, b) + fp.Cswap(z1, z2, b) + fp.AddSub(x1, z1) + fp.Mul(z1, z1, mu) + fp.AddSub(x1, z1) + fp.Sqr(x1, x1) + fp.Sqr(z1, z1) + fp.Mul(x1, x1, z2) + fp.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp.Elt{} + t1 := &fp.Elt{} + fp.AddSub(x2, z2) + fp.AddSub(x3, z3) + fp.Mul(t0, x2, z3) + fp.Mul(t1, x3, z2) + fp.AddSub(t0, t1) + fp.Cmov(x2, x3, b) + fp.Cmov(z2, z3, b) + fp.Sqr(x3, t0) + fp.Sqr(z3, t1) + fp.Mul(z3, x1, z3) + fp.Sqr(x2, x2) + fp.Sqr(z2, z2) + fp.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z2) + fp.Mul(x2, x2, z2) + fp.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp.Elt) { + const A24 = 121666 + const n = 8 + var xx [4]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + + var c3 uint64 + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, 0, c2) + xx[0], _ = bits.Add64(l0, (-c3)&38, 0) + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go new file mode 100644 index 00000000..07fab97d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go @@ -0,0 +1,11 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package x25519 + +import fp "github.com/cloudflare/circl/math/fp25519" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/doc.go b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go new file mode 100644 index 00000000..3ce102d1 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go @@ -0,0 +1,19 @@ +/* +Package x25519 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) +*/ +package x25519 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/key.go b/vendor/github.com/cloudflare/circl/dh/x25519/key.go new file mode 100644 index 00000000..c76f72ac --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/key.go @@ -0,0 +1,47 @@ +package x25519 + +import ( + "crypto/subtle" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +// Size is the length in bytes of a X25519 key. +const Size = 32 + +// Key represents a X25519 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 248 + k[31] = (k[31] & 127) | 64 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + var isLowOrder int + for _, P := range lowOrderPoints { + isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:]) + } + return isLowOrder == 0 +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + validPk[31] &= (1 << (255 % 8)) - 1 + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/table.go b/vendor/github.com/cloudflare/circl/dh/x25519/table.go new file mode 100644 index 00000000..28c8c4ac --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/table.go @@ -0,0 +1,268 @@ +package x25519 + +import "github.com/cloudflare/circl/math/fp25519" + +// tableGenerator contains the set of points: +// +// t[i] = (xi+1)/(xi-1), +// +// where (xi,yi) = 2^iG and G is the generator point +// Size = (256)*(256/8) = 8192 bytes. +var tableGenerator = [256 * fp25519.Size]byte{ + /* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f, + /* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51, + /* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b, + /* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30, + /* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17, + /* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c, + /* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29, + /* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69, + /* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a, + /* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d, + /* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d, + /* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75, + /* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75, + /* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e, + /* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f, + /* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37, + /* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41, + /* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d, + /* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20, + /* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51, + /* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a, + /* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61, + /* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29, + /* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d, + /* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31, + /* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02, + /* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f, + /* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23, + /* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18, + /* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27, + /* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60, + /* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79, + /* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13, + /* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f, + /* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74, + /* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f, + /* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23, + /* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29, + /* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40, + /* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a, + /* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26, + /* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d, + /* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39, + /* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48, + /* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07, + /* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70, + /* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62, + /* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26, + /* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37, + /* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32, + /* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d, + /* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26, + /* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a, + /* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c, + /* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f, + /* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a, + /* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25, + /* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e, + /* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75, + /* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77, + /* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b, + /* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c, + /* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61, + /* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44, + /* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a, + /* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69, + /* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49, + /* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e, + /* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59, + /* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44, + /* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79, + /* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f, + /* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e, + /* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e, + /* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56, + /* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04, + /* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22, + /* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61, + /* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29, + /* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a, + /* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f, + /* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68, + /* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c, + /* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61, + /* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14, + /* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f, + /* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34, + /* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e, + /* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01, + /* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c, + /* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23, + /* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a, + /* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b, + /* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18, + /* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c, + /* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72, + /* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b, + /* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40, + /* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00, + /* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45, + /* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e, + /* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70, + /* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37, + /* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09, + /* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62, + /* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a, + /* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13, + /* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f, + /* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66, + /* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04, + /* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47, + /* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48, + /* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31, + /* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56, + /* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22, + /* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77, + /* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a, + /* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32, + /* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25, + /* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e, + /* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67, + /* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68, + /* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e, + /* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d, + /* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48, + /* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47, + /* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a, + /* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c, + /* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26, + /* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c, + /* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72, + /* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c, + /* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06, + /* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11, + /* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10, + /* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b, + /* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b, + /* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50, + /* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15, + /* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c, + /* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35, + /* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f, + /* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61, + /* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e, + /* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66, + /* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d, + /* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a, + /* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76, + /* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02, + /* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35, + /* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d, + /* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f, + /* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52, + /* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07, + /* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a, + /* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77, + /* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34, + /* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c, + /* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d, + /* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58, + /* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30, + /* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28, + /* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a, + /* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60, + /* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74, + /* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67, + /* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48, + /* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e, + /* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58, + /* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f, + /* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27, + /* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b, + /* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74, + /* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06, + /* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63, + /* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b, + /* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a, + /* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a, + /* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f, + /* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f, + /* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29, + /* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07, + /* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f, + /* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d, + /* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44, + /* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21, + /* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e, + /* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49, + /* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56, + /* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59, + /* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c, + /* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61, + /* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d, + /* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09, + /* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e, + /* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f, + /* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c, + /* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58, + /* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53, + /* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72, + /* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58, + /* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e, + /* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d, + /* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c, + /* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07, + /* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59, + /* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e, + /* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18, + /* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e, + /* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51, + /* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54, + /* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22, + /* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43, + /* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e, + /* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43, + /* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e, + /* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69, + /* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09, + /* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42, + /* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49, + /* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53, + /* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25, + /* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51, + /* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71, + /* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48, + /* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07, + /* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c, + /* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33, + /* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27, + /* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78, + /* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50, + /* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53, + /* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a, + /* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78, + /* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48, + /* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41, + /* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16, + /* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31, + /* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05, + /* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70, + /* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e, + /* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60, + /* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52, + /* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f, + /* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25, + /* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46, + /* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f, + /* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b, + /* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31, + /* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b, + /* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d, + /* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02, + /* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05, + /* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79, + /* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b, + /* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve.go b/vendor/github.com/cloudflare/circl/dh/x448/curve.go new file mode 100644 index 00000000..d59564e4 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve.go @@ -0,0 +1,104 @@ +package x448 + +import ( + fp "github.com/cloudflare/circl/math/fp448" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + w[1] = fp.Elt{ // x1 = S + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac, + 0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23, + 0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1, + 0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29, + 0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda, + 0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a, + 0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 448 + const h = 2 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 448 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [3]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve448 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) a point of order 4 on the twist of Curve448 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (-1,_,1) point of order 4 on Curve448 */ + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go new file mode 100644 index 00000000..a0622666 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go @@ -0,0 +1,30 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package x448 + +import ( + fp "github.com/cloudflare/circl/math/fp448" + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h new file mode 100644 index 00000000..8c1ae4d0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s new file mode 100644 index 00000000..810aa9e6 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s @@ -0,0 +1,193 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp448 package +#include "../../math/fp448/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve448 +#define CTE_A24 39082 + +#define Size 56 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, cmov, adx +#define multiplyA24Leg(z,x) \ + MOVQ $CTE_A24, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R9; \ + MULXQ 8+x, AX, R10; ADDQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCQ AX, R13; \ + MULXQ 48+x, AX, DX; ADCQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp448.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + +// func ladderStepAmd64(w *[5]fp448.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// w = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(work *[5]fp.Elt, swap uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +// This is Equation 7 at https://eprint.iacr.org/2017/264. +TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp448.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go new file mode 100644 index 00000000..b0b65ccf --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go @@ -0,0 +1,100 @@ +package x448 + +import ( + "encoding/binary" + "math/bits" + + "github.com/cloudflare/circl/math/fp448" +) + +func doubleGeneric(x, z *fp448.Elt) { + t0, t1 := &fp448.Elt{}, &fp448.Elt{} + fp448.AddSub(x, z) + fp448.Sqr(x, x) + fp448.Sqr(z, z) + fp448.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z) + fp448.Mul(x, x, z) + fp448.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp448.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp448.Cswap(x1, x2, b) + fp448.Cswap(z1, z2, b) + fp448.AddSub(x1, z1) + fp448.Mul(z1, z1, mu) + fp448.AddSub(x1, z1) + fp448.Sqr(x1, x1) + fp448.Sqr(z1, z1) + fp448.Mul(x1, x1, z2) + fp448.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp448.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp448.Elt{} + t1 := &fp448.Elt{} + fp448.AddSub(x2, z2) + fp448.AddSub(x3, z3) + fp448.Mul(t0, x2, z3) + fp448.Mul(t1, x3, z2) + fp448.AddSub(t0, t1) + fp448.Cmov(x2, x3, b) + fp448.Cmov(z2, z3, b) + fp448.Sqr(x3, t0) + fp448.Sqr(z3, t1) + fp448.Mul(z3, x1, z3) + fp448.Sqr(x2, x2) + fp448.Sqr(z2, z2) + fp448.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z2) + fp448.Mul(x2, x2, z2) + fp448.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp448.Elt) { + const A24 = 39082 + const n = 8 + var xx [7]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + h4, l4 := bits.Mul64(xx[4], A24) + h5, l5 := bits.Mul64(xx[5], A24) + h6, l6 := bits.Mul64(xx[6], A24) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, c3 := bits.Add64(h3, l4, c2) + l5, c4 := bits.Add64(h4, l5, c3) + l6, c5 := bits.Add64(h5, l6, c4) + l7, _ := bits.Add64(h6, 0, c5) + + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + xx[0], c0 = bits.Add64(l0, l7, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, l7<<32, c2) + xx[4], c4 = bits.Add64(l4, 0, c3) + xx[5], c5 = bits.Add64(l5, 0, c4) + xx[6], _ = bits.Add64(l6, 0, c5) + + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go new file mode 100644 index 00000000..3755b7c8 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go @@ -0,0 +1,11 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package x448 + +import fp "github.com/cloudflare/circl/math/fp448" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/vendor/github.com/cloudflare/circl/dh/x448/doc.go b/vendor/github.com/cloudflare/circl/dh/x448/doc.go new file mode 100644 index 00000000..c02904fe --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/doc.go @@ -0,0 +1,19 @@ +/* +Package x448 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) +*/ +package x448 diff --git a/vendor/github.com/cloudflare/circl/dh/x448/key.go b/vendor/github.com/cloudflare/circl/dh/x448/key.go new file mode 100644 index 00000000..2fdde511 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/key.go @@ -0,0 +1,46 @@ +package x448 + +import ( + "crypto/subtle" + + fp "github.com/cloudflare/circl/math/fp448" +) + +// Size is the length in bytes of a X448 key. +const Size = 56 + +// Key represents a X448 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 252 + k[55] |= 128 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + var isLowOrder int + for _, P := range lowOrderPoints { + isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:]) + } + return isLowOrder == 0 +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/table.go b/vendor/github.com/cloudflare/circl/dh/x448/table.go new file mode 100644 index 00000000..eef53c30 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/table.go @@ -0,0 +1,460 @@ +package x448 + +import fp "github.com/cloudflare/circl/math/fp448" + +// tableGenerator contains the set of points: +// +// t[i] = (xi+1)/(xi-1), +// +// where (xi,yi) = 2^iG and G is the generator point +// Size = (448)*(448/8) = 25088 bytes. +var tableGenerator = [448 * fp.Size]byte{ + /* (2^ 0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + /* (2^ 1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28, + /* (2^ 2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8, + /* (2^ 3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03, + /* (2^ 4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa, + /* (2^ 5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9, + /* (2^ 6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67, + /* (2^ 7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e, + /* (2^ 8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7, + /* (2^ 9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a, + /* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d, + /* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60, + /* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a, + /* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae, + /* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95, + /* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b, + /* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34, + /* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06, + /* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17, + /* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d, + /* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc, + /* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde, + /* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11, + /* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98, + /* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c, + /* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed, + /* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9, + /* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f, + /* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75, + /* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7, + /* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c, + /* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b, + /* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e, + /* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28, + /* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2, + /* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9, + /* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08, + /* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8, + /* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20, + /* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29, + /* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e, + /* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57, + /* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1, + /* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d, + /* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59, + /* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba, + /* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee, + /* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1, + /* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe, + /* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae, + /* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb, + /* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71, + /* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f, + /* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41, + /* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc, + /* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef, + /* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5, + /* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14, + /* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91, + /* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a, + /* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4, + /* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08, + /* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74, + /* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9, + /* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95, + /* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa, + /* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25, + /* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc, + /* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b, + /* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85, + /* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51, + /* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc, + /* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85, + /* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5, + /* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9, + /* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b, + /* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82, + /* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99, + /* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb, + /* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1, + /* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0, + /* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42, + /* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b, + /* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb, + /* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42, + /* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd, + /* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57, + /* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e, + /* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59, + /* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81, + /* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54, + /* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b, + /* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68, + /* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9, + /* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77, + /* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb, + /* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3, + /* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0, + /* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c, + /* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01, + /* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7, + /* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1, + /* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8, + /* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda, + /* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec, + /* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90, + /* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29, + /* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20, + /* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8, + /* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d, + /* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d, + /* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6, + /* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32, + /* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47, + /* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb, + /* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e, + /* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7, + /* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f, + /* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5, + /* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c, + /* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94, + /* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf, + /* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1, + /* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f, + /* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8, + /* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e, + /* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24, + /* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac, + /* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc, + /* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69, + /* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7, + /* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51, + /* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68, + /* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8, + /* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12, + /* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29, + /* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9, + /* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd, + /* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43, + /* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9, + /* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02, + /* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70, + /* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32, + /* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10, + /* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74, + /* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f, + /* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda, + /* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf, + /* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0, + /* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b, + /* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe, + /* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e, + /* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45, + /* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9, + /* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33, + /* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8, + /* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed, + /* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43, + /* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a, + /* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1, + /* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a, + /* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9, + /* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a, + /* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29, + /* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52, + /* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45, + /* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3, + /* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04, + /* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73, + /* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4, + /* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd, + /* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa, + /* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2, + /* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed, + /* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0, + /* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22, + /* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69, + /* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea, + /* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f, + /* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91, + /* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf, + /* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a, + /* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12, + /* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54, + /* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad, + /* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9, + /* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2, + /* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3, + /* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2, + /* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1, + /* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b, + /* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27, + /* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7, + /* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d, + /* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9, + /* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52, + /* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a, + /* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c, + /* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5, + /* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74, + /* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92, + /* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4, + /* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7, + /* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1, + /* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d, + /* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69, + /* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe, + /* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5, + /* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d, + /* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e, + /* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6, + /* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e, + /* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed, + /* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51, + /* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48, + /* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b, + /* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94, + /* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c, + /* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8, + /* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7, + /* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79, + /* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2, + /* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70, + /* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82, + /* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f, + /* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa, + /* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c, + /* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02, + /* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16, + /* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76, + /* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3, + /* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c, + /* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65, + /* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f, + /* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b, + /* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6, + /* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda, + /* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b, + /* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1, + /* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1, + /* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee, + /* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22, + /* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95, + /* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f, + /* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd, + /* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5, + /* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f, + /* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6, + /* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6, + /* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b, + /* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80, + /* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4, + /* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0, + /* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95, + /* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82, + /* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18, + /* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82, + /* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53, + /* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9, + /* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8, + /* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82, + /* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7, + /* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8, + /* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3, + /* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5, + /* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87, + /* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56, + /* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65, + /* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce, + /* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a, + /* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1, + /* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0, + /* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e, + /* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45, + /* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9, + /* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63, + /* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36, + /* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55, + /* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3, + /* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc, + /* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9, + /* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35, + /* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb, + /* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33, + /* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1, + /* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48, + /* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08, + /* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7, + /* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17, + /* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16, + /* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec, + /* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92, + /* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c, + /* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b, + /* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3, + /* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8, + /* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe, + /* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60, + /* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61, + /* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b, + /* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2, + /* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23, + /* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf, + /* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96, + /* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6, + /* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb, + /* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2, + /* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7, + /* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03, + /* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57, + /* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89, + /* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f, + /* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56, + /* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27, + /* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37, + /* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5, + /* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc, + /* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5, + /* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12, + /* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28, + /* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2, + /* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97, + /* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0, + /* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14, + /* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8, + /* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64, + /* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0, + /* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28, + /* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2, + /* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9, + /* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7, + /* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b, + /* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca, + /* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86, + /* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28, + /* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02, + /* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c, + /* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc, + /* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f, + /* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00, + /* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c, + /* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96, + /* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3, + /* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75, + /* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a, + /* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4, + /* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04, + /* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1, + /* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0, + /* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08, + /* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f, + /* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18, + /* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a, + /* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38, + /* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8, + /* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35, + /* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf, + /* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d, + /* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98, + /* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e, + /* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed, + /* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad, + /* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc, + /* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1, + /* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7, + /* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b, + /* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48, + /* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93, + /* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06, + /* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4, + /* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5, + /* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5, + /* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa, + /* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9, + /* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5, + /* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1, + /* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24, + /* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda, + /* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba, + /* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7, + /* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a, + /* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10, + /* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59, + /* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d, + /* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21, + /* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5, + /* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0, + /* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc, + /* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f, + /* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0, + /* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9, + /* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7, + /* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6, + /* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f, + /* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb, + /* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb, + /* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93, + /* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c, + /* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2, + /* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a, + /* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f, + /* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5, + /* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75, + /* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f, + /* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad, + /* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f, + /* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7, + /* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e, + /* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95, + /* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0, + /* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35, + /* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9, + /* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67, + /* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd, + /* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7, + /* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce, + /* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd, + /* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a, + /* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96, + /* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24, + /* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46, + /* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7, + /* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29, + /* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87, + /* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec, + /* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3, + /* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4, + /* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2, + /* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83, + /* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67, + /* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25, + /* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d, + /* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91, + /* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9, + /* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb, + /* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87, + /* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12, + /* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2, + /* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32, + /* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc, + /* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a, + /* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36, + /* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2, + /* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e, + /* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b, + /* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd, + /* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d, + /* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67, +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/constants.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/constants.go new file mode 100644 index 00000000..b6b236e5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/constants.go @@ -0,0 +1,71 @@ +package goldilocks + +import fp "github.com/cloudflare/circl/math/fp448" + +var ( + // genX is the x-coordinate of the generator of Goldilocks curve. + genX = fp.Elt{ + 0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26, + 0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43, + 0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12, + 0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea, + 0x67, 0x17, 0x0f, 0x47, 0x70, 0x65, 0x14, 0x9e, + 0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22, + 0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f, + } + // genY is the y-coordinate of the generator of Goldilocks curve. + genY = fp.Elt{ + 0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98, + 0xad, 0xc8, 0xd7, 0x4e, 0x2c, 0x13, 0xbd, 0xfd, + 0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a, + 0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87, + 0x40, 0x98, 0xa3, 0x6c, 0x73, 0x73, 0xea, 0x4b, + 0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88, + 0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69, + } + // paramD is -39081 in Fp. + paramD = fp.Elt{ + 0x56, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + // order is 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d, + // which is the number of points in the prime subgroup. + order = Scalar{ + 0xf3, 0x44, 0x58, 0xab, 0x92, 0xc2, 0x78, 0x23, + 0x55, 0x8f, 0xc5, 0x8d, 0x72, 0xc2, 0x6c, 0x21, + 0x90, 0x36, 0xd6, 0xae, 0x49, 0xdb, 0x4e, 0xc4, + 0xe9, 0x23, 0xca, 0x7c, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, + } + // residue448 is 2^448 mod order. + residue448 = [4]uint64{ + 0x721cf5b5529eec34, 0x7a4cf635c8e9c2ab, 0xeec492d944a725bf, 0x20cd77058, + } + // invFour is 1/4 mod order. + invFour = Scalar{ + 0x3d, 0x11, 0xd6, 0xaa, 0xa4, 0x30, 0xde, 0x48, + 0xd5, 0x63, 0x71, 0xa3, 0x9c, 0x30, 0x5b, 0x08, + 0xa4, 0x8d, 0xb5, 0x6b, 0xd2, 0xb6, 0x13, 0x71, + 0xfa, 0x88, 0x32, 0xdf, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, + } + // paramDTwist is -39082 in Fp. The D parameter of the twist curve. + paramDTwist = fp.Elt{ + 0x55, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } +) diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/curve.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/curve.go new file mode 100644 index 00000000..5a939100 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/curve.go @@ -0,0 +1,80 @@ +// Package goldilocks provides elliptic curve operations over the goldilocks curve. +package goldilocks + +import fp "github.com/cloudflare/circl/math/fp448" + +// Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2. +type Curve struct{} + +// Identity returns the identity point. +func (Curve) Identity() *Point { + return &Point{ + y: fp.One(), + z: fp.One(), + } +} + +// IsOnCurve returns true if the point lies on the curve. +func (Curve) IsOnCurve(P *Point) bool { + x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + rhs, lhs := &fp.Elt{}, &fp.Elt{} + fp.Mul(t, &P.ta, &P.tb) // t = ta*tb + fp.Sqr(x2, &P.x) // x^2 + fp.Sqr(y2, &P.y) // y^2 + fp.Sqr(z2, &P.z) // z^2 + fp.Sqr(t2, t) // t^2 + fp.Add(lhs, x2, y2) // x^2 + y^2 + fp.Mul(rhs, t2, ¶mD) // dt^2 + fp.Add(rhs, rhs, z2) // z^2 + dt^2 + fp.Sub(lhs, lhs, rhs) // x^2 + y^2 - (z^2 + dt^2) + eq0 := fp.IsZero(lhs) + + fp.Mul(lhs, &P.x, &P.y) // xy + fp.Mul(rhs, t, &P.z) // tz + fp.Sub(lhs, lhs, rhs) // xy - tz + eq1 := fp.IsZero(lhs) + return eq0 && eq1 +} + +// Generator returns the generator point. +func (Curve) Generator() *Point { + return &Point{ + x: genX, + y: genY, + z: fp.One(), + ta: genX, + tb: genY, + } +} + +// Order returns the number of points in the prime subgroup. +func (Curve) Order() Scalar { return order } + +// Double returns 2P. +func (Curve) Double(P *Point) *Point { R := *P; R.Double(); return &R } + +// Add returns P+Q. +func (Curve) Add(P, Q *Point) *Point { R := *P; R.Add(Q); return &R } + +// ScalarMult returns kP. This function runs in constant time. +func (e Curve) ScalarMult(k *Scalar, P *Point) *Point { + k4 := &Scalar{} + k4.divBy4(k) + return e.pull(twistCurve{}.ScalarMult(k4, e.push(P))) +} + +// ScalarBaseMult returns kG where G is the generator point. This function runs in constant time. +func (e Curve) ScalarBaseMult(k *Scalar) *Point { + k4 := &Scalar{} + k4.divBy4(k) + return e.pull(twistCurve{}.ScalarBaseMult(k4)) +} + +// CombinedMult returns mG+nP, where G is the generator point. This function is non-constant time. +func (e Curve) CombinedMult(m, n *Scalar, P *Point) *Point { + m4 := &Scalar{} + n4 := &Scalar{} + m4.divBy4(m) + n4.divBy4(n) + return e.pull(twistCurve{}.CombinedMult(m4, n4, twistCurve{}.pull(P))) +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/isogeny.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/isogeny.go new file mode 100644 index 00000000..b1daab85 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/isogeny.go @@ -0,0 +1,52 @@ +package goldilocks + +import fp "github.com/cloudflare/circl/math/fp448" + +func (Curve) pull(P *twistPoint) *Point { return twistCurve{}.push(P) } +func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) } + +// push sends a point on the Goldilocks curve to a point on the twist curve. +func (Curve) push(P *Point) *twistPoint { + Q := &twistPoint{} + Px, Py, Pz := &P.x, &P.y, &P.z + a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + *d = *a // D = A + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, a) // (x+y)^2-A + fp.Sub(e, e, b) // E = (x+y)^2-A-B + fp.Add(h, b, d) // H = B+D + fp.Sub(g, b, d) // G = B-D + fp.Sub(f, c, h) // F = C-H + fp.Mul(&Q.z, f, g) // Z = F * G + fp.Mul(&Q.x, e, f) // X = E * F + fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H + return Q +} + +// push sends a point on the twist curve to a point on the Goldilocks curve. +func (twistCurve) push(P *twistPoint) *Point { + Q := &Point{} + Px, Py, Pz := &P.x, &P.y, &P.z + a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Neg(d, a) // D = -A + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, a) // (x+y)^2-A + fp.Sub(e, e, b) // E = (x+y)^2-A-B + fp.Add(h, b, d) // H = B+D + fp.Sub(g, b, d) // G = B-D + fp.Sub(f, c, h) // F = C-H + fp.Mul(&Q.z, f, g) // Z = F * G + fp.Mul(&Q.x, e, f) // X = E * F + fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H + return Q +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/point.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/point.go new file mode 100644 index 00000000..11f73de0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/point.go @@ -0,0 +1,171 @@ +package goldilocks + +import ( + "errors" + "fmt" + + fp "github.com/cloudflare/circl/math/fp448" +) + +// Point is a point on the Goldilocks Curve. +type Point struct{ x, y, z, ta, tb fp.Elt } + +func (P Point) String() string { + return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) +} + +// FromAffine creates a point from affine coordinates. +func FromAffine(x, y *fp.Elt) (*Point, error) { + P := &Point{ + x: *x, + y: *y, + z: fp.One(), + ta: *x, + tb: *y, + } + if !(Curve{}).IsOnCurve(P) { + return P, errors.New("point not on curve") + } + return P, nil +} + +// isLessThan returns true if 0 <= x < y, and assumes that slices are of the +// same length and are interpreted in little-endian order. +func isLessThan(x, y []byte) bool { + i := len(x) - 1 + for i > 0 && x[i] == y[i] { + i-- + } + return x[i] < y[i] +} + +// FromBytes returns a point from the input buffer. +func FromBytes(in []byte) (*Point, error) { + if len(in) < fp.Size+1 { + return nil, errors.New("wrong input length") + } + err := errors.New("invalid decoding") + P := &Point{} + signX := in[fp.Size] >> 7 + copy(P.y[:], in[:fp.Size]) + p := fp.P() + if !isLessThan(P.y[:], p[:]) { + return nil, err + } + + u, v := &fp.Elt{}, &fp.Elt{} + one := fp.One() + fp.Sqr(u, &P.y) // u = y^2 + fp.Mul(v, u, ¶mD) // v = dy^2 + fp.Sub(u, u, &one) // u = y^2-1 + fp.Sub(v, v, &one) // v = dy^2-1 + isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) + if !isQR { + return nil, err + } + fp.Modp(&P.x) // x = x mod p + if fp.IsZero(&P.x) && signX == 1 { + return nil, err + } + if signX != (P.x[0] & 1) { + fp.Neg(&P.x, &P.x) + } + P.ta = P.x + P.tb = P.y + P.z = fp.One() + return P, nil +} + +// IsIdentity returns true is P is the identity Point. +func (P *Point) IsIdentity() bool { + return fp.IsZero(&P.x) && !fp.IsZero(&P.y) && !fp.IsZero(&P.z) && P.y == P.z +} + +// IsEqual returns true if P is equivalent to Q. +func (P *Point) IsEqual(Q *Point) bool { + l, r := &fp.Elt{}, &fp.Elt{} + fp.Mul(l, &P.x, &Q.z) + fp.Mul(r, &Q.x, &P.z) + fp.Sub(l, l, r) + b := fp.IsZero(l) + fp.Mul(l, &P.y, &Q.z) + fp.Mul(r, &Q.y, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + fp.Mul(l, &P.ta, &P.tb) + fp.Mul(l, l, &Q.z) + fp.Mul(r, &Q.ta, &Q.tb) + fp.Mul(r, r, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + return b +} + +// Neg obtains the inverse of the Point. +func (P *Point) Neg() { fp.Neg(&P.x, &P.x); fp.Neg(&P.ta, &P.ta) } + +// ToAffine returns the x,y affine coordinates of P. +func (P *Point) ToAffine() (x, y fp.Elt) { + fp.Inv(&P.z, &P.z) // 1/z + fp.Mul(&P.x, &P.x, &P.z) // x/z + fp.Mul(&P.y, &P.y, &P.z) // y/z + fp.Modp(&P.x) + fp.Modp(&P.y) + fp.SetOne(&P.z) + P.ta = P.x + P.tb = P.y + return P.x, P.y +} + +// ToBytes stores P into a slice of bytes. +func (P *Point) ToBytes(out []byte) error { + if len(out) < fp.Size+1 { + return errors.New("invalid decoding") + } + x, y := P.ToAffine() + out[fp.Size] = (x[0] & 1) << 7 + return fp.ToBytes(out[:fp.Size], &y) +} + +// MarshalBinary encodes the receiver into a binary form and returns the result. +func (P *Point) MarshalBinary() (data []byte, err error) { + data = make([]byte, fp.Size+1) + err = P.ToBytes(data[:fp.Size+1]) + return data, err +} + +// UnmarshalBinary must be able to decode the form generated by MarshalBinary. +func (P *Point) UnmarshalBinary(data []byte) error { Q, err := FromBytes(data); *P = *Q; return err } + +// Double sets P = 2Q. +func (P *Point) Double() { P.Add(P) } + +// Add sets P =P+Q.. +func (P *Point) Add(Q *Point) { + // This is formula (5) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + x1, y1, z1, ta1, tb1 := &P.x, &P.y, &P.z, &P.ta, &P.tb + x2, y2, z2, ta2, tb2 := &Q.x, &Q.y, &Q.z, &Q.ta, &Q.tb + x3, y3, z3, E, H := &P.x, &P.y, &P.z, &P.ta, &P.tb + A, B, C, D := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + t1, t2, F, G := C, D, &fp.Elt{}, &fp.Elt{} + fp.Mul(t1, ta1, tb1) // t1 = ta1*tb1 + fp.Mul(t2, ta2, tb2) // t2 = ta2*tb2 + fp.Mul(A, x1, x2) // A = x1*x2 + fp.Mul(B, y1, y2) // B = y1*y2 + fp.Mul(C, t1, t2) // t1*t2 + fp.Mul(C, C, ¶mD) // C = d*t1*t2 + fp.Mul(D, z1, z2) // D = z1*z2 + fp.Add(F, x1, y1) // x1+y1 + fp.Add(E, x2, y2) // x2+y2 + fp.Mul(E, E, F) // (x1+y1)*(x2+y2) + fp.Sub(E, E, A) // (x1+y1)*(x2+y2)-A + fp.Sub(E, E, B) // E = (x1+y1)*(x2+y2)-A-B + fp.Sub(F, D, C) // F = D-C + fp.Add(G, D, C) // G = D+C + fp.Sub(H, B, A) // H = B-A + fp.Mul(z3, F, G) // Z = F * G + fp.Mul(x3, E, F) // X = E * F + fp.Mul(y3, G, H) // Y = G * H, T = E * H +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/scalar.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/scalar.go new file mode 100644 index 00000000..f98117b2 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/scalar.go @@ -0,0 +1,203 @@ +package goldilocks + +import ( + "encoding/binary" + "math/bits" +) + +// ScalarSize is the size (in bytes) of scalars. +const ScalarSize = 56 // 448 / 8 + +// _N is the number of 64-bit words to store scalars. +const _N = 7 // 448 / 64 + +// Scalar represents a positive integer stored in little-endian order. +type Scalar [ScalarSize]byte + +type scalar64 [_N]uint64 + +func (z *scalar64) fromScalar(x *Scalar) { + z[0] = binary.LittleEndian.Uint64(x[0*8 : 1*8]) + z[1] = binary.LittleEndian.Uint64(x[1*8 : 2*8]) + z[2] = binary.LittleEndian.Uint64(x[2*8 : 3*8]) + z[3] = binary.LittleEndian.Uint64(x[3*8 : 4*8]) + z[4] = binary.LittleEndian.Uint64(x[4*8 : 5*8]) + z[5] = binary.LittleEndian.Uint64(x[5*8 : 6*8]) + z[6] = binary.LittleEndian.Uint64(x[6*8 : 7*8]) +} + +func (z *scalar64) toScalar(x *Scalar) { + binary.LittleEndian.PutUint64(x[0*8:1*8], z[0]) + binary.LittleEndian.PutUint64(x[1*8:2*8], z[1]) + binary.LittleEndian.PutUint64(x[2*8:3*8], z[2]) + binary.LittleEndian.PutUint64(x[3*8:4*8], z[3]) + binary.LittleEndian.PutUint64(x[4*8:5*8], z[4]) + binary.LittleEndian.PutUint64(x[5*8:6*8], z[5]) + binary.LittleEndian.PutUint64(x[6*8:7*8], z[6]) +} + +// add calculates z = x + y. Assumes len(z) > max(len(x),len(y)). +func add(z, x, y []uint64) uint64 { + l, L, zz := len(x), len(y), y + if l > L { + l, L, zz = L, l, x + } + c := uint64(0) + for i := 0; i < l; i++ { + z[i], c = bits.Add64(x[i], y[i], c) + } + for i := l; i < L; i++ { + z[i], c = bits.Add64(zz[i], 0, c) + } + return c +} + +// sub calculates z = x - y. Assumes len(z) > max(len(x),len(y)). +func sub(z, x, y []uint64) uint64 { + l, L, zz := len(x), len(y), y + if l > L { + l, L, zz = L, l, x + } + c := uint64(0) + for i := 0; i < l; i++ { + z[i], c = bits.Sub64(x[i], y[i], c) + } + for i := l; i < L; i++ { + z[i], c = bits.Sub64(zz[i], 0, c) + } + return c +} + +// mulWord calculates z = x * y. Assumes len(z) >= len(x)+1. +func mulWord(z, x []uint64, y uint64) { + for i := range z { + z[i] = 0 + } + carry := uint64(0) + for i := range x { + hi, lo := bits.Mul64(x[i], y) + lo, cc := bits.Add64(lo, z[i], 0) + hi, _ = bits.Add64(hi, 0, cc) + z[i], cc = bits.Add64(lo, carry, 0) + carry, _ = bits.Add64(hi, 0, cc) + } + z[len(x)] = carry +} + +// Cmov moves x into z if b=1. +func (z *scalar64) Cmov(b uint64, x *scalar64) { + m := uint64(0) - b + for i := range z { + z[i] = (z[i] &^ m) | (x[i] & m) + } +} + +// leftShift shifts to the left the words of z returning the more significant word. +func (z *scalar64) leftShift(low uint64) uint64 { + high := z[_N-1] + for i := _N - 1; i > 0; i-- { + z[i] = z[i-1] + } + z[0] = low + return high +} + +// reduceOneWord calculates z = z + 2^448*x such that the result fits in a Scalar. +func (z *scalar64) reduceOneWord(x uint64) { + prod := (&scalar64{})[:] + mulWord(prod, residue448[:], x) + cc := add(z[:], z[:], prod) + mulWord(prod, residue448[:], cc) + add(z[:], z[:], prod) +} + +// modOrder reduces z mod order. +func (z *scalar64) modOrder() { + var o64, x scalar64 + o64.fromScalar(&order) + // Performs: while (z >= order) { z = z-order } + // At most 8 (eight) iterations reduce 3 bits by subtracting. + for i := 0; i < 8; i++ { + c := sub(x[:], z[:], o64[:]) // (c || x) = z-order + z.Cmov(1-c, &x) // if c != 0 { z = x } + } +} + +// FromBytes stores z = x mod order, where x is a number stored in little-endian order. +func (z *Scalar) FromBytes(x []byte) { + n := len(x) + nCeil := (n + 7) >> 3 + for i := range z { + z[i] = 0 + } + if nCeil < _N { + copy(z[:], x) + return + } + copy(z[:], x[8*(nCeil-_N):]) + var z64 scalar64 + z64.fromScalar(z) + for i := nCeil - _N - 1; i >= 0; i-- { + low := binary.LittleEndian.Uint64(x[8*i:]) + high := z64.leftShift(low) + z64.reduceOneWord(high) + } + z64.modOrder() + z64.toScalar(z) +} + +// divBy4 calculates z = x/4 mod order. +func (z *Scalar) divBy4(x *Scalar) { z.Mul(x, &invFour) } + +// Red reduces z mod order. +func (z *Scalar) Red() { var t scalar64; t.fromScalar(z); t.modOrder(); t.toScalar(z) } + +// Neg calculates z = -z mod order. +func (z *Scalar) Neg() { z.Sub(&order, z) } + +// Add calculates z = x+y mod order. +func (z *Scalar) Add(x, y *Scalar) { + var z64, x64, y64, t scalar64 + x64.fromScalar(x) + y64.fromScalar(y) + c := add(z64[:], x64[:], y64[:]) + add(t[:], z64[:], residue448[:]) + z64.Cmov(c, &t) + z64.modOrder() + z64.toScalar(z) +} + +// Sub calculates z = x-y mod order. +func (z *Scalar) Sub(x, y *Scalar) { + var z64, x64, y64, t scalar64 + x64.fromScalar(x) + y64.fromScalar(y) + c := sub(z64[:], x64[:], y64[:]) + sub(t[:], z64[:], residue448[:]) + z64.Cmov(c, &t) + z64.modOrder() + z64.toScalar(z) +} + +// Mul calculates z = x*y mod order. +func (z *Scalar) Mul(x, y *Scalar) { + var z64, x64, y64 scalar64 + prod := (&[_N + 1]uint64{})[:] + x64.fromScalar(x) + y64.fromScalar(y) + mulWord(prod, x64[:], y64[_N-1]) + copy(z64[:], prod[:_N]) + z64.reduceOneWord(prod[_N]) + for i := _N - 2; i >= 0; i-- { + h := z64.leftShift(0) + z64.reduceOneWord(h) + mulWord(prod, x64[:], y64[i]) + c := add(z64[:], z64[:], prod[:_N]) + z64.reduceOneWord(prod[_N] + c) + } + z64.modOrder() + z64.toScalar(z) +} + +// IsZero returns true if z=0. +func (z *Scalar) IsZero() bool { z.Red(); return *z == Scalar{} } diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist.go new file mode 100644 index 00000000..8cd4e333 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist.go @@ -0,0 +1,138 @@ +package goldilocks + +import ( + "crypto/subtle" + "math/bits" + + "github.com/cloudflare/circl/internal/conv" + "github.com/cloudflare/circl/math" + fp "github.com/cloudflare/circl/math/fp448" +) + +// twistCurve is -x^2+y^2=1-39082x^2y^2 and is 4-isogeneous to Goldilocks. +type twistCurve struct{} + +// Identity returns the identity point. +func (twistCurve) Identity() *twistPoint { + return &twistPoint{ + y: fp.One(), + z: fp.One(), + } +} + +// subYDiv16 update x = (x - y) / 16. +func subYDiv16(x *scalar64, y int64) { + s := uint64(y >> 63) + x0, b0 := bits.Sub64((*x)[0], uint64(y), 0) + x1, b1 := bits.Sub64((*x)[1], s, b0) + x2, b2 := bits.Sub64((*x)[2], s, b1) + x3, b3 := bits.Sub64((*x)[3], s, b2) + x4, b4 := bits.Sub64((*x)[4], s, b3) + x5, b5 := bits.Sub64((*x)[5], s, b4) + x6, _ := bits.Sub64((*x)[6], s, b5) + x[0] = (x0 >> 4) | (x1 << 60) + x[1] = (x1 >> 4) | (x2 << 60) + x[2] = (x2 >> 4) | (x3 << 60) + x[3] = (x3 >> 4) | (x4 << 60) + x[4] = (x4 >> 4) | (x5 << 60) + x[5] = (x5 >> 4) | (x6 << 60) + x[6] = (x6 >> 4) +} + +func recodeScalar(d *[113]int8, k *Scalar) { + var k64 scalar64 + k64.fromScalar(k) + for i := 0; i < 112; i++ { + d[i] = int8((k64[0] & 0x1f) - 16) + subYDiv16(&k64, int64(d[i])) + } + d[112] = int8(k64[0]) +} + +// ScalarMult returns kP. +func (e twistCurve) ScalarMult(k *Scalar, P *twistPoint) *twistPoint { + var TabP [8]preTwistPointProy + var S preTwistPointProy + var d [113]int8 + + var isZero int + if k.IsZero() { + isZero = 1 + } + subtle.ConstantTimeCopy(isZero, k[:], order[:]) + + minusK := *k + isEven := 1 - int(k[0]&0x1) + minusK.Neg() + subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) + recodeScalar(&d, k) + + P.oddMultiples(TabP[:]) + Q := e.Identity() + for i := 112; i >= 0; i-- { + Q.Double() + Q.Double() + Q.Double() + Q.Double() + mask := d[i] >> 7 + absDi := (d[i] + mask) ^ mask + inx := int32((absDi - 1) >> 1) + sig := int((d[i] >> 7) & 0x1) + for j := range TabP { + S.cmov(&TabP[j], uint(subtle.ConstantTimeEq(inx, int32(j)))) + } + S.cneg(sig) + Q.mixAdd(&S) + } + Q.cneg(uint(isEven)) + return Q +} + +const ( + omegaFix = 7 + omegaVar = 5 +) + +// CombinedMult returns mG+nP. +func (e twistCurve) CombinedMult(m, n *Scalar, P *twistPoint) *twistPoint { + nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m[:]), omegaFix) + nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n[:]), omegaVar) + + if len(nafFix) > len(nafVar) { + nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) + } else if len(nafFix) < len(nafVar) { + nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) + } + + var TabQ [1 << (omegaVar - 2)]preTwistPointProy + P.oddMultiples(TabQ[:]) + Q := e.Identity() + for i := len(nafFix) - 1; i >= 0; i-- { + Q.Double() + // Generator point + if nafFix[i] != 0 { + idxM := absolute(nafFix[i]) >> 1 + R := tabVerif[idxM] + if nafFix[i] < 0 { + R.neg() + } + Q.mixAddZ1(&R) + } + // Variable input point + if nafVar[i] != 0 { + idxN := absolute(nafVar[i]) >> 1 + S := TabQ[idxN] + if nafVar[i] < 0 { + S.neg() + } + Q.mixAdd(&S) + } + } + return Q +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistPoint.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistPoint.go new file mode 100644 index 00000000..c55db77b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistPoint.go @@ -0,0 +1,135 @@ +package goldilocks + +import ( + "fmt" + + fp "github.com/cloudflare/circl/math/fp448" +) + +type twistPoint struct{ x, y, z, ta, tb fp.Elt } + +type preTwistPointAffine struct{ addYX, subYX, dt2 fp.Elt } + +type preTwistPointProy struct { + preTwistPointAffine + z2 fp.Elt +} + +func (P *twistPoint) String() string { + return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) +} + +// cneg conditionally negates the point if b=1. +func (P *twistPoint) cneg(b uint) { + t := &fp.Elt{} + fp.Neg(t, &P.x) + fp.Cmov(&P.x, t, b) + fp.Neg(t, &P.ta) + fp.Cmov(&P.ta, t, b) +} + +// Double updates P with 2P. +func (P *twistPoint) Double() { + // This is formula (7) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Add(h, a, b) // H = A+B + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, h) // E = (x+y)^2-A-B + fp.Sub(g, b, a) // G = B-A + fp.Sub(f, c, g) // F = C-G + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q = 1. +func (P *twistPoint) mixAddZ1(Q *preTwistPointAffine) { + fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 (z2=1) + P.coreAddition(Q) +} + +// coreAddition calculates P=P+Q for curves with A=-1. +func (P *twistPoint) coreAddition(Q *preTwistPointAffine) { + // This is the formula following (5) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 + a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb + fp.Mul(c, Pta, Ptb) // t1 = ta*tb + fp.Sub(h, Py, Px) // y1-x1 + fp.Add(b, Py, Px) // y1+x1 + fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) + fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) + fp.Mul(c, c, dt2) // C = 2*D*t1*t2 + fp.Sub(e, b, a) // E = B-A + fp.Add(h, b, a) // H = B+A + fp.Sub(f, d, c) // F = D-C + fp.Add(g, d, c) // G = D+C + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *preTwistPointAffine) neg() { + P.addYX, P.subYX = P.subYX, P.addYX + fp.Neg(&P.dt2, &P.dt2) +} + +func (P *preTwistPointAffine) cneg(b int) { + t := &fp.Elt{} + fp.Cswap(&P.addYX, &P.subYX, uint(b)) + fp.Neg(t, &P.dt2) + fp.Cmov(&P.dt2, t, uint(b)) +} + +func (P *preTwistPointAffine) cmov(Q *preTwistPointAffine, b uint) { + fp.Cmov(&P.addYX, &Q.addYX, b) + fp.Cmov(&P.subYX, &Q.subYX, b) + fp.Cmov(&P.dt2, &Q.dt2, b) +} + +// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q != 1. +func (P *twistPoint) mixAdd(Q *preTwistPointProy) { + fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 + P.coreAddition(&Q.preTwistPointAffine) +} + +// oddMultiples calculates T[i] = (2*i-1)P for 0 < i < len(T). +func (P *twistPoint) oddMultiples(T []preTwistPointProy) { + if n := len(T); n > 0 { + T[0].FromTwistPoint(P) + _2P := *P + _2P.Double() + R := &preTwistPointProy{} + R.FromTwistPoint(&_2P) + for i := 1; i < n; i++ { + P.mixAdd(R) + T[i].FromTwistPoint(P) + } + } +} + +// cmov conditionally moves Q into P if b=1. +func (P *preTwistPointProy) cmov(Q *preTwistPointProy, b uint) { + P.preTwistPointAffine.cmov(&Q.preTwistPointAffine, b) + fp.Cmov(&P.z2, &Q.z2, b) +} + +// FromTwistPoint precomputes some coordinates of Q for missed addition. +func (P *preTwistPointProy) FromTwistPoint(Q *twistPoint) { + fp.Add(&P.addYX, &Q.y, &Q.x) // addYX = X + Y + fp.Sub(&P.subYX, &Q.y, &Q.x) // subYX = Y - X + fp.Mul(&P.dt2, &Q.ta, &Q.tb) // T = ta*tb + fp.Mul(&P.dt2, &P.dt2, ¶mDTwist) // D*T + fp.Add(&P.dt2, &P.dt2, &P.dt2) // dt2 = 2*D*T + fp.Add(&P.z2, &Q.z, &Q.z) // z2 = 2*Z +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistTables.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistTables.go new file mode 100644 index 00000000..ed432e02 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twistTables.go @@ -0,0 +1,216 @@ +package goldilocks + +import fp "github.com/cloudflare/circl/math/fp448" + +var tabFixMult = [fxV][fx2w1]preTwistPointAffine{ + { + { + addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, + }, + { + addYX: fp.Elt{0xca, 0xd8, 0x7d, 0x86, 0x1a, 0xef, 0xad, 0x11, 0xe3, 0x27, 0x41, 0x7e, 0x7f, 0x3e, 0xa9, 0xd2, 0xb5, 0x4e, 0x50, 0xe0, 0x77, 0x91, 0xc2, 0x13, 0x52, 0x73, 0x41, 0x09, 0xa6, 0x57, 0x9a, 0xc8, 0xa8, 0x90, 0x9d, 0x26, 0x14, 0xbb, 0xa1, 0x2a, 0xf7, 0x45, 0x43, 0x4e, 0xea, 0x35, 0x62, 0xe1, 0x08, 0x85, 0x46, 0xb8, 0x24, 0x05, 0x2d, 0xab}, + subYX: fp.Elt{0x9b, 0xe6, 0xd3, 0xe5, 0xfe, 0x50, 0x36, 0x3c, 0x3c, 0x6d, 0x74, 0x1d, 0x74, 0xc0, 0xde, 0x5b, 0x45, 0x27, 0xe5, 0x12, 0xee, 0x63, 0x35, 0x6b, 0x13, 0xe2, 0x41, 0x6b, 0x3a, 0x05, 0x2b, 0xb1, 0x89, 0x26, 0xb6, 0xc6, 0xd1, 0x84, 0xff, 0x0e, 0x9b, 0xa3, 0xfb, 0x21, 0x36, 0x6b, 0x01, 0xf7, 0x9f, 0x7c, 0xeb, 0xf5, 0x18, 0x7a, 0x2a, 0x70}, + dt2: fp.Elt{0x09, 0xad, 0x99, 0x1a, 0x38, 0xd3, 0xdf, 0x22, 0x37, 0x32, 0x61, 0x8b, 0xf3, 0x19, 0x48, 0x08, 0xe8, 0x49, 0xb6, 0x4a, 0xa7, 0xed, 0xa4, 0xa2, 0xee, 0x86, 0xd7, 0x31, 0x5e, 0xce, 0x95, 0x76, 0x86, 0x42, 0x1c, 0x9d, 0x07, 0x14, 0x8c, 0x34, 0x18, 0x9c, 0x6d, 0x3a, 0xdf, 0xa9, 0xe8, 0x36, 0x7e, 0xe4, 0x95, 0xbe, 0xb5, 0x09, 0xf8, 0x9c}, + }, + { + addYX: fp.Elt{0x51, 0xdb, 0x49, 0xa8, 0x9f, 0xe3, 0xd7, 0xec, 0x0d, 0x0f, 0x49, 0xe8, 0xb6, 0xc5, 0x0f, 0x5a, 0x1c, 0xce, 0x54, 0x0d, 0xb1, 0x8d, 0x5b, 0xbf, 0xf4, 0xaa, 0x34, 0x77, 0xc4, 0x5d, 0x59, 0xb6, 0xc5, 0x0e, 0x5a, 0xd8, 0x5b, 0x30, 0xc2, 0x1d, 0xec, 0x85, 0x1c, 0x42, 0xbe, 0x24, 0x2e, 0x50, 0x55, 0x44, 0xb2, 0x3a, 0x01, 0xaa, 0x98, 0xfb}, + subYX: fp.Elt{0xe7, 0x29, 0xb7, 0xd0, 0xaa, 0x4f, 0x32, 0x53, 0x56, 0xde, 0xbc, 0xd1, 0x92, 0x5d, 0x19, 0xbe, 0xa3, 0xe3, 0x75, 0x48, 0xe0, 0x7a, 0x1b, 0x54, 0x7a, 0xb7, 0x41, 0x77, 0x84, 0x38, 0xdd, 0x14, 0x9f, 0xca, 0x3f, 0xa3, 0xc8, 0xa7, 0x04, 0x70, 0xf1, 0x4d, 0x3d, 0xb3, 0x84, 0x79, 0xcb, 0xdb, 0xe4, 0xc5, 0x42, 0x9b, 0x57, 0x19, 0xf1, 0x2d}, + dt2: fp.Elt{0x20, 0xb4, 0x94, 0x9e, 0xdf, 0x31, 0x44, 0x0b, 0xc9, 0x7b, 0x75, 0x40, 0x9d, 0xd1, 0x96, 0x39, 0x70, 0x71, 0x15, 0xc8, 0x93, 0xd5, 0xc5, 0xe5, 0xba, 0xfe, 0xee, 0x08, 0x6a, 0x98, 0x0a, 0x1b, 0xb2, 0xaa, 0x3a, 0xf4, 0xa4, 0x79, 0xf9, 0x8e, 0x4d, 0x65, 0x10, 0x9b, 0x3a, 0x6e, 0x7c, 0x87, 0x94, 0x92, 0x11, 0x65, 0xbf, 0x1a, 0x09, 0xde}, + }, + { + addYX: fp.Elt{0xf3, 0x84, 0x76, 0x77, 0xa5, 0x6b, 0x27, 0x3b, 0x83, 0x3d, 0xdf, 0xa0, 0xeb, 0x32, 0x6d, 0x58, 0x81, 0x57, 0x64, 0xc2, 0x21, 0x7c, 0x9b, 0xea, 0xe6, 0xb0, 0x93, 0xf9, 0xe7, 0xc3, 0xed, 0x5a, 0x8e, 0xe2, 0xb4, 0x72, 0x76, 0x66, 0x0f, 0x22, 0x29, 0x94, 0x3e, 0x63, 0x48, 0x5e, 0x80, 0xcb, 0xac, 0xfa, 0x95, 0xb6, 0x4b, 0xc4, 0x95, 0x33}, + subYX: fp.Elt{0x0c, 0x55, 0xd1, 0x5e, 0x5f, 0xbf, 0xbf, 0xe2, 0x4c, 0xfc, 0x37, 0x4a, 0xc4, 0xb1, 0xf4, 0x83, 0x61, 0x93, 0x60, 0x8e, 0x9f, 0x31, 0xf0, 0xa0, 0x41, 0xff, 0x1d, 0xe2, 0x7f, 0xca, 0x40, 0xd6, 0x88, 0xe8, 0x91, 0x61, 0xe2, 0x11, 0x18, 0x83, 0xf3, 0x25, 0x2f, 0x3f, 0x49, 0x40, 0xd4, 0x83, 0xe2, 0xd7, 0x74, 0x6a, 0x16, 0x86, 0x4e, 0xab}, + dt2: fp.Elt{0xdd, 0x58, 0x65, 0xd8, 0x9f, 0xdd, 0x70, 0x7f, 0x0f, 0xec, 0xbd, 0x5c, 0x5c, 0x9b, 0x7e, 0x1b, 0x9f, 0x79, 0x36, 0x1f, 0xfd, 0x79, 0x10, 0x1c, 0x52, 0xf3, 0x22, 0xa4, 0x1f, 0x71, 0x6e, 0x63, 0x14, 0xf4, 0xa7, 0x3e, 0xbe, 0xad, 0x43, 0x30, 0x38, 0x8c, 0x29, 0xc6, 0xcf, 0x50, 0x75, 0x21, 0xe5, 0x78, 0xfd, 0xb0, 0x9a, 0xc4, 0x6d, 0xd4}, + }, + }, + { + { + addYX: fp.Elt{0x7a, 0xa1, 0x38, 0xa6, 0xfd, 0x0e, 0x96, 0xd5, 0x26, 0x76, 0x86, 0x70, 0x80, 0x30, 0xa6, 0x67, 0xeb, 0xf4, 0x39, 0xdb, 0x22, 0xf5, 0x9f, 0x98, 0xe4, 0xb5, 0x3a, 0x0c, 0x59, 0xbf, 0x85, 0xc6, 0xf0, 0x0b, 0x1c, 0x41, 0x38, 0x09, 0x01, 0xdb, 0xd6, 0x3c, 0xb7, 0xf1, 0x08, 0x6b, 0x4b, 0x9e, 0x63, 0x53, 0x83, 0xd3, 0xab, 0xa3, 0x72, 0x0d}, + subYX: fp.Elt{0x84, 0x68, 0x25, 0xe8, 0xe9, 0x8f, 0x91, 0xbf, 0xf7, 0xa4, 0x30, 0xae, 0xea, 0x9f, 0xdd, 0x56, 0x64, 0x09, 0xc9, 0x54, 0x68, 0x4e, 0x33, 0xc5, 0x6f, 0x7b, 0x2d, 0x52, 0x2e, 0x42, 0xbe, 0xbe, 0xf5, 0x64, 0xbf, 0x77, 0x54, 0xdf, 0xb0, 0x10, 0xd2, 0x16, 0x5d, 0xce, 0xaf, 0x9f, 0xfb, 0xa3, 0x63, 0x50, 0xcb, 0xc0, 0xd0, 0x88, 0x44, 0xa3}, + dt2: fp.Elt{0xc3, 0x8b, 0xa5, 0xf1, 0x44, 0xe4, 0x41, 0xcd, 0x75, 0xe3, 0x17, 0x69, 0x5b, 0xb9, 0xbb, 0xee, 0x82, 0xbb, 0xce, 0x57, 0xdf, 0x2a, 0x9c, 0x12, 0xab, 0x66, 0x08, 0x68, 0x05, 0x1b, 0x87, 0xee, 0x5d, 0x1e, 0x18, 0x14, 0x22, 0x4b, 0x99, 0x61, 0x75, 0x28, 0xe7, 0x65, 0x1c, 0x36, 0xb6, 0x18, 0x09, 0xa8, 0xdf, 0xef, 0x30, 0x35, 0xbc, 0x58}, + }, + { + addYX: fp.Elt{0xc5, 0xd3, 0x0e, 0x6f, 0xaf, 0x06, 0x69, 0xc4, 0x07, 0x9e, 0x58, 0x6e, 0x3f, 0x49, 0xd9, 0x0a, 0x3c, 0x2c, 0x37, 0xcd, 0x27, 0x4d, 0x87, 0x91, 0x7a, 0xb0, 0x28, 0xad, 0x2f, 0x68, 0x92, 0x05, 0x97, 0xf1, 0x30, 0x5f, 0x4c, 0x10, 0x20, 0x30, 0xd3, 0x08, 0x3f, 0xc1, 0xc6, 0xb7, 0xb5, 0xd1, 0x71, 0x7b, 0xa8, 0x0a, 0xd8, 0xf5, 0x17, 0xcf}, + subYX: fp.Elt{0x64, 0xd4, 0x8f, 0x91, 0x40, 0xab, 0x6e, 0x1a, 0x62, 0x83, 0xdc, 0xd7, 0x30, 0x1a, 0x4a, 0x2a, 0x4c, 0x54, 0x86, 0x19, 0x81, 0x5d, 0x04, 0x52, 0xa3, 0xca, 0x82, 0x38, 0xdc, 0x1e, 0xf0, 0x7a, 0x78, 0x76, 0x49, 0x4f, 0x71, 0xc4, 0x74, 0x2f, 0xf0, 0x5b, 0x2e, 0x5e, 0xac, 0xef, 0x17, 0xe4, 0x8e, 0x6e, 0xed, 0x43, 0x23, 0x61, 0x99, 0x49}, + dt2: fp.Elt{0x64, 0x90, 0x72, 0x76, 0xf8, 0x2c, 0x7d, 0x57, 0xf9, 0x30, 0x5e, 0x7a, 0x10, 0x74, 0x19, 0x39, 0xd9, 0xaf, 0x0a, 0xf1, 0x43, 0xed, 0x88, 0x9c, 0x8b, 0xdc, 0x9b, 0x1c, 0x90, 0xe7, 0xf7, 0xa3, 0xa5, 0x0d, 0xc6, 0xbc, 0x30, 0xfb, 0x91, 0x1a, 0x51, 0xba, 0x2d, 0xbe, 0x89, 0xdf, 0x1d, 0xdc, 0x53, 0xa8, 0x82, 0x8a, 0xd3, 0x8d, 0x16, 0x68}, + }, + { + addYX: fp.Elt{0xef, 0x5c, 0xe3, 0x74, 0xbf, 0x13, 0x4a, 0xbf, 0x66, 0x73, 0x64, 0xb7, 0xd4, 0xce, 0x98, 0x82, 0x05, 0xfa, 0x98, 0x0c, 0x0a, 0xae, 0xe5, 0x6b, 0x9f, 0xac, 0xbb, 0x6e, 0x1f, 0xcf, 0xff, 0xa6, 0x71, 0x9a, 0xa8, 0x7a, 0x9e, 0x64, 0x1f, 0x20, 0x4a, 0x61, 0xa2, 0xd6, 0x50, 0xe3, 0xba, 0x81, 0x0c, 0x50, 0x59, 0x69, 0x59, 0x15, 0x55, 0xdb}, + subYX: fp.Elt{0xe8, 0x77, 0x4d, 0xe8, 0x66, 0x3d, 0xc1, 0x00, 0x3c, 0xf2, 0x25, 0x00, 0xdc, 0xb2, 0xe5, 0x9b, 0x12, 0x89, 0xf3, 0xd6, 0xea, 0x85, 0x60, 0xfe, 0x67, 0x91, 0xfd, 0x04, 0x7c, 0xe0, 0xf1, 0x86, 0x06, 0x11, 0x66, 0xee, 0xd4, 0xd5, 0xbe, 0x3b, 0x0f, 0xe3, 0x59, 0xb3, 0x4f, 0x00, 0xb6, 0xce, 0x80, 0xc1, 0x61, 0xf7, 0xaf, 0x04, 0x6a, 0x3c}, + dt2: fp.Elt{0x00, 0xd7, 0x32, 0x93, 0x67, 0x70, 0x6f, 0xd7, 0x69, 0xab, 0xb1, 0xd3, 0xdc, 0xd6, 0xa8, 0xdd, 0x35, 0x25, 0xca, 0xd3, 0x8a, 0x6d, 0xce, 0xfb, 0xfd, 0x2b, 0x83, 0xf0, 0xd4, 0xac, 0x66, 0xfb, 0x72, 0x87, 0x7e, 0x55, 0xb7, 0x91, 0x58, 0x10, 0xc3, 0x11, 0x7e, 0x15, 0xfe, 0x7c, 0x55, 0x90, 0xa3, 0x9e, 0xed, 0x9a, 0x7f, 0xa7, 0xb7, 0xeb}, + }, + { + addYX: fp.Elt{0x25, 0x0f, 0xc2, 0x09, 0x9c, 0x10, 0xc8, 0x7c, 0x93, 0xa7, 0xbe, 0xe9, 0x26, 0x25, 0x7c, 0x21, 0xfe, 0xe7, 0x5f, 0x3c, 0x02, 0x83, 0xa7, 0x9e, 0xdf, 0xc0, 0x94, 0x2b, 0x7d, 0x1a, 0xd0, 0x1d, 0xcc, 0x2e, 0x7d, 0xd4, 0x85, 0xe7, 0xc1, 0x15, 0x66, 0xd6, 0xd6, 0x32, 0xb8, 0xf7, 0x63, 0xaa, 0x3b, 0xa5, 0xea, 0x49, 0xad, 0x88, 0x9b, 0x66}, + subYX: fp.Elt{0x09, 0x97, 0x79, 0x36, 0x41, 0x56, 0x9b, 0xdf, 0x15, 0xd8, 0x43, 0x28, 0x17, 0x5b, 0x96, 0xc9, 0xcf, 0x39, 0x1f, 0x13, 0xf7, 0x4d, 0x1d, 0x1f, 0xda, 0x51, 0x56, 0xe7, 0x0a, 0x5a, 0x65, 0xb6, 0x2a, 0x87, 0x49, 0x86, 0xc2, 0x2b, 0xcd, 0xfe, 0x07, 0xf6, 0x4c, 0xe2, 0x1d, 0x9b, 0xd8, 0x82, 0x09, 0x5b, 0x11, 0x10, 0x62, 0x56, 0x89, 0xbd}, + dt2: fp.Elt{0xd9, 0x15, 0x73, 0xf2, 0x96, 0x35, 0x53, 0xb0, 0xe7, 0xa8, 0x0b, 0x93, 0x35, 0x0b, 0x3a, 0x00, 0xf5, 0x18, 0xb1, 0xc3, 0x12, 0x3f, 0x91, 0x17, 0xc1, 0x4c, 0x15, 0x5a, 0x86, 0x92, 0x11, 0xbd, 0x44, 0x40, 0x5a, 0x7b, 0x15, 0x89, 0xba, 0xc1, 0xc1, 0xbc, 0x43, 0x45, 0xe6, 0x52, 0x02, 0x73, 0x0a, 0xd0, 0x2a, 0x19, 0xda, 0x47, 0xa8, 0xff}, + }, + }, +} + +// tabVerif contains the odd multiples of P. The entry T[i] = (2i+1)P, where +// P = phi(G) and G is the generator of the Goldilocks curve, and phi is a +// 4-degree isogeny. +var tabVerif = [1 << (omegaFix - 2)]preTwistPointAffine{ + { /* 1P*/ + addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, + }, + { /* 3P*/ + addYX: fp.Elt{0xd1, 0xe9, 0xa8, 0x33, 0x20, 0x76, 0x18, 0x08, 0x45, 0x2a, 0xc9, 0x67, 0x2a, 0xc3, 0x15, 0x24, 0xf9, 0x74, 0x21, 0x30, 0x99, 0x59, 0x8b, 0xb2, 0xf0, 0xa4, 0x07, 0xe2, 0x6a, 0x36, 0x8d, 0xd9, 0xd2, 0x4a, 0x7f, 0x73, 0x50, 0x39, 0x3d, 0xaa, 0xa7, 0x51, 0x73, 0x0d, 0x2b, 0x8b, 0x96, 0x47, 0xac, 0x3c, 0x5d, 0xaa, 0x39, 0x9c, 0xcf, 0xd5}, + subYX: fp.Elt{0x6b, 0x11, 0x5d, 0x1a, 0xf9, 0x41, 0x9d, 0xc5, 0x30, 0x3e, 0xad, 0x25, 0x2c, 0x04, 0x45, 0xea, 0xcc, 0x67, 0x07, 0x85, 0xe9, 0xda, 0x0e, 0xb5, 0x40, 0xb7, 0x32, 0xb4, 0x49, 0xdd, 0xff, 0xaa, 0xfc, 0xbb, 0x19, 0xca, 0x8b, 0x79, 0x2b, 0x8f, 0x8d, 0x00, 0x33, 0xc2, 0xad, 0xe9, 0xd3, 0x12, 0xa8, 0xaa, 0x87, 0x62, 0xad, 0x2d, 0xff, 0xa4}, + dt2: fp.Elt{0xb0, 0xaf, 0x3b, 0xea, 0xf0, 0x42, 0x0b, 0x5e, 0x88, 0xd3, 0x98, 0x08, 0x87, 0x59, 0x72, 0x0a, 0xc2, 0xdf, 0xcb, 0x7f, 0x59, 0xb5, 0x4c, 0x63, 0x68, 0xe8, 0x41, 0x38, 0x67, 0x4f, 0xe9, 0xc6, 0xb2, 0x6b, 0x08, 0xa7, 0xf7, 0x0e, 0xcd, 0xea, 0xca, 0x3d, 0xaf, 0x8e, 0xda, 0x4b, 0x2e, 0xd2, 0x88, 0x64, 0x8d, 0xc5, 0x5f, 0x76, 0x0f, 0x3d}, + }, + { /* 5P*/ + addYX: fp.Elt{0xe5, 0x65, 0xc9, 0xe2, 0x75, 0xf0, 0x7d, 0x1a, 0xba, 0xa4, 0x40, 0x4b, 0x93, 0x12, 0xa2, 0x80, 0x95, 0x0d, 0x03, 0x93, 0xe8, 0xa5, 0x4d, 0xe2, 0x3d, 0x81, 0xf5, 0xce, 0xd4, 0x2d, 0x25, 0x59, 0x16, 0x5c, 0xe7, 0xda, 0xc7, 0x45, 0xd2, 0x7e, 0x2c, 0x38, 0xd4, 0x37, 0x64, 0xb2, 0xc2, 0x28, 0xc5, 0x72, 0x16, 0x32, 0x45, 0x36, 0x6f, 0x9f}, + subYX: fp.Elt{0x09, 0xf4, 0x7e, 0xbd, 0x89, 0xdb, 0x19, 0x58, 0xe1, 0x08, 0x00, 0x8a, 0xf4, 0x5f, 0x2a, 0x32, 0x40, 0xf0, 0x2c, 0x3f, 0x5d, 0xe4, 0xfc, 0x89, 0x11, 0x24, 0xb4, 0x2f, 0x97, 0xad, 0xac, 0x8f, 0x19, 0xab, 0xfa, 0x12, 0xe5, 0xf9, 0x50, 0x4e, 0x50, 0x6f, 0x32, 0x30, 0x88, 0xa6, 0xe5, 0x48, 0x28, 0xa2, 0x1b, 0x9f, 0xcd, 0xe2, 0x43, 0x38}, + dt2: fp.Elt{0xa9, 0xcc, 0x53, 0x39, 0x86, 0x02, 0x60, 0x75, 0x34, 0x99, 0x57, 0xbd, 0xfc, 0x5a, 0x8e, 0xce, 0x5e, 0x98, 0x22, 0xd0, 0xa5, 0x24, 0xff, 0x90, 0x28, 0x9f, 0x58, 0xf3, 0x39, 0xe9, 0xba, 0x36, 0x23, 0xfb, 0x7f, 0x41, 0xcc, 0x2b, 0x5a, 0x25, 0x3f, 0x4c, 0x2a, 0xf1, 0x52, 0x6f, 0x2f, 0x07, 0xe3, 0x88, 0x81, 0x77, 0xdd, 0x7c, 0x88, 0x82}, + }, + { /* 7P*/ + addYX: fp.Elt{0xf7, 0xee, 0x88, 0xfd, 0x3a, 0xbf, 0x7e, 0x28, 0x39, 0x23, 0x79, 0xe6, 0x5c, 0x56, 0xcb, 0xb5, 0x48, 0x6a, 0x80, 0x6d, 0x37, 0x60, 0x6c, 0x10, 0x35, 0x49, 0x4b, 0x46, 0x60, 0xd4, 0x79, 0xd4, 0x53, 0xd3, 0x67, 0x88, 0xd0, 0x41, 0xd5, 0x43, 0x85, 0xc8, 0x71, 0xe3, 0x1c, 0xb6, 0xda, 0x22, 0x64, 0x8f, 0x80, 0xac, 0xad, 0x7d, 0xd5, 0x82}, + subYX: fp.Elt{0x92, 0x40, 0xc1, 0x83, 0x21, 0x9b, 0xd5, 0x7d, 0x3f, 0x29, 0xb6, 0x26, 0xef, 0x12, 0xb9, 0x27, 0x39, 0x42, 0x37, 0x97, 0x09, 0x9a, 0x08, 0xe1, 0x68, 0xb6, 0x7a, 0x3f, 0x9f, 0x45, 0xf8, 0x37, 0x19, 0x83, 0x97, 0xe6, 0x73, 0x30, 0x32, 0x35, 0xcf, 0xae, 0x5c, 0x12, 0x68, 0xdf, 0x6e, 0x2b, 0xde, 0x83, 0xa0, 0x44, 0x74, 0x2e, 0x4a, 0xe9}, + dt2: fp.Elt{0xcb, 0x22, 0x0a, 0xda, 0x6b, 0xc1, 0x8a, 0x29, 0xa1, 0xac, 0x8b, 0x5b, 0x8b, 0x32, 0x20, 0xf2, 0x21, 0xae, 0x0c, 0x43, 0xc4, 0xd7, 0x19, 0x37, 0x3d, 0x79, 0x25, 0x98, 0x6c, 0x9c, 0x22, 0x31, 0x2a, 0x55, 0x9f, 0xda, 0x5e, 0xa8, 0x13, 0xdb, 0x8e, 0x2e, 0x16, 0x39, 0xf4, 0x91, 0x6f, 0xec, 0x71, 0x71, 0xc9, 0x10, 0xf2, 0xa4, 0x8f, 0x11}, + }, + { /* 9P*/ + addYX: fp.Elt{0x85, 0xdd, 0x37, 0x62, 0x74, 0x8e, 0x33, 0x5b, 0x25, 0x12, 0x1b, 0xe7, 0xdf, 0x47, 0xe5, 0x12, 0xfd, 0x3a, 0x3a, 0xf5, 0x5d, 0x4c, 0xa2, 0x29, 0x3c, 0x5c, 0x2f, 0xee, 0x18, 0x19, 0x0a, 0x2b, 0xef, 0x67, 0x50, 0x7a, 0x0d, 0x29, 0xae, 0x55, 0x82, 0xcd, 0xd6, 0x41, 0x90, 0xb4, 0x13, 0x31, 0x5d, 0x11, 0xb8, 0xaa, 0x12, 0x86, 0x08, 0xac}, + subYX: fp.Elt{0xcc, 0x37, 0x8d, 0x83, 0x5f, 0xfd, 0xde, 0xd5, 0xf7, 0xf1, 0xae, 0x0a, 0xa7, 0x0b, 0xeb, 0x6d, 0x19, 0x8a, 0xb6, 0x1a, 0x59, 0xd8, 0xff, 0x3c, 0xbc, 0xbc, 0xef, 0x9c, 0xda, 0x7b, 0x75, 0x12, 0xaf, 0x80, 0x8f, 0x2c, 0x3c, 0xaa, 0x0b, 0x17, 0x86, 0x36, 0x78, 0x18, 0xc8, 0x8a, 0xf6, 0xb8, 0x2c, 0x2f, 0x57, 0x2c, 0x62, 0x57, 0xf6, 0x90}, + dt2: fp.Elt{0x83, 0xbc, 0xa2, 0x07, 0xa5, 0x38, 0x96, 0xea, 0xfe, 0x11, 0x46, 0x1d, 0x3b, 0xcd, 0x42, 0xc5, 0xee, 0x67, 0x04, 0x72, 0x08, 0xd8, 0xd9, 0x96, 0x07, 0xf7, 0xac, 0xc3, 0x64, 0xf1, 0x98, 0x2c, 0x55, 0xd7, 0x7d, 0xc8, 0x6c, 0xbd, 0x2c, 0xff, 0x15, 0xd6, 0x6e, 0xb8, 0x17, 0x8e, 0xa8, 0x27, 0x66, 0xb1, 0x73, 0x79, 0x96, 0xff, 0x29, 0x10}, + }, + { /* 11P*/ + addYX: fp.Elt{0x76, 0xcb, 0x9b, 0x0c, 0x5b, 0xfe, 0xe1, 0x2a, 0xdd, 0x6f, 0x6c, 0xdd, 0x6f, 0xb4, 0xc0, 0xc2, 0x1b, 0x4b, 0x38, 0xe8, 0x66, 0x8c, 0x1e, 0x31, 0x63, 0xb9, 0x94, 0xcd, 0xc3, 0x8c, 0x44, 0x25, 0x7b, 0xd5, 0x39, 0x80, 0xfc, 0x01, 0xaa, 0xf7, 0x2a, 0x61, 0x8a, 0x25, 0xd2, 0x5f, 0xc5, 0x66, 0x38, 0xa4, 0x17, 0xcf, 0x3e, 0x11, 0x0f, 0xa3}, + subYX: fp.Elt{0xe0, 0xb6, 0xd1, 0x9c, 0x71, 0x49, 0x2e, 0x7b, 0xde, 0x00, 0xda, 0x6b, 0xf1, 0xec, 0xe6, 0x7a, 0x15, 0x38, 0x71, 0xe9, 0x7b, 0xdb, 0xf8, 0x98, 0xc0, 0x91, 0x2e, 0x53, 0xee, 0x92, 0x87, 0x25, 0xc9, 0xb0, 0xbb, 0x33, 0x15, 0x46, 0x7f, 0xfd, 0x4f, 0x8b, 0x77, 0x05, 0x96, 0xb6, 0xe2, 0x08, 0xdb, 0x0d, 0x09, 0xee, 0x5b, 0xd1, 0x2a, 0x63}, + dt2: fp.Elt{0x8f, 0x7b, 0x57, 0x8c, 0xbf, 0x06, 0x0d, 0x43, 0x21, 0x92, 0x94, 0x2d, 0x6a, 0x38, 0x07, 0x0f, 0xa0, 0xf1, 0xe3, 0xd8, 0x2a, 0xbf, 0x46, 0xc6, 0x9e, 0x1f, 0x8f, 0x2b, 0x46, 0x84, 0x0b, 0x74, 0xed, 0xff, 0xf8, 0xa5, 0x94, 0xae, 0xf1, 0x67, 0xb1, 0x9b, 0xdd, 0x4a, 0xd0, 0xdb, 0xc2, 0xb5, 0x58, 0x49, 0x0c, 0xa9, 0x1d, 0x7d, 0xa9, 0xd3}, + }, + { /* 13P*/ + addYX: fp.Elt{0x73, 0x84, 0x2e, 0x31, 0x1f, 0xdc, 0xed, 0x9f, 0x74, 0xfa, 0xe0, 0x35, 0xb1, 0x85, 0x6a, 0x8d, 0x86, 0xd0, 0xff, 0xd6, 0x08, 0x43, 0x73, 0x1a, 0xd5, 0xf8, 0x43, 0xd4, 0xb3, 0xe5, 0x3f, 0xa8, 0x84, 0x17, 0x59, 0x65, 0x4e, 0xe6, 0xee, 0x54, 0x9c, 0xda, 0x5e, 0x7e, 0x98, 0x29, 0x6d, 0x73, 0x34, 0x1f, 0x99, 0x80, 0x54, 0x54, 0x81, 0x0b}, + subYX: fp.Elt{0xb1, 0xe5, 0xbb, 0x80, 0x22, 0x9c, 0x81, 0x6d, 0xaf, 0x27, 0x65, 0x6f, 0x7e, 0x9c, 0xb6, 0x8d, 0x35, 0x5c, 0x2e, 0x20, 0x48, 0x7a, 0x28, 0xf0, 0x97, 0xfe, 0xb7, 0x71, 0xce, 0xd6, 0xad, 0x3a, 0x81, 0xf6, 0x74, 0x5e, 0xf3, 0xfd, 0x1b, 0xd4, 0x1e, 0x7c, 0xc2, 0xb7, 0xc8, 0xa6, 0xc9, 0x89, 0x03, 0x47, 0xec, 0x24, 0xd6, 0x0e, 0xec, 0x9c}, + dt2: fp.Elt{0x91, 0x0a, 0x43, 0x34, 0x20, 0xc2, 0x64, 0xf7, 0x4e, 0x48, 0xc8, 0xd2, 0x95, 0x83, 0xd1, 0xa4, 0xfb, 0x4e, 0x41, 0x3b, 0x0d, 0xd5, 0x07, 0xd9, 0xf1, 0x13, 0x16, 0x78, 0x54, 0x57, 0xd0, 0xf1, 0x4f, 0x20, 0xac, 0xcf, 0x9c, 0x3b, 0x33, 0x0b, 0x99, 0x54, 0xc3, 0x7f, 0x3e, 0x57, 0x26, 0x86, 0xd5, 0xa5, 0x2b, 0x8d, 0xe3, 0x19, 0x36, 0xf7}, + }, + { /* 15P*/ + addYX: fp.Elt{0x23, 0x69, 0x47, 0x14, 0xf9, 0x9a, 0x50, 0xff, 0x64, 0xd1, 0x50, 0x35, 0xc3, 0x11, 0xd3, 0x19, 0xcf, 0x87, 0xda, 0x30, 0x0b, 0x50, 0xda, 0xc0, 0xe0, 0x25, 0x00, 0xe5, 0x68, 0x93, 0x04, 0xc2, 0xaf, 0xbd, 0x2f, 0x36, 0x5f, 0x47, 0x96, 0x10, 0xa8, 0xbd, 0xe4, 0x88, 0xac, 0x80, 0x52, 0x61, 0x73, 0xe9, 0x63, 0xdd, 0x99, 0xad, 0x20, 0x5b}, + subYX: fp.Elt{0x1b, 0x5e, 0xa2, 0x2a, 0x25, 0x0f, 0x86, 0xc0, 0xb1, 0x2e, 0x0c, 0x13, 0x40, 0x8d, 0xf0, 0xe6, 0x00, 0x55, 0x08, 0xc5, 0x7d, 0xf4, 0xc9, 0x31, 0x25, 0x3a, 0x99, 0x69, 0xdd, 0x67, 0x63, 0x9a, 0xd6, 0x89, 0x2e, 0xa1, 0x19, 0xca, 0x2c, 0xd9, 0x59, 0x5f, 0x5d, 0xc3, 0x6e, 0x62, 0x36, 0x12, 0x59, 0x15, 0xe1, 0xdc, 0xa4, 0xad, 0xc9, 0xd0}, + dt2: fp.Elt{0xbc, 0xea, 0xfc, 0xaf, 0x66, 0x23, 0xb7, 0x39, 0x6b, 0x2a, 0x96, 0xa8, 0x54, 0x43, 0xe9, 0xaa, 0x32, 0x40, 0x63, 0x92, 0x5e, 0xdf, 0x35, 0xc2, 0x9f, 0x24, 0x0c, 0xed, 0xfc, 0xde, 0x73, 0x8f, 0xa7, 0xd5, 0xa3, 0x2b, 0x18, 0x1f, 0xb0, 0xf8, 0xeb, 0x55, 0xd9, 0xc3, 0xfd, 0x28, 0x7c, 0x4f, 0xce, 0x0d, 0xf7, 0xae, 0xc2, 0x83, 0xc3, 0x78}, + }, + { /* 17P*/ + addYX: fp.Elt{0x71, 0xe6, 0x60, 0x93, 0x37, 0xdb, 0x01, 0xa5, 0x4c, 0xba, 0xe8, 0x8e, 0xd5, 0xf9, 0xd3, 0x98, 0xe5, 0xeb, 0xab, 0x3a, 0x15, 0x8b, 0x35, 0x60, 0xbe, 0xe5, 0x9c, 0x2d, 0x10, 0x9b, 0x2e, 0xcf, 0x65, 0x64, 0xea, 0x8f, 0x72, 0xce, 0xf5, 0x18, 0xe5, 0xe2, 0xf0, 0x0e, 0xae, 0x04, 0xec, 0xa0, 0x20, 0x65, 0x63, 0x07, 0xb1, 0x9f, 0x03, 0x97}, + subYX: fp.Elt{0x9e, 0x41, 0x64, 0x30, 0x95, 0x7f, 0x3a, 0x89, 0x7b, 0x0a, 0x79, 0x59, 0x23, 0x9a, 0x3b, 0xfe, 0xa4, 0x13, 0x08, 0xb2, 0x2e, 0x04, 0x50, 0x10, 0x30, 0xcd, 0x2e, 0xa4, 0x91, 0x71, 0x50, 0x36, 0x4a, 0x02, 0xf4, 0x8d, 0xa3, 0x36, 0x1b, 0xf4, 0x52, 0xba, 0x15, 0x04, 0x8b, 0x80, 0x25, 0xd9, 0xae, 0x67, 0x20, 0xd9, 0x88, 0x8f, 0x97, 0xa6}, + dt2: fp.Elt{0xb5, 0xe7, 0x46, 0xbd, 0x55, 0x23, 0xa0, 0x68, 0xc0, 0x12, 0xd9, 0xf1, 0x0a, 0x75, 0xe2, 0xda, 0xf4, 0x6b, 0xca, 0x14, 0xe4, 0x9f, 0x0f, 0xb5, 0x3c, 0xa6, 0xa5, 0xa2, 0x63, 0x94, 0xd1, 0x1c, 0x39, 0x58, 0x57, 0x02, 0x27, 0x98, 0xb6, 0x47, 0xc6, 0x61, 0x4b, 0x5c, 0xab, 0x6f, 0x2d, 0xab, 0xe3, 0xc1, 0x69, 0xf9, 0x12, 0xb0, 0xc8, 0xd5}, + }, + { /* 19P*/ + addYX: fp.Elt{0x19, 0x7d, 0xd5, 0xac, 0x79, 0xa2, 0x82, 0x9b, 0x28, 0x31, 0x22, 0xc0, 0x73, 0x02, 0x76, 0x17, 0x10, 0x70, 0x79, 0x57, 0xc9, 0x84, 0x62, 0x8e, 0x04, 0x04, 0x61, 0x67, 0x08, 0x48, 0xb4, 0x4b, 0xde, 0x53, 0x8c, 0xff, 0x36, 0x1b, 0x62, 0x86, 0x5d, 0xe1, 0x9b, 0xb1, 0xe5, 0xe8, 0x44, 0x64, 0xa1, 0x68, 0x3f, 0xa8, 0x45, 0x52, 0x91, 0xed}, + subYX: fp.Elt{0x42, 0x1a, 0x36, 0x1f, 0x90, 0x15, 0x24, 0x8d, 0x24, 0x80, 0xe6, 0xfe, 0x1e, 0xf0, 0xad, 0xaf, 0x6a, 0x93, 0xf0, 0xa6, 0x0d, 0x5d, 0xea, 0xf6, 0x62, 0x96, 0x7a, 0x05, 0x76, 0x85, 0x74, 0x32, 0xc7, 0xc8, 0x64, 0x53, 0x62, 0xe7, 0x54, 0x84, 0xe0, 0x40, 0x66, 0x19, 0x70, 0x40, 0x95, 0x35, 0x68, 0x64, 0x43, 0xcd, 0xba, 0x29, 0x32, 0xa8}, + dt2: fp.Elt{0x3e, 0xf6, 0xd6, 0xe4, 0x99, 0xeb, 0x20, 0x66, 0x08, 0x2e, 0x26, 0x64, 0xd7, 0x76, 0xf3, 0xb4, 0xc5, 0xa4, 0x35, 0x92, 0xd2, 0x99, 0x70, 0x5a, 0x1a, 0xe9, 0xe9, 0x3d, 0x3b, 0xe1, 0xcd, 0x0e, 0xee, 0x24, 0x13, 0x03, 0x22, 0xd6, 0xd6, 0x72, 0x08, 0x2b, 0xde, 0xfd, 0x93, 0xed, 0x0c, 0x7f, 0x5e, 0x31, 0x22, 0x4d, 0x80, 0x78, 0xc0, 0x48}, + }, + { /* 21P*/ + addYX: fp.Elt{0x8f, 0x72, 0xd2, 0x9e, 0xc4, 0xcd, 0x2c, 0xbf, 0xa8, 0xd3, 0x24, 0x62, 0x28, 0xee, 0x39, 0x0a, 0x19, 0x3a, 0x58, 0xff, 0x21, 0x2e, 0x69, 0x6c, 0x6e, 0x18, 0xd0, 0xcd, 0x61, 0xc1, 0x18, 0x02, 0x5a, 0xe9, 0xe3, 0xef, 0x1f, 0x8e, 0x10, 0xe8, 0x90, 0x2b, 0x48, 0xcd, 0xee, 0x38, 0xbd, 0x3a, 0xca, 0xbc, 0x2d, 0xe2, 0x3a, 0x03, 0x71, 0x02}, + subYX: fp.Elt{0xf8, 0xa4, 0x32, 0x26, 0x66, 0xaf, 0x3b, 0x53, 0xe7, 0xb0, 0x91, 0x92, 0xf5, 0x3c, 0x74, 0xce, 0xf2, 0xdd, 0x68, 0xa9, 0xf4, 0xcd, 0x5f, 0x60, 0xab, 0x71, 0xdf, 0xcd, 0x5c, 0x5d, 0x51, 0x72, 0x3a, 0x96, 0xea, 0xd6, 0xde, 0x54, 0x8e, 0x55, 0x4c, 0x08, 0x4c, 0x60, 0xdd, 0x34, 0xa9, 0x6f, 0xf3, 0x04, 0x02, 0xa8, 0xa6, 0x4e, 0x4d, 0x62}, + dt2: fp.Elt{0x76, 0x4a, 0xae, 0x38, 0x62, 0x69, 0x72, 0xdc, 0xe8, 0x43, 0xbe, 0x1d, 0x61, 0xde, 0x31, 0xc3, 0x42, 0x8f, 0x33, 0x9d, 0xca, 0xc7, 0x9c, 0xec, 0x6a, 0xe2, 0xaa, 0x01, 0x49, 0x78, 0x8d, 0x72, 0x4f, 0x38, 0xea, 0x52, 0xc2, 0xd3, 0xc9, 0x39, 0x71, 0xba, 0xb9, 0x09, 0x9b, 0xa3, 0x7f, 0x45, 0x43, 0x65, 0x36, 0x29, 0xca, 0xe7, 0x5c, 0x5f}, + }, + { /* 23P*/ + addYX: fp.Elt{0x89, 0x42, 0x35, 0x48, 0x6d, 0x74, 0xe5, 0x1f, 0xc3, 0xdd, 0x28, 0x5b, 0x84, 0x41, 0x33, 0x9f, 0x42, 0xf3, 0x1d, 0x5d, 0x15, 0x6d, 0x76, 0x33, 0x36, 0xaf, 0xe9, 0xdd, 0xfa, 0x63, 0x4f, 0x7a, 0x9c, 0xeb, 0x1c, 0x4f, 0x34, 0x65, 0x07, 0x54, 0xbb, 0x4c, 0x8b, 0x62, 0x9d, 0xd0, 0x06, 0x99, 0xb3, 0xe9, 0xda, 0x85, 0x19, 0xb0, 0x3d, 0x3c}, + subYX: fp.Elt{0xbb, 0x99, 0xf6, 0xbf, 0xaf, 0x2c, 0x22, 0x0d, 0x7a, 0xaa, 0x98, 0x6f, 0x01, 0x82, 0x99, 0xcf, 0x88, 0xbd, 0x0e, 0x3a, 0x89, 0xe0, 0x9c, 0x8c, 0x17, 0x20, 0xc4, 0xe0, 0xcf, 0x43, 0x7a, 0xef, 0x0d, 0x9f, 0x87, 0xd4, 0xfb, 0xf2, 0x96, 0xb8, 0x03, 0xe8, 0xcb, 0x5c, 0xec, 0x65, 0x5f, 0x49, 0xa4, 0x7c, 0x85, 0xb4, 0xf6, 0xc7, 0xdb, 0xa3}, + dt2: fp.Elt{0x11, 0xf3, 0x32, 0xa3, 0xa7, 0xb2, 0x7d, 0x51, 0x82, 0x44, 0xeb, 0xa2, 0x7d, 0x72, 0xcb, 0xc6, 0xf6, 0xc7, 0xb2, 0x38, 0x0e, 0x0f, 0x4f, 0x29, 0x00, 0xe4, 0x5b, 0x94, 0x46, 0x86, 0x66, 0xa1, 0x83, 0xb3, 0xeb, 0x15, 0xb6, 0x31, 0x50, 0x28, 0xeb, 0xed, 0x0d, 0x32, 0x39, 0xe9, 0x23, 0x81, 0x99, 0x3e, 0xff, 0x17, 0x4c, 0x11, 0x43, 0xd1}, + }, + { /* 25P*/ + addYX: fp.Elt{0xce, 0xe7, 0xf8, 0x94, 0x8f, 0x96, 0xf8, 0x96, 0xe6, 0x72, 0x20, 0x44, 0x2c, 0xa7, 0xfc, 0xba, 0xc8, 0xe1, 0xbb, 0xc9, 0x16, 0x85, 0xcd, 0x0b, 0xe5, 0xb5, 0x5a, 0x7f, 0x51, 0x43, 0x63, 0x8b, 0x23, 0x8e, 0x1d, 0x31, 0xff, 0x46, 0x02, 0x66, 0xcc, 0x9e, 0x4d, 0xa2, 0xca, 0xe2, 0xc7, 0xfd, 0x22, 0xb1, 0xdb, 0xdf, 0x6f, 0xe6, 0xa5, 0x82}, + subYX: fp.Elt{0xd0, 0xf5, 0x65, 0x40, 0xec, 0x8e, 0x65, 0x42, 0x78, 0xc1, 0x65, 0xe4, 0x10, 0xc8, 0x0b, 0x1b, 0xdd, 0x96, 0x68, 0xce, 0xee, 0x45, 0x55, 0xd8, 0x6e, 0xd3, 0xe6, 0x77, 0x19, 0xae, 0xc2, 0x8d, 0x8d, 0x3e, 0x14, 0x3f, 0x6d, 0x00, 0x2f, 0x9b, 0xd1, 0x26, 0x60, 0x28, 0x0f, 0x3a, 0x47, 0xb3, 0xe6, 0x68, 0x28, 0x24, 0x25, 0xca, 0xc8, 0x06}, + dt2: fp.Elt{0x54, 0xbb, 0x60, 0x92, 0xdb, 0x8f, 0x0f, 0x38, 0xe0, 0xe6, 0xe4, 0xc9, 0xcc, 0x14, 0x62, 0x01, 0xc4, 0x2b, 0x0f, 0xcf, 0xed, 0x7d, 0x8e, 0xa4, 0xd9, 0x73, 0x0b, 0xba, 0x0c, 0xaf, 0x0c, 0xf9, 0xe2, 0xeb, 0x29, 0x2a, 0x53, 0xdf, 0x2c, 0x5a, 0xfa, 0x8f, 0xc1, 0x01, 0xd7, 0xb1, 0x45, 0x73, 0x92, 0x32, 0x83, 0x85, 0x12, 0x74, 0x89, 0x44}, + }, + { /* 27P*/ + addYX: fp.Elt{0x0b, 0x73, 0x3c, 0xc2, 0xb1, 0x2e, 0xe1, 0xa7, 0xf5, 0xc9, 0x7a, 0xfb, 0x3d, 0x2d, 0xac, 0x59, 0xdb, 0xfa, 0x36, 0x11, 0xd1, 0x13, 0x04, 0x51, 0x1d, 0xab, 0x9b, 0x6b, 0x93, 0xfe, 0xda, 0xb0, 0x8e, 0xb4, 0x79, 0x11, 0x21, 0x0f, 0x65, 0xb9, 0xbb, 0x79, 0x96, 0x2a, 0xfd, 0x30, 0xe0, 0xb4, 0x2d, 0x9a, 0x55, 0x25, 0x5d, 0xd4, 0xad, 0x2a}, + subYX: fp.Elt{0x9e, 0xc5, 0x04, 0xfe, 0xec, 0x3c, 0x64, 0x1c, 0xed, 0x95, 0xed, 0xae, 0xaf, 0x5c, 0x6e, 0x08, 0x9e, 0x02, 0x29, 0x59, 0x7e, 0x5f, 0xc4, 0x9a, 0xd5, 0x32, 0x72, 0x86, 0xe1, 0x4e, 0x3c, 0xce, 0x99, 0x69, 0x3b, 0xc4, 0xdd, 0x4d, 0xb7, 0xbb, 0xda, 0x3b, 0x1a, 0x99, 0xaa, 0x62, 0x15, 0xc1, 0xf0, 0xb6, 0x6c, 0xec, 0x56, 0xc1, 0xff, 0x0c}, + dt2: fp.Elt{0x2f, 0xf1, 0x3f, 0x7a, 0x2d, 0x56, 0x19, 0x7f, 0xea, 0xbe, 0x59, 0x2e, 0x13, 0x67, 0x81, 0xfb, 0xdb, 0xc8, 0xa3, 0x1d, 0xd5, 0xe9, 0x13, 0x8b, 0x29, 0xdf, 0xcf, 0x9f, 0xe7, 0xd9, 0x0b, 0x70, 0xd3, 0x15, 0x57, 0x4a, 0xe9, 0x50, 0x12, 0x1b, 0x81, 0x4b, 0x98, 0x98, 0xa8, 0x31, 0x1d, 0x27, 0x47, 0x38, 0xed, 0x57, 0x99, 0x26, 0xb2, 0xee}, + }, + { /* 29P*/ + addYX: fp.Elt{0x1c, 0xb2, 0xb2, 0x67, 0x3b, 0x8b, 0x3d, 0x5a, 0x30, 0x7e, 0x38, 0x7e, 0x3c, 0x3d, 0x28, 0x56, 0x59, 0xd8, 0x87, 0x53, 0x8b, 0xe6, 0x6c, 0x5d, 0xe5, 0x0a, 0x33, 0x10, 0xce, 0xa2, 0x17, 0x0d, 0xe8, 0x76, 0xee, 0x68, 0xa8, 0x72, 0x54, 0xbd, 0xa6, 0x24, 0x94, 0x6e, 0x77, 0xc7, 0x53, 0xb7, 0x89, 0x1c, 0x7a, 0xe9, 0x78, 0x9a, 0x74, 0x5f}, + subYX: fp.Elt{0x76, 0x96, 0x1c, 0xcf, 0x08, 0x55, 0xd8, 0x1e, 0x0d, 0xa3, 0x59, 0x95, 0x32, 0xf4, 0xc2, 0x8e, 0x84, 0x5e, 0x4b, 0x04, 0xda, 0x71, 0xc9, 0x78, 0x52, 0xde, 0x14, 0xb4, 0x31, 0xf4, 0xd4, 0xb8, 0x58, 0xc5, 0x20, 0xe8, 0xdd, 0x15, 0xb5, 0xee, 0xea, 0x61, 0xe0, 0xf5, 0xd6, 0xae, 0x55, 0x59, 0x05, 0x3e, 0xaf, 0x74, 0xac, 0x1f, 0x17, 0x82}, + dt2: fp.Elt{0x59, 0x24, 0xcd, 0xfc, 0x11, 0x7e, 0x85, 0x18, 0x3d, 0x69, 0xf7, 0x71, 0x31, 0x66, 0x98, 0x42, 0x95, 0x00, 0x8c, 0xb2, 0xae, 0x39, 0x7e, 0x85, 0xd6, 0xb0, 0x02, 0xec, 0xce, 0xfc, 0x25, 0xb2, 0xe3, 0x99, 0x8e, 0x5b, 0x61, 0x96, 0x2e, 0x6d, 0x96, 0x57, 0x71, 0xa5, 0x93, 0x41, 0x0e, 0x6f, 0xfd, 0x0a, 0xbf, 0xa9, 0xf7, 0x56, 0xa9, 0x3e}, + }, + { /* 31P*/ + addYX: fp.Elt{0xa2, 0x2e, 0x0c, 0x17, 0x4d, 0xcc, 0x85, 0x2c, 0x18, 0xa0, 0xd2, 0x08, 0xba, 0x11, 0xfa, 0x47, 0x71, 0x86, 0xaf, 0x36, 0x6a, 0xd7, 0xfe, 0xb9, 0xb0, 0x2f, 0x89, 0x98, 0x49, 0x69, 0xf8, 0x6a, 0xad, 0x27, 0x5e, 0x0a, 0x22, 0x60, 0x5e, 0x5d, 0xca, 0x06, 0x51, 0x27, 0x99, 0x29, 0x85, 0x68, 0x98, 0xe1, 0xc4, 0x21, 0x50, 0xa0, 0xe9, 0xc1}, + subYX: fp.Elt{0x4d, 0x70, 0xee, 0x91, 0x92, 0x3f, 0xb7, 0xd3, 0x1d, 0xdb, 0x8d, 0x6e, 0x16, 0xf5, 0x65, 0x7d, 0x5f, 0xb5, 0x6c, 0x59, 0x26, 0x70, 0x4b, 0xf2, 0xfc, 0xe7, 0xdf, 0x86, 0xfe, 0xa5, 0xa7, 0xa6, 0x5d, 0xfb, 0x06, 0xe9, 0xf9, 0xcc, 0xc0, 0x37, 0xcc, 0xd8, 0x09, 0x04, 0xd2, 0xa5, 0x1d, 0xd7, 0xb7, 0xce, 0x92, 0xac, 0x3c, 0xad, 0xfb, 0xae}, + dt2: fp.Elt{0x17, 0xa3, 0x9a, 0xc7, 0x86, 0x2a, 0x51, 0xf7, 0x96, 0x79, 0x49, 0x22, 0x2e, 0x5a, 0x01, 0x5c, 0xb5, 0x95, 0xd4, 0xe8, 0xcb, 0x00, 0xca, 0x2d, 0x55, 0xb6, 0x34, 0x36, 0x0b, 0x65, 0x46, 0xf0, 0x49, 0xfc, 0x87, 0x86, 0xe5, 0xc3, 0x15, 0xdb, 0x32, 0xcd, 0xf2, 0xd3, 0x82, 0x4c, 0xe6, 0x61, 0x8a, 0xaf, 0xd4, 0x9e, 0x0f, 0x5a, 0xf2, 0x81}, + }, + { /* 33P*/ + addYX: fp.Elt{0x88, 0x10, 0xc0, 0xcb, 0xf5, 0x77, 0xae, 0xa5, 0xbe, 0xf6, 0xcd, 0x2e, 0x8b, 0x7e, 0xbd, 0x79, 0x62, 0x4a, 0xeb, 0x69, 0xc3, 0x28, 0xaa, 0x72, 0x87, 0xa9, 0x25, 0x87, 0x46, 0xea, 0x0e, 0x62, 0xa3, 0x6a, 0x1a, 0xe2, 0xba, 0xdc, 0x81, 0x10, 0x33, 0x01, 0xf6, 0x16, 0x89, 0x80, 0xc6, 0xcd, 0xdb, 0xdc, 0xba, 0x0e, 0x09, 0x4a, 0x35, 0x4a}, + subYX: fp.Elt{0x86, 0xb2, 0x2b, 0xd0, 0xb8, 0x4a, 0x6d, 0x66, 0x7b, 0x32, 0xdf, 0x3b, 0x1a, 0x19, 0x1f, 0x63, 0xee, 0x1f, 0x3d, 0x1c, 0x5c, 0x14, 0x60, 0x5b, 0x72, 0x49, 0x07, 0xb1, 0x0d, 0x72, 0xc6, 0x35, 0xf0, 0xbc, 0x5e, 0xda, 0x80, 0x6b, 0x64, 0x5b, 0xe5, 0x34, 0x54, 0x39, 0xdd, 0xe6, 0x3c, 0xcb, 0xe5, 0x29, 0x32, 0x06, 0xc6, 0xb1, 0x96, 0x34}, + dt2: fp.Elt{0x85, 0x86, 0xf5, 0x84, 0x86, 0xe6, 0x77, 0x8a, 0x71, 0x85, 0x0c, 0x4f, 0x81, 0x5b, 0x29, 0x06, 0xb5, 0x2e, 0x26, 0x71, 0x07, 0x78, 0x07, 0xae, 0xbc, 0x95, 0x46, 0xc3, 0x65, 0xac, 0xe3, 0x76, 0x51, 0x7d, 0xd4, 0x85, 0x31, 0xe3, 0x43, 0xf3, 0x1b, 0x7c, 0xf7, 0x6b, 0x2c, 0xf8, 0x1c, 0xbb, 0x8d, 0xca, 0xab, 0x4b, 0xba, 0x7f, 0xa4, 0xe2}, + }, + { /* 35P*/ + addYX: fp.Elt{0x1a, 0xee, 0xe7, 0xa4, 0x8a, 0x9d, 0x53, 0x80, 0xc6, 0xb8, 0x4e, 0xdc, 0x89, 0xe0, 0xc4, 0x2b, 0x60, 0x52, 0x6f, 0xec, 0x81, 0xd2, 0x55, 0x6b, 0x1b, 0x6f, 0x17, 0x67, 0x8e, 0x42, 0x26, 0x4c, 0x65, 0x23, 0x29, 0xc6, 0x7b, 0xcd, 0x9f, 0xad, 0x4b, 0x42, 0xd3, 0x0c, 0x75, 0xc3, 0x8a, 0xf5, 0xbe, 0x9e, 0x55, 0xf7, 0x47, 0x5d, 0xbd, 0x3a}, + subYX: fp.Elt{0x0d, 0xa8, 0x3b, 0xf9, 0xc7, 0x7e, 0xc6, 0x86, 0x94, 0xc0, 0x01, 0xff, 0x27, 0xce, 0x43, 0xac, 0xe5, 0xe1, 0xd2, 0x8d, 0xc1, 0x22, 0x31, 0xbe, 0xe1, 0xaf, 0xf9, 0x4a, 0x78, 0xa1, 0x0c, 0xaa, 0xd4, 0x80, 0xe4, 0x09, 0x8d, 0xfb, 0x1d, 0x52, 0xc8, 0x60, 0x2d, 0xf2, 0xa2, 0x89, 0x02, 0x56, 0x3d, 0x56, 0x27, 0x85, 0xc7, 0xf0, 0x2b, 0x9a}, + dt2: fp.Elt{0x62, 0x7c, 0xc7, 0x6b, 0x2c, 0x9d, 0x0a, 0x7c, 0xe5, 0x50, 0x3c, 0xe6, 0x87, 0x1c, 0x82, 0x30, 0x67, 0x3c, 0x39, 0xb6, 0xa0, 0x31, 0xfb, 0x03, 0x7b, 0xa1, 0x58, 0xdf, 0x12, 0x76, 0x5d, 0x5d, 0x0a, 0x8f, 0x9b, 0x37, 0x32, 0xc3, 0x60, 0x33, 0xea, 0x9f, 0x0a, 0x99, 0xfa, 0x20, 0xd0, 0x33, 0x21, 0xc3, 0x94, 0xd4, 0x86, 0x49, 0x7c, 0x4e}, + }, + { /* 37P*/ + addYX: fp.Elt{0xc7, 0x0c, 0x71, 0xfe, 0x55, 0xd1, 0x95, 0x8f, 0x43, 0xbb, 0x6b, 0x74, 0x30, 0xbd, 0xe8, 0x6f, 0x1c, 0x1b, 0x06, 0x62, 0xf5, 0xfc, 0x65, 0xa0, 0xeb, 0x81, 0x12, 0xc9, 0x64, 0x66, 0x61, 0xde, 0xf3, 0x6d, 0xd4, 0xae, 0x8e, 0xb1, 0x72, 0xe0, 0xcd, 0x37, 0x01, 0x28, 0x52, 0xd7, 0x39, 0x46, 0x0c, 0x55, 0xcf, 0x47, 0x70, 0xef, 0xa1, 0x17}, + subYX: fp.Elt{0x8d, 0x58, 0xde, 0x83, 0x88, 0x16, 0x0e, 0x12, 0x42, 0x03, 0x50, 0x60, 0x4b, 0xdf, 0xbf, 0x95, 0xcc, 0x7d, 0x18, 0x17, 0x7e, 0x31, 0x5d, 0x8a, 0x66, 0xc1, 0xcf, 0x14, 0xea, 0xf4, 0xf4, 0xe5, 0x63, 0x2d, 0x32, 0x86, 0x9b, 0xed, 0x1f, 0x4f, 0x03, 0xaf, 0x33, 0x92, 0xcb, 0xaf, 0x9c, 0x05, 0x0d, 0x47, 0x1b, 0x42, 0xba, 0x13, 0x22, 0x98}, + dt2: fp.Elt{0xb5, 0x48, 0xeb, 0x7d, 0x3d, 0x10, 0x9f, 0x59, 0xde, 0xf8, 0x1c, 0x4f, 0x7d, 0x9d, 0x40, 0x4d, 0x9e, 0x13, 0x24, 0xb5, 0x21, 0x09, 0xb7, 0xee, 0x98, 0x5c, 0x56, 0xbc, 0x5e, 0x2b, 0x78, 0x38, 0x06, 0xac, 0xe3, 0xe0, 0xfa, 0x2e, 0xde, 0x4f, 0xd2, 0xb3, 0xfb, 0x2d, 0x71, 0x84, 0xd1, 0x9d, 0x12, 0x5b, 0x35, 0xc8, 0x03, 0x68, 0x67, 0xc7}, + }, + { /* 39P*/ + addYX: fp.Elt{0xb6, 0x65, 0xfb, 0xa7, 0x06, 0x35, 0xbb, 0xe0, 0x31, 0x8d, 0x91, 0x40, 0x98, 0xab, 0x30, 0xe4, 0xca, 0x12, 0x59, 0x89, 0xed, 0x65, 0x5d, 0x7f, 0xae, 0x69, 0xa0, 0xa4, 0xfa, 0x78, 0xb4, 0xf7, 0xed, 0xae, 0x86, 0x78, 0x79, 0x64, 0x24, 0xa6, 0xd4, 0xe1, 0xf6, 0xd3, 0xa0, 0x89, 0xba, 0x20, 0xf4, 0x54, 0x0d, 0x8f, 0xdb, 0x1a, 0x79, 0xdb}, + subYX: fp.Elt{0xe1, 0x82, 0x0c, 0x4d, 0xde, 0x9f, 0x40, 0xf0, 0xc1, 0xbd, 0x8b, 0xd3, 0x24, 0x03, 0xcd, 0xf2, 0x92, 0x7d, 0xe2, 0x68, 0x7f, 0xf1, 0xbe, 0x69, 0xde, 0x34, 0x67, 0x4c, 0x85, 0x3b, 0xec, 0x98, 0xcc, 0x4d, 0x3e, 0xc0, 0x96, 0x27, 0xe6, 0x75, 0xfc, 0xdf, 0x37, 0xc0, 0x1e, 0x27, 0xe0, 0xf6, 0xc2, 0xbd, 0xbc, 0x3d, 0x9b, 0x39, 0xdc, 0xe2}, + dt2: fp.Elt{0xd8, 0x29, 0xa7, 0x39, 0xe3, 0x9f, 0x2f, 0x0e, 0x4b, 0x24, 0x21, 0x70, 0xef, 0xfd, 0x91, 0xea, 0xbf, 0xe1, 0x72, 0x90, 0xcc, 0xc9, 0x84, 0x0e, 0xad, 0xd5, 0xe6, 0xbb, 0xc5, 0x99, 0x7f, 0xa4, 0xf0, 0x2e, 0xcc, 0x95, 0x64, 0x27, 0x19, 0xd8, 0x4c, 0x27, 0x0d, 0xff, 0xb6, 0x29, 0xe2, 0x6c, 0xfa, 0xbb, 0x4d, 0x9c, 0xbb, 0xaf, 0xa5, 0xec}, + }, + { /* 41P*/ + addYX: fp.Elt{0xd6, 0x33, 0x3f, 0x9f, 0xcf, 0xfd, 0x4c, 0xd1, 0xfe, 0xe5, 0xeb, 0x64, 0x27, 0xae, 0x7a, 0xa2, 0x82, 0x50, 0x6d, 0xaa, 0xe3, 0x5d, 0xe2, 0x48, 0x60, 0xb3, 0x76, 0x04, 0xd9, 0x19, 0xa7, 0xa1, 0x73, 0x8d, 0x38, 0xa9, 0xaf, 0x45, 0xb5, 0xb2, 0x62, 0x9b, 0xf1, 0x35, 0x7b, 0x84, 0x66, 0xeb, 0x06, 0xef, 0xf1, 0xb2, 0x2d, 0x6a, 0x61, 0x15}, + subYX: fp.Elt{0x86, 0x50, 0x42, 0xf7, 0xda, 0x59, 0xb2, 0xcf, 0x0d, 0x3d, 0xee, 0x8e, 0x53, 0x5d, 0xf7, 0x9e, 0x6a, 0x26, 0x2d, 0xc7, 0x8c, 0x8e, 0x18, 0x50, 0x6d, 0xb7, 0x51, 0x4c, 0xa7, 0x52, 0x6e, 0x0e, 0x0a, 0x16, 0x74, 0xb2, 0x81, 0x8b, 0x56, 0x27, 0x22, 0x84, 0xf4, 0x56, 0xc5, 0x06, 0xe1, 0x8b, 0xca, 0x2d, 0xdb, 0x9a, 0xf6, 0x10, 0x9c, 0x51}, + dt2: fp.Elt{0x1f, 0x16, 0xa2, 0x78, 0x96, 0x1b, 0x85, 0x9c, 0x76, 0x49, 0xd4, 0x0f, 0xac, 0xb0, 0xf4, 0xd0, 0x06, 0x2c, 0x7e, 0x6d, 0x6e, 0x8e, 0xc7, 0x9f, 0x18, 0xad, 0xfc, 0x88, 0x0c, 0x0c, 0x09, 0x05, 0x05, 0xa0, 0x79, 0x72, 0x32, 0x72, 0x87, 0x0f, 0x49, 0x87, 0x0c, 0xb4, 0x12, 0xc2, 0x09, 0xf8, 0x9f, 0x30, 0x72, 0xa9, 0x47, 0x13, 0x93, 0x49}, + }, + { /* 43P*/ + addYX: fp.Elt{0xcc, 0xb1, 0x4c, 0xd3, 0xc0, 0x9e, 0x9e, 0x4d, 0x6d, 0x28, 0x0b, 0xa5, 0x94, 0xa7, 0x2e, 0xc2, 0xc7, 0xaf, 0x29, 0x73, 0xc9, 0x68, 0xea, 0x0f, 0x34, 0x37, 0x8d, 0x96, 0x8f, 0x3a, 0x3d, 0x73, 0x1e, 0x6d, 0x9f, 0xcf, 0x8d, 0x83, 0xb5, 0x71, 0xb9, 0xe1, 0x4b, 0x67, 0x71, 0xea, 0xcf, 0x56, 0xe5, 0xeb, 0x72, 0x15, 0x2f, 0x9e, 0xa8, 0xaa}, + subYX: fp.Elt{0xf4, 0x3e, 0x85, 0x1c, 0x1a, 0xef, 0x50, 0xd1, 0xb4, 0x20, 0xb2, 0x60, 0x05, 0x98, 0xfe, 0x47, 0x3b, 0xc1, 0x76, 0xca, 0x2c, 0x4e, 0x5a, 0x42, 0xa3, 0xf7, 0x20, 0xaa, 0x57, 0x39, 0xee, 0x34, 0x1f, 0xe1, 0x68, 0xd3, 0x7e, 0x06, 0xc4, 0x6c, 0xc7, 0x76, 0x2b, 0xe4, 0x1c, 0x48, 0x44, 0xe6, 0xe5, 0x44, 0x24, 0x8d, 0xb3, 0xb6, 0x88, 0x32}, + dt2: fp.Elt{0x18, 0xa7, 0xba, 0xd0, 0x44, 0x6f, 0x33, 0x31, 0x00, 0xf8, 0xf6, 0x12, 0xe3, 0xc5, 0xc7, 0xb5, 0x91, 0x9c, 0x91, 0xb5, 0x75, 0x18, 0x18, 0x8a, 0xab, 0xed, 0x24, 0x11, 0x2e, 0xce, 0x5a, 0x0f, 0x94, 0x5f, 0x2e, 0xca, 0xd3, 0x80, 0xea, 0xe5, 0x34, 0x96, 0x67, 0x8b, 0x6a, 0x26, 0x5e, 0xc8, 0x9d, 0x2c, 0x5e, 0x6c, 0xa2, 0x0c, 0xbf, 0xf0}, + }, + { /* 45P*/ + addYX: fp.Elt{0xb3, 0xbf, 0xa3, 0x85, 0xee, 0xf6, 0x58, 0x02, 0x78, 0xc4, 0x30, 0xd6, 0x57, 0x59, 0x8c, 0x88, 0x08, 0x7c, 0xbc, 0xbe, 0x0a, 0x74, 0xa9, 0xde, 0x69, 0xe7, 0x41, 0xd8, 0xbf, 0x66, 0x8d, 0x3d, 0x28, 0x00, 0x8c, 0x47, 0x65, 0x34, 0xfe, 0x86, 0x9e, 0x6a, 0xf2, 0x41, 0x6a, 0x94, 0xc4, 0x88, 0x75, 0x23, 0x0d, 0x52, 0x69, 0xee, 0x07, 0x89}, + subYX: fp.Elt{0x22, 0x3c, 0xa1, 0x70, 0x58, 0x97, 0x93, 0xbe, 0x59, 0xa8, 0x0b, 0x8a, 0x46, 0x2a, 0x38, 0x1e, 0x08, 0x6b, 0x61, 0x9f, 0xf2, 0x4a, 0x8b, 0x80, 0x68, 0x6e, 0xc8, 0x92, 0x60, 0xf3, 0xc9, 0x89, 0xb2, 0x6d, 0x63, 0xb0, 0xeb, 0x83, 0x15, 0x63, 0x0e, 0x64, 0xbb, 0xb8, 0xfe, 0xb4, 0x81, 0x90, 0x01, 0x28, 0x10, 0xb9, 0x74, 0x6e, 0xde, 0xa4}, + dt2: fp.Elt{0x1a, 0x23, 0x45, 0xa8, 0x6f, 0x4e, 0xa7, 0x4a, 0x0c, 0xeb, 0xb0, 0x43, 0xf9, 0xef, 0x99, 0x60, 0x5b, 0xdb, 0x66, 0xc0, 0x86, 0x71, 0x43, 0xb1, 0x22, 0x7b, 0x1c, 0xe7, 0x8d, 0x09, 0x1d, 0x83, 0x76, 0x9c, 0xd3, 0x5a, 0xdd, 0x42, 0xd9, 0x2f, 0x2d, 0xba, 0x7a, 0xc2, 0xd9, 0x6b, 0xd4, 0x7a, 0xf1, 0xd5, 0x5f, 0x6b, 0x85, 0xbf, 0x0b, 0xf1}, + }, + { /* 47P*/ + addYX: fp.Elt{0xb2, 0x83, 0xfa, 0x1f, 0xd2, 0xce, 0xb6, 0xf2, 0x2d, 0xea, 0x1b, 0xe5, 0x29, 0xa5, 0x72, 0xf9, 0x25, 0x48, 0x4e, 0xf2, 0x50, 0x1b, 0x39, 0xda, 0x34, 0xc5, 0x16, 0x13, 0xb4, 0x0c, 0xa1, 0x00, 0x79, 0x7a, 0xf5, 0x8b, 0xf3, 0x70, 0x14, 0xb6, 0xfc, 0x9a, 0x47, 0x68, 0x1e, 0x42, 0x70, 0x64, 0x2a, 0x84, 0x3e, 0x3d, 0x20, 0x58, 0xf9, 0x6a}, + subYX: fp.Elt{0xd9, 0xee, 0xc0, 0xc4, 0xf5, 0xc2, 0x86, 0xaf, 0x45, 0xd2, 0xd2, 0x87, 0x1b, 0x64, 0xd5, 0xe0, 0x8c, 0x44, 0x00, 0x4f, 0x43, 0x89, 0x04, 0x48, 0x4a, 0x0b, 0xca, 0x94, 0x06, 0x2f, 0x23, 0x5b, 0x6c, 0x8d, 0x44, 0x66, 0x53, 0xf5, 0x5a, 0x20, 0x72, 0x28, 0x58, 0x84, 0xcc, 0x73, 0x22, 0x5e, 0xd1, 0x0b, 0x56, 0x5e, 0x6a, 0xa3, 0x11, 0x91}, + dt2: fp.Elt{0x6e, 0x9f, 0x88, 0xa8, 0x68, 0x2f, 0x12, 0x37, 0x88, 0xfc, 0x92, 0x8f, 0x24, 0xeb, 0x5b, 0x2a, 0x2a, 0xd0, 0x14, 0x40, 0x4c, 0xa9, 0xa4, 0x03, 0x0c, 0x45, 0x48, 0x13, 0xe8, 0xa6, 0x37, 0xab, 0xc0, 0x06, 0x38, 0x6c, 0x96, 0x73, 0x40, 0x6c, 0xc6, 0xea, 0x56, 0xc6, 0xe9, 0x1a, 0x69, 0xeb, 0x7a, 0xd1, 0x33, 0x69, 0x58, 0x2b, 0xea, 0x2f}, + }, + { /* 49P*/ + addYX: fp.Elt{0x58, 0xa8, 0x05, 0x41, 0x00, 0x9d, 0xaa, 0xd9, 0x98, 0xcf, 0xb9, 0x41, 0xb5, 0x4a, 0x8d, 0xe2, 0xe7, 0xc0, 0x72, 0xef, 0xc8, 0x28, 0x6b, 0x68, 0x9d, 0xc9, 0xdf, 0x05, 0x8b, 0xd0, 0x04, 0x74, 0x79, 0x45, 0x52, 0x05, 0xa3, 0x6e, 0x35, 0x3a, 0xe3, 0xef, 0xb2, 0xdc, 0x08, 0x6f, 0x4e, 0x76, 0x85, 0x67, 0xba, 0x23, 0x8f, 0xdd, 0xaf, 0x09}, + subYX: fp.Elt{0xb4, 0x38, 0xc8, 0xff, 0x4f, 0x65, 0x2a, 0x7e, 0xad, 0xb1, 0xc6, 0xb9, 0x3d, 0xd6, 0xf7, 0x14, 0xcf, 0xf6, 0x98, 0x75, 0xbb, 0x47, 0x83, 0x90, 0xe7, 0xe1, 0xf6, 0x14, 0x99, 0x7e, 0xfa, 0xe4, 0x77, 0x24, 0xe3, 0xe7, 0xf0, 0x1e, 0xdb, 0x27, 0x4e, 0x16, 0x04, 0xf2, 0x08, 0x52, 0xfc, 0xec, 0x55, 0xdb, 0x2e, 0x67, 0xe1, 0x94, 0x32, 0x89}, + dt2: fp.Elt{0x00, 0xad, 0x03, 0x35, 0x1a, 0xb1, 0x88, 0xf0, 0xc9, 0x11, 0xe4, 0x12, 0x52, 0x61, 0xfd, 0x8a, 0x1b, 0x6a, 0x0a, 0x4c, 0x42, 0x46, 0x22, 0x0e, 0xa5, 0xf9, 0xe2, 0x50, 0xf2, 0xb2, 0x1f, 0x20, 0x78, 0x10, 0xf6, 0xbf, 0x7f, 0x0c, 0x9c, 0xad, 0x40, 0x8b, 0x82, 0xd4, 0xba, 0x69, 0x09, 0xac, 0x4b, 0x6d, 0xc4, 0x49, 0x17, 0x81, 0x57, 0x3b}, + }, + { /* 51P*/ + addYX: fp.Elt{0x0d, 0xfe, 0xb4, 0x35, 0x11, 0xbd, 0x1d, 0x6b, 0xc2, 0xc5, 0x3b, 0xd2, 0x23, 0x2c, 0x72, 0xe3, 0x48, 0xb1, 0x48, 0x73, 0xfb, 0xa3, 0x21, 0x6e, 0xc0, 0x09, 0x69, 0xac, 0xe1, 0x60, 0xbc, 0x24, 0x03, 0x99, 0x63, 0x0a, 0x00, 0xf0, 0x75, 0xf6, 0x92, 0xc5, 0xd6, 0xdb, 0x51, 0xd4, 0x7d, 0xe6, 0xf4, 0x11, 0x79, 0xd7, 0xc3, 0xaf, 0x48, 0xd0}, + subYX: fp.Elt{0xf4, 0x4f, 0xaf, 0x31, 0xe3, 0x10, 0x89, 0x95, 0xf0, 0x8a, 0xf6, 0x31, 0x9f, 0x48, 0x02, 0xba, 0x42, 0x2b, 0x3c, 0x22, 0x8b, 0xcc, 0x12, 0x98, 0x6e, 0x7a, 0x64, 0x3a, 0xc4, 0xca, 0x32, 0x2a, 0x72, 0xf8, 0x2c, 0xcf, 0x78, 0x5e, 0x7a, 0x75, 0x6e, 0x72, 0x46, 0x48, 0x62, 0x28, 0xac, 0x58, 0x1a, 0xc6, 0x59, 0x88, 0x2a, 0x44, 0x9e, 0x83}, + dt2: fp.Elt{0xb3, 0xde, 0x36, 0xfd, 0xeb, 0x1b, 0xd4, 0x24, 0x1b, 0x08, 0x8c, 0xfe, 0xa9, 0x41, 0xa1, 0x64, 0xf2, 0x6d, 0xdb, 0xf9, 0x94, 0xae, 0x86, 0x71, 0xab, 0x10, 0xbf, 0xa3, 0xb2, 0xa0, 0xdf, 0x10, 0x8c, 0x74, 0xce, 0xb3, 0xfc, 0xdb, 0xba, 0x15, 0xf6, 0x91, 0x7a, 0x9c, 0x36, 0x1e, 0x45, 0x07, 0x3c, 0xec, 0x1a, 0x61, 0x26, 0x93, 0xe3, 0x50}, + }, + { /* 53P*/ + addYX: fp.Elt{0xc5, 0x50, 0xc5, 0x83, 0xb0, 0xbd, 0xd9, 0xf6, 0x6d, 0x15, 0x5e, 0xc1, 0x1a, 0x33, 0xa0, 0xce, 0x13, 0x70, 0x3b, 0xe1, 0x31, 0xc6, 0xc4, 0x02, 0xec, 0x8c, 0xd5, 0x9c, 0x97, 0xd3, 0x12, 0xc4, 0xa2, 0xf9, 0xd5, 0xfb, 0x22, 0x69, 0x94, 0x09, 0x2f, 0x59, 0xce, 0xdb, 0xf2, 0xf2, 0x00, 0xe0, 0xa9, 0x08, 0x44, 0x2e, 0x8b, 0x6b, 0xf5, 0xb3}, + subYX: fp.Elt{0x90, 0xdd, 0xec, 0xa2, 0x65, 0xb7, 0x61, 0xbc, 0xaa, 0x70, 0xa2, 0x15, 0xd8, 0xb0, 0xf8, 0x8e, 0x23, 0x3d, 0x9f, 0x46, 0xa3, 0x29, 0x20, 0xd1, 0xa1, 0x15, 0x81, 0xc6, 0xb6, 0xde, 0xbe, 0x60, 0x63, 0x24, 0xac, 0x15, 0xfb, 0xeb, 0xd3, 0xea, 0x57, 0x13, 0x86, 0x38, 0x1e, 0x22, 0xf4, 0x8c, 0x5d, 0xaf, 0x1b, 0x27, 0x21, 0x4f, 0xa3, 0x63}, + dt2: fp.Elt{0x07, 0x15, 0x87, 0xc4, 0xfd, 0xa1, 0x97, 0x7a, 0x07, 0x1f, 0x56, 0xcc, 0xe3, 0x6a, 0x01, 0x90, 0xce, 0xf9, 0xfa, 0x50, 0xb2, 0xe0, 0x87, 0x8b, 0x6c, 0x63, 0x6c, 0xf6, 0x2a, 0x09, 0xef, 0xef, 0xd2, 0x31, 0x40, 0x25, 0xf6, 0x84, 0xcb, 0xe0, 0xc4, 0x23, 0xc1, 0xcb, 0xe2, 0x02, 0x83, 0x2d, 0xed, 0x74, 0x74, 0x8b, 0xf8, 0x7c, 0x81, 0x18}, + }, + { /* 55P*/ + addYX: fp.Elt{0x9e, 0xe5, 0x59, 0x95, 0x63, 0x2e, 0xac, 0x8b, 0x03, 0x3c, 0xc1, 0x8e, 0xe1, 0x5b, 0x56, 0x3c, 0x16, 0x41, 0xe4, 0xc2, 0x60, 0x0c, 0x6d, 0x65, 0x9f, 0xfc, 0x27, 0x68, 0x43, 0x44, 0x05, 0x12, 0x6c, 0xda, 0x04, 0xef, 0xcf, 0xcf, 0xdc, 0x0a, 0x1a, 0x7f, 0x12, 0xd3, 0xeb, 0x02, 0xb6, 0x04, 0xca, 0xd6, 0xcb, 0xf0, 0x22, 0xba, 0x35, 0x6d}, + subYX: fp.Elt{0x09, 0x6d, 0xf9, 0x64, 0x4c, 0xe6, 0x41, 0xff, 0x01, 0x4d, 0xce, 0x1e, 0xfa, 0x38, 0xa2, 0x25, 0x62, 0xff, 0x03, 0x39, 0x18, 0x91, 0xbb, 0x9d, 0xce, 0x02, 0xf0, 0xf1, 0x3c, 0x55, 0x18, 0xa9, 0xab, 0x4d, 0xd2, 0x35, 0xfd, 0x8d, 0xa9, 0xb2, 0xad, 0xb7, 0x06, 0x6e, 0xc6, 0x69, 0x49, 0xd6, 0x98, 0x98, 0x0b, 0x22, 0x81, 0x6b, 0xbd, 0xa0}, + dt2: fp.Elt{0x22, 0xf4, 0x85, 0x5d, 0x2b, 0xf1, 0x55, 0xa5, 0xd6, 0x27, 0x86, 0x57, 0x12, 0x1f, 0x16, 0x0a, 0x5a, 0x9b, 0xf2, 0x38, 0xb6, 0x28, 0xd8, 0x99, 0x0c, 0x89, 0x1d, 0x7f, 0xca, 0x21, 0x17, 0x1a, 0x0b, 0x02, 0x5f, 0x77, 0x2f, 0x73, 0x30, 0x7c, 0xc8, 0xd7, 0x2b, 0xcc, 0xe7, 0xf3, 0x21, 0xac, 0x53, 0xa7, 0x11, 0x5d, 0xd8, 0x1d, 0x9b, 0xf5}, + }, + { /* 57P*/ + addYX: fp.Elt{0x94, 0x63, 0x5d, 0xef, 0xfd, 0x6d, 0x25, 0x4e, 0x6d, 0x29, 0x03, 0xed, 0x24, 0x28, 0x27, 0x57, 0x47, 0x3e, 0x6a, 0x1a, 0xfe, 0x37, 0xee, 0x5f, 0x83, 0x29, 0x14, 0xfd, 0x78, 0x25, 0x8a, 0xe1, 0x02, 0x38, 0xd8, 0xca, 0x65, 0x55, 0x40, 0x7d, 0x48, 0x2c, 0x7c, 0x7e, 0x60, 0xb6, 0x0c, 0x6d, 0xf7, 0xe8, 0xb3, 0x62, 0x53, 0xd6, 0x9c, 0x2b}, + subYX: fp.Elt{0x47, 0x25, 0x70, 0x62, 0xf5, 0x65, 0x93, 0x62, 0x08, 0xac, 0x59, 0x66, 0xdb, 0x08, 0xd9, 0x1a, 0x19, 0xaf, 0xf4, 0xef, 0x02, 0xa2, 0x78, 0xa9, 0x55, 0x1c, 0xfa, 0x08, 0x11, 0xcb, 0xa3, 0x71, 0x74, 0xb1, 0x62, 0xe7, 0xc7, 0xf3, 0x5a, 0xb5, 0x8b, 0xd4, 0xf6, 0x10, 0x57, 0x79, 0x72, 0x2f, 0x13, 0x86, 0x7b, 0x44, 0x5f, 0x48, 0xfd, 0x88}, + dt2: fp.Elt{0x10, 0x02, 0xcd, 0x05, 0x9a, 0xc3, 0x32, 0x6d, 0x10, 0x3a, 0x74, 0xba, 0x06, 0xc4, 0x3b, 0x34, 0xbc, 0x36, 0xed, 0xa3, 0xba, 0x9a, 0xdb, 0x6d, 0xd4, 0x69, 0x99, 0x97, 0xd0, 0xe4, 0xdd, 0xf5, 0xd4, 0x7c, 0xd3, 0x4e, 0xab, 0xd1, 0x3b, 0xbb, 0xe9, 0xc7, 0x6a, 0x94, 0x25, 0x61, 0xf0, 0x06, 0xc5, 0x12, 0xa8, 0x86, 0xe5, 0x35, 0x46, 0xeb}, + }, + { /* 59P*/ + addYX: fp.Elt{0x9e, 0x95, 0x11, 0xc6, 0xc7, 0xe8, 0xee, 0x5a, 0x26, 0xa0, 0x72, 0x72, 0x59, 0x91, 0x59, 0x16, 0x49, 0x99, 0x7e, 0xbb, 0xd7, 0x15, 0xb4, 0xf2, 0x40, 0xf9, 0x5a, 0x4d, 0xc8, 0xa0, 0xe2, 0x34, 0x7b, 0x34, 0xf3, 0x99, 0xbf, 0xa9, 0xf3, 0x79, 0xc1, 0x1a, 0x0c, 0xf4, 0x86, 0x74, 0x4e, 0xcb, 0xbc, 0x90, 0xad, 0xb6, 0x51, 0x6d, 0xaa, 0x33}, + subYX: fp.Elt{0x9f, 0xd1, 0xc5, 0xa2, 0x6c, 0x24, 0x88, 0x15, 0x71, 0x68, 0xf6, 0x07, 0x45, 0x02, 0xc4, 0x73, 0x7e, 0x75, 0x87, 0xca, 0x7c, 0xf0, 0x92, 0x00, 0x75, 0xd6, 0x5a, 0xdd, 0xe0, 0x64, 0x16, 0x9d, 0x62, 0x80, 0x33, 0x9f, 0xf4, 0x8e, 0x1a, 0x15, 0x1c, 0xd3, 0x0f, 0x4d, 0x4f, 0x62, 0x2d, 0xd7, 0xa5, 0x77, 0xe3, 0xea, 0xf0, 0xfb, 0x1a, 0xdb}, + dt2: fp.Elt{0x6a, 0xa2, 0xb1, 0xaa, 0xfb, 0x5a, 0x32, 0x4e, 0xff, 0x47, 0x06, 0xd5, 0x9a, 0x4f, 0xce, 0x83, 0x5b, 0x82, 0x34, 0x3e, 0x47, 0xb8, 0xf8, 0xe9, 0x7c, 0x67, 0x69, 0x8d, 0x9c, 0xb7, 0xde, 0x57, 0xf4, 0x88, 0x41, 0x56, 0x0c, 0x87, 0x1e, 0xc9, 0x2f, 0x54, 0xbf, 0x5c, 0x68, 0x2c, 0xd9, 0xc4, 0xef, 0x53, 0x73, 0x1e, 0xa6, 0x38, 0x02, 0x10}, + }, + { /* 61P*/ + addYX: fp.Elt{0x08, 0x80, 0x4a, 0xc9, 0xb7, 0xa8, 0x88, 0xd9, 0xfc, 0x6a, 0xc0, 0x3e, 0xc2, 0x33, 0x4d, 0x2b, 0x2a, 0xa3, 0x6d, 0x72, 0x3e, 0xdc, 0x34, 0x68, 0x08, 0xbf, 0x27, 0xef, 0xf4, 0xff, 0xe2, 0x0c, 0x31, 0x0c, 0xa2, 0x0a, 0x1f, 0x65, 0xc1, 0x4c, 0x61, 0xd3, 0x1b, 0xbc, 0x25, 0xb1, 0xd0, 0xd4, 0x89, 0xb2, 0x53, 0xfb, 0x43, 0xa5, 0xaf, 0x04}, + subYX: fp.Elt{0xe3, 0xe1, 0x37, 0xad, 0x58, 0xa9, 0x55, 0x81, 0xee, 0x64, 0x21, 0xb9, 0xf5, 0x4c, 0x35, 0xea, 0x4a, 0xd3, 0x26, 0xaa, 0x90, 0xd4, 0x60, 0x46, 0x09, 0x4b, 0x4a, 0x62, 0xf9, 0xcd, 0xe1, 0xee, 0xbb, 0xc2, 0x09, 0x0b, 0xb0, 0x96, 0x8e, 0x43, 0x77, 0xaf, 0x25, 0x20, 0x5e, 0x47, 0xe4, 0x1d, 0x50, 0x69, 0x74, 0x08, 0xd7, 0xb9, 0x90, 0x13}, + dt2: fp.Elt{0x51, 0x91, 0x95, 0x64, 0x03, 0x16, 0xfd, 0x6e, 0x26, 0x94, 0x6b, 0x61, 0xe7, 0xd9, 0xe0, 0x4a, 0x6d, 0x7c, 0xfa, 0xc0, 0xe2, 0x43, 0x23, 0x53, 0x70, 0xf5, 0x6f, 0x73, 0x8b, 0x81, 0xb0, 0x0c, 0xee, 0x2e, 0x46, 0xf2, 0x8d, 0xa6, 0xfb, 0xb5, 0x1c, 0x33, 0xbf, 0x90, 0x59, 0xc9, 0x7c, 0xb8, 0x6f, 0xad, 0x75, 0x02, 0x90, 0x8e, 0x59, 0x75}, + }, + { /* 63P*/ + addYX: fp.Elt{0x36, 0x4d, 0x77, 0x04, 0xb8, 0x7d, 0x4a, 0xd1, 0xc5, 0xbb, 0x7b, 0x50, 0x5f, 0x8d, 0x9d, 0x62, 0x0f, 0x66, 0x71, 0xec, 0x87, 0xc5, 0x80, 0x82, 0xc8, 0xf4, 0x6a, 0x94, 0x92, 0x5b, 0xb0, 0x16, 0x9b, 0xb2, 0xc9, 0x6f, 0x2b, 0x2d, 0xee, 0x95, 0x73, 0x2e, 0xc2, 0x1b, 0xc5, 0x55, 0x36, 0x86, 0x24, 0xf8, 0x20, 0x05, 0x0d, 0x93, 0xd7, 0x76}, + subYX: fp.Elt{0x7f, 0x01, 0xeb, 0x2e, 0x48, 0x4d, 0x1d, 0xf1, 0x06, 0x7e, 0x7c, 0x2a, 0x43, 0xbf, 0x28, 0xac, 0xe9, 0x58, 0x13, 0xc8, 0xbf, 0x8e, 0xc0, 0xef, 0xe8, 0x4f, 0x46, 0x8a, 0xe7, 0xc0, 0xf6, 0x0f, 0x0a, 0x03, 0x48, 0x91, 0x55, 0x39, 0x2a, 0xe3, 0xdc, 0xf6, 0x22, 0x9d, 0x4d, 0x71, 0x55, 0x68, 0x25, 0x6e, 0x95, 0x52, 0xee, 0x4c, 0xd9, 0x01}, + dt2: fp.Elt{0xac, 0x33, 0x3f, 0x7c, 0x27, 0x35, 0x15, 0x91, 0x33, 0x8d, 0xf9, 0xc4, 0xf4, 0xf3, 0x90, 0x09, 0x75, 0x69, 0x62, 0x9f, 0x61, 0x35, 0x83, 0x92, 0x04, 0xef, 0x96, 0x38, 0x80, 0x9e, 0x88, 0xb3, 0x67, 0x95, 0xbe, 0x79, 0x3c, 0x35, 0xd8, 0xdc, 0xb2, 0x3e, 0x2d, 0xe6, 0x46, 0xbe, 0x81, 0xf3, 0x32, 0x0e, 0x37, 0x23, 0x75, 0x2a, 0x3d, 0xa0}, + }, +} diff --git a/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go new file mode 100644 index 00000000..f6ac5edb --- /dev/null +++ b/vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go @@ -0,0 +1,62 @@ +package goldilocks + +import ( + "crypto/subtle" + + mlsb "github.com/cloudflare/circl/math/mlsbset" +) + +const ( + // MLSBRecoding parameters + fxT = 448 + fxV = 2 + fxW = 3 + fx2w1 = 1 << (uint(fxW) - 1) +) + +// ScalarBaseMult returns kG where G is the generator point. +func (e twistCurve) ScalarBaseMult(k *Scalar) *twistPoint { + m, err := mlsb.New(fxT, fxV, fxW) + if err != nil { + panic(err) + } + if m.IsExtended() { + panic("not extended") + } + + var isZero int + if k.IsZero() { + isZero = 1 + } + subtle.ConstantTimeCopy(isZero, k[:], order[:]) + + minusK := *k + isEven := 1 - int(k[0]&0x1) + minusK.Neg() + subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) + c, err := m.Encode(k[:]) + if err != nil { + panic(err) + } + + gP := c.Exp(groupMLSB{}) + P := gP.(*twistPoint) + P.cneg(uint(isEven)) + return P +} + +type groupMLSB struct{} + +func (e groupMLSB) ExtendedEltP() mlsb.EltP { return nil } +func (e groupMLSB) Sqr(x mlsb.EltG) { x.(*twistPoint).Double() } +func (e groupMLSB) Mul(x mlsb.EltG, y mlsb.EltP) { x.(*twistPoint).mixAddZ1(y.(*preTwistPointAffine)) } +func (e groupMLSB) Identity() mlsb.EltG { return twistCurve{}.Identity() } +func (e groupMLSB) NewEltP() mlsb.EltP { return &preTwistPointAffine{} } +func (e groupMLSB) Lookup(a mlsb.EltP, v uint, s, u int32) { + Tabj := &tabFixMult[v] + P := a.(*preTwistPointAffine) + for k := range Tabj { + P.cmov(&Tabj[k], uint(subtle.ConstantTimeEq(int32(k), u))) + } + P.cneg(int(s >> 31)) +} diff --git a/vendor/github.com/cloudflare/circl/internal/conv/conv.go b/vendor/github.com/cloudflare/circl/internal/conv/conv.go new file mode 100644 index 00000000..649a8e93 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/conv/conv.go @@ -0,0 +1,140 @@ +package conv + +import ( + "encoding/binary" + "fmt" + "math/big" + "strings" +) + +// BytesLe2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func BytesLe2Hex(x []byte) string { + b := &strings.Builder{} + b.Grow(2*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%02x", x[i]) + } + return b.String() +} + +// BytesLe2BigInt converts a little-endian slice x into a big-endian +// math/big.Int. +func BytesLe2BigInt(x []byte) *big.Int { + n := len(x) + b := new(big.Int) + if len(x) > 0 { + y := make([]byte, n) + for i := 0; i < n; i++ { + y[n-1-i] = x[i] + } + b.SetBytes(y) + } + return b +} + +// BytesBe2Uint64Le converts a big-endian slice x to a little-endian slice of uint64. +func BytesBe2Uint64Le(x []byte) []uint64 { + l := len(x) + z := make([]uint64, (l+7)/8) + blocks := l / 8 + for i := 0; i < blocks; i++ { + z[i] = binary.BigEndian.Uint64(x[l-8*(i+1):]) + } + remBytes := l % 8 + for i := 0; i < remBytes; i++ { + z[blocks] |= uint64(x[l-1-8*blocks-i]) << uint(8*i) + } + return z +} + +// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2BytesLe(z []byte, x *big.Int) { + xLen := (x.BitLen() + 7) >> 3 + zLen := len(z) + if zLen >= xLen && x.Sign() >= 0 { + y := x.Bytes() + for i := 0; i < xLen; i++ { + z[i] = y[xLen-1-i] + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } + } +} + +// Uint64Le2BigInt converts a little-endian slice x into a big number. +func Uint64Le2BigInt(x []uint64) *big.Int { + n := len(x) + b := new(big.Int) + var bi big.Int + for i := n - 1; i >= 0; i-- { + bi.SetUint64(x[i]) + b.Lsh(b, 64) + b.Add(b, &bi) + } + return b +} + +// Uint64Le2BytesLe converts a little-endian slice x to a little-endian slice of bytes. +func Uint64Le2BytesLe(x []uint64) []byte { + b := make([]byte, 8*len(x)) + n := len(x) + for i := 0; i < n; i++ { + binary.LittleEndian.PutUint64(b[i*8:], x[i]) + } + return b +} + +// Uint64Le2BytesBe converts a little-endian slice x to a big-endian slice of bytes. +func Uint64Le2BytesBe(x []uint64) []byte { + b := make([]byte, 8*len(x)) + n := len(x) + for i := 0; i < n; i++ { + binary.BigEndian.PutUint64(b[i*8:], x[n-1-i]) + } + return b +} + +// Uint64Le2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func Uint64Le2Hex(x []uint64) string { + b := new(strings.Builder) + b.Grow(16*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%016x", x[i]) + } + return b.String() +} + +// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2Uint64Le(z []uint64, x *big.Int) { + xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words + zLen := len(z) + if zLen >= xLen && x.Sign() > 0 { + var y, yi big.Int + y.Set(x) + two64 := big.NewInt(1) + two64.Lsh(two64, 64).Sub(two64, big.NewInt(1)) + for i := 0; i < xLen; i++ { + yi.And(&y, two64) + z[i] = yi.Uint64() + y.Rsh(&y, 64) + } + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/doc.go b/vendor/github.com/cloudflare/circl/internal/sha3/doc.go new file mode 100644 index 00000000..7e023090 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/doc.go @@ -0,0 +1,62 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package sha3 implements the SHA-3 fixed-output-length hash functions and +// the SHAKE variable-output-length hash functions defined by FIPS-202. +// +// Both types of hash function use the "sponge" construction and the Keccak +// permutation. For a detailed specification see http://keccak.noekeon.org/ +// +// # Guidance +// +// If you aren't sure what function you need, use SHAKE256 with at least 64 +// bytes of output. The SHAKE instances are faster than the SHA3 instances; +// the latter have to allocate memory to conform to the hash.Hash interface. +// +// If you need a secret-key MAC (message authentication code), prepend the +// secret key to the input, hash with SHAKE256 and read at least 32 bytes of +// output. +// +// # Security strengths +// +// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security +// strength against preimage attacks of x bits. Since they only produce "x" +// bits of output, their collision-resistance is only "x/2" bits. +// +// The SHAKE-256 and -128 functions have a generic security strength of 256 and +// 128 bits against all attacks, provided that at least 2x bits of their output +// is used. Requesting more than 64 or 32 bytes of output, respectively, does +// not increase the collision-resistance of the SHAKE functions. +// +// # The sponge construction +// +// A sponge builds a pseudo-random function from a public pseudo-random +// permutation, by applying the permutation to a state of "rate + capacity" +// bytes, but hiding "capacity" of the bytes. +// +// A sponge starts out with a zero state. To hash an input using a sponge, up +// to "rate" bytes of the input are XORed into the sponge's state. The sponge +// is then "full" and the permutation is applied to "empty" it. This process is +// repeated until all the input has been "absorbed". The input is then padded. +// The digest is "squeezed" from the sponge in the same way, except that output +// is copied out instead of input being XORed in. +// +// A sponge is parameterized by its generic security strength, which is equal +// to half its capacity; capacity + rate is equal to the permutation's width. +// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means +// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. +// +// # Recommendations +// +// The SHAKE functions are recommended for most new uses. They can produce +// output of arbitrary length. SHAKE256, with an output length of at least +// 64 bytes, provides 256-bit security against all attacks. The Keccak team +// recommends it for most applications upgrading from SHA2-512. (NIST chose a +// much stronger, but much slower, sponge instance for SHA3-512.) +// +// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. +// They produce output of the same length, with the same security strengths +// against all attacks. This means, in particular, that SHA3-256 only has +// 128-bit collision resistance, because its output length is 32 bytes. +package sha3 diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go b/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go new file mode 100644 index 00000000..7d2365a7 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go @@ -0,0 +1,69 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file provides functions for creating instances of the SHA-3 +// and SHAKE hash functions, as well as utility functions for hashing +// bytes. + +// New224 creates a new SHA3-224 hash. +// Its generic security strength is 224 bits against preimage attacks, +// and 112 bits against collision attacks. +func New224() State { + return State{rate: 144, outputLen: 28, dsbyte: 0x06} +} + +// New256 creates a new SHA3-256 hash. +// Its generic security strength is 256 bits against preimage attacks, +// and 128 bits against collision attacks. +func New256() State { + return State{rate: 136, outputLen: 32, dsbyte: 0x06} +} + +// New384 creates a new SHA3-384 hash. +// Its generic security strength is 384 bits against preimage attacks, +// and 192 bits against collision attacks. +func New384() State { + return State{rate: 104, outputLen: 48, dsbyte: 0x06} +} + +// New512 creates a new SHA3-512 hash. +// Its generic security strength is 512 bits against preimage attacks, +// and 256 bits against collision attacks. +func New512() State { + return State{rate: 72, outputLen: 64, dsbyte: 0x06} +} + +// Sum224 returns the SHA3-224 digest of the data. +func Sum224(data []byte) (digest [28]byte) { + h := New224() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum256 returns the SHA3-256 digest of the data. +func Sum256(data []byte) (digest [32]byte) { + h := New256() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum384 returns the SHA3-384 digest of the data. +func Sum384(data []byte) (digest [48]byte) { + h := New384() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum512 returns the SHA3-512 digest of the data. +func Sum512(data []byte) (digest [64]byte) { + h := New512() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go new file mode 100644 index 00000000..ab19d0ad --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go @@ -0,0 +1,383 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// KeccakF1600 applies the Keccak permutation to a 1600b-wide +// state represented as a slice of 25 uint64s. +// nolint:funlen +func KeccakF1600(a *[25]uint64) { + // Implementation translated from Keccak-inplace.c + // in the keccak reference code. + var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 + + for i := 0; i < 24; i += 4 { + // Combines the 5 steps in each round into 2 steps. + // Unrolls 4 rounds per loop and spreads some steps across rounds. + + // Round 1 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[6] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[12] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[18] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[24] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i] + a[6] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[16] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[22] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[3] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[10] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[1] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[7] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[19] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[20] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[11] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[23] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[4] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[5] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[2] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[8] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[14] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[15] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + // Round 2 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[16] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[7] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[23] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[14] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+1] + a[16] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[11] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[2] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[18] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[20] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[6] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[22] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[4] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[15] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[1] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[8] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[24] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[10] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[12] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[3] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[19] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[5] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + // Round 3 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[11] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[22] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[8] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[19] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+2] + a[11] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[1] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[12] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[23] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[15] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[16] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[2] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[24] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[5] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[6] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[3] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[14] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[20] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[7] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[18] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[4] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[10] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + // Round 4 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[1] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[2] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[3] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[4] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+3] + a[1] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[6] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[7] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[8] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[5] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[11] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[12] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[14] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[10] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[16] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[18] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[19] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[15] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[22] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[23] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[24] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[20] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/rc.go b/vendor/github.com/cloudflare/circl/internal/sha3/rc.go new file mode 100644 index 00000000..6a3df42f --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/rc.go @@ -0,0 +1,29 @@ +package sha3 + +// RC stores the round constants for use in the ι step. +var RC = [24]uint64{ + 0x0000000000000001, + 0x0000000000008082, + 0x800000000000808A, + 0x8000000080008000, + 0x000000000000808B, + 0x0000000080000001, + 0x8000000080008081, + 0x8000000000008009, + 0x000000000000008A, + 0x0000000000000088, + 0x0000000080008009, + 0x000000008000000A, + 0x000000008000808B, + 0x800000000000008B, + 0x8000000000008089, + 0x8000000000008003, + 0x8000000000008002, + 0x8000000000000080, + 0x000000000000800A, + 0x800000008000000A, + 0x8000000080008081, + 0x8000000000008080, + 0x0000000080000001, + 0x8000000080008008, +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go b/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go new file mode 100644 index 00000000..b35cd006 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go @@ -0,0 +1,195 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// spongeDirection indicates the direction bytes are flowing through the sponge. +type spongeDirection int + +const ( + // spongeAbsorbing indicates that the sponge is absorbing input. + spongeAbsorbing spongeDirection = iota + // spongeSqueezing indicates that the sponge is being squeezed. + spongeSqueezing +) + +const ( + // maxRate is the maximum size of the internal buffer. SHAKE-256 + // currently needs the largest buffer. + maxRate = 168 +) + +func (d *State) buf() []byte { + return d.storage.asBytes()[d.bufo:d.bufe] +} + +type State struct { + // Generic sponge components. + a [25]uint64 // main state of the hash + rate int // the number of bytes of state to use + + bufo int // offset of buffer in storage + bufe int // end of buffer in storage + + // dsbyte contains the "domain separation" bits and the first bit of + // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the + // SHA-3 and SHAKE functions by appending bitstrings to the message. + // Using a little-endian bit-ordering convention, these are "01" for SHA-3 + // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the + // padding rule from section 5.1 is applied to pad the message to a multiple + // of the rate, which involves adding a "1" bit, zero or more "0" bits, and + // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, + // giving 00000110b (0x06) and 00011111b (0x1f). + // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf + // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and + // Extendable-Output Functions (May 2014)" + dsbyte byte + + storage storageBuf + + // Specific to SHA-3 and SHAKE. + outputLen int // the default output size in bytes + state spongeDirection // whether the sponge is absorbing or squeezing +} + +// BlockSize returns the rate of sponge underlying this hash function. +func (d *State) BlockSize() int { return d.rate } + +// Size returns the output size of the hash function in bytes. +func (d *State) Size() int { return d.outputLen } + +// Reset clears the internal state by zeroing the sponge state and +// the byte buffer, and setting Sponge.state to absorbing. +func (d *State) Reset() { + // Zero the permutation's state. + for i := range d.a { + d.a[i] = 0 + } + d.state = spongeAbsorbing + d.bufo = 0 + d.bufe = 0 +} + +func (d *State) clone() *State { + ret := *d + return &ret +} + +// permute applies the KeccakF-1600 permutation. It handles +// any input-output buffering. +func (d *State) permute() { + switch d.state { + case spongeAbsorbing: + // If we're absorbing, we need to xor the input into the state + // before applying the permutation. + xorIn(d, d.buf()) + d.bufe = 0 + d.bufo = 0 + KeccakF1600(&d.a) + case spongeSqueezing: + // If we're squeezing, we need to apply the permutation before + // copying more output. + KeccakF1600(&d.a) + d.bufe = d.rate + d.bufo = 0 + copyOut(d, d.buf()) + } +} + +// pads appends the domain separation bits in dsbyte, applies +// the multi-bitrate 10..1 padding rule, and permutes the state. +func (d *State) padAndPermute(dsbyte byte) { + // Pad with this instance's domain-separator bits. We know that there's + // at least one byte of space in d.buf() because, if it were full, + // permute would have been called to empty it. dsbyte also contains the + // first one bit for the padding. See the comment in the state struct. + zerosStart := d.bufe + 1 + d.bufe = d.rate + buf := d.buf() + buf[zerosStart-1] = dsbyte + for i := zerosStart; i < d.rate; i++ { + buf[i] = 0 + } + // This adds the final one bit for the padding. Because of the way that + // bits are numbered from the LSB upwards, the final bit is the MSB of + // the last byte. + buf[d.rate-1] ^= 0x80 + // Apply the permutation + d.permute() + d.state = spongeSqueezing + d.bufe = d.rate + copyOut(d, buf) +} + +// Write absorbs more data into the hash's state. It produces an error +// if more data is written to the ShakeHash after writing +func (d *State) Write(p []byte) (written int, err error) { + if d.state != spongeAbsorbing { + panic("sha3: write to sponge after read") + } + written = len(p) + + for len(p) > 0 { + bufl := d.bufe - d.bufo + if bufl == 0 && len(p) >= d.rate { + // The fast path; absorb a full "rate" bytes of input and apply the permutation. + xorIn(d, p[:d.rate]) + p = p[d.rate:] + KeccakF1600(&d.a) + } else { + // The slow path; buffer the input until we can fill the sponge, and then xor it in. + todo := d.rate - bufl + if todo > len(p) { + todo = len(p) + } + d.bufe += todo + buf := d.buf() + copy(buf[bufl:], p[:todo]) + p = p[todo:] + + // If the sponge is full, apply the permutation. + if d.bufe == d.rate { + d.permute() + } + } + } + + return written, nil +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (d *State) Read(out []byte) (n int, err error) { + // If we're still absorbing, pad and apply the permutation. + if d.state == spongeAbsorbing { + d.padAndPermute(d.dsbyte) + } + + n = len(out) + + // Now, do the squeezing. + for len(out) > 0 { + buf := d.buf() + n := copy(out, buf) + d.bufo += n + out = out[n:] + + // Apply the permutation if we've squeezed the sponge dry. + if d.bufo == d.bufe { + d.permute() + } + } + + return +} + +// Sum applies padding to the hash state and then squeezes out the desired +// number of output bytes. +func (d *State) Sum(in []byte) []byte { + // Make a copy of the original hash so that caller can keep writing + // and summing. + dup := d.clone() + hash := make([]byte, dup.outputLen) + _, _ = dup.Read(hash) + return append(in, hash...) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s b/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s new file mode 100644 index 00000000..8a4458f6 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s @@ -0,0 +1,33 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !gccgo,!appengine + +#include "textflag.h" + +// func kimd(function code, chain *[200]byte, src []byte) +TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG src+16(FP), R2, R3 // R2=base, R3=len + +continue: + WORD $0xB93E0002 // KIMD --, R2 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET + +// func klmd(function code, chain *[200]byte, dst, src []byte) +TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 + // TODO: SHAKE support + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG dst+16(FP), R2, R3 // R2=base, R3=len + LMG src+40(FP), R4, R5 // R4=base, R5=len + +continue: + WORD $0xB93F0024 // KLMD R2, R4 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/shake.go b/vendor/github.com/cloudflare/circl/internal/sha3/shake.go new file mode 100644 index 00000000..b92c5b7d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/shake.go @@ -0,0 +1,79 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file defines the ShakeHash interface, and provides +// functions for creating SHAKE and cSHAKE instances, as well as utility +// functions for hashing bytes to arbitrary-length output. +// +// +// SHAKE implementation is based on FIPS PUB 202 [1] +// cSHAKE implementations is based on NIST SP 800-185 [2] +// +// [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf +// [2] https://doi.org/10.6028/NIST.SP.800-185 + +import ( + "io" +) + +// ShakeHash defines the interface to hash functions that +// support arbitrary-length output. +type ShakeHash interface { + // Write absorbs more data into the hash's state. It panics if input is + // written to it after output has been read from it. + io.Writer + + // Read reads more output from the hash; reading affects the hash's + // state. (ShakeHash.Read is thus very different from Hash.Sum) + // It never returns an error. + io.Reader + + // Clone returns a copy of the ShakeHash in its current state. + Clone() ShakeHash + + // Reset resets the ShakeHash to its initial state. + Reset() +} + +// Consts for configuring initial SHA-3 state +const ( + dsbyteShake = 0x1f + rate128 = 168 + rate256 = 136 +) + +// Clone returns copy of SHAKE context within its current state. +func (d *State) Clone() ShakeHash { + return d.clone() +} + +// NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. +// Its generic security strength is 128 bits against all attacks if at +// least 32 bytes of its output are used. +func NewShake128() State { + return State{rate: rate128, dsbyte: dsbyteShake} +} + +// NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. +// Its generic security strength is 256 bits against all attacks if +// at least 64 bytes of its output are used. +func NewShake256() State { + return State{rate: rate256, dsbyte: dsbyteShake} +} + +// ShakeSum128 writes an arbitrary-length digest of data into hash. +func ShakeSum128(hash, data []byte) { + h := NewShake128() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} + +// ShakeSum256 writes an arbitrary-length digest of data into hash. +func ShakeSum256(hash, data []byte) { + h := NewShake256() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor.go new file mode 100644 index 00000000..1e213374 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor.go @@ -0,0 +1,15 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (!amd64 && !386 && !ppc64le) || appengine +// +build !amd64,!386,!ppc64le appengine + +package sha3 + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate]byte + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(b) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go new file mode 100644 index 00000000..2b0c6617 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go @@ -0,0 +1,33 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (!amd64 || appengine) && (!386 || appengine) && (!ppc64le || appengine) +// +build !amd64 appengine +// +build !386 appengine +// +build !ppc64le appengine + +package sha3 + +import "encoding/binary" + +// xorIn xors the bytes in buf into the state; it +// makes no non-portable assumptions about memory layout +// or alignment. +func xorIn(d *State, buf []byte) { + n := len(buf) / 8 + + for i := 0; i < n; i++ { + a := binary.LittleEndian.Uint64(buf) + d.a[i] ^= a + buf = buf[8:] + } +} + +// copyOut copies ulint64s to a byte buffer. +func copyOut(d *State, b []byte) { + for i := 0; len(b) >= 8; i++ { + binary.LittleEndian.PutUint64(b, d.a[i]) + b = b[8:] + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go new file mode 100644 index 00000000..052fc8d3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go @@ -0,0 +1,61 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (amd64 || 386 || ppc64le) && !appengine +// +build amd64 386 ppc64le +// +build !appengine + +package sha3 + +import "unsafe" + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate / 8]uint64 + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(unsafe.Pointer(b)) +} + +// xorInuses unaligned reads and writes to update d.a to contain d.a +// XOR buf. +func xorIn(d *State, buf []byte) { + n := len(buf) + bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] + if n >= 72 { + d.a[0] ^= bw[0] + d.a[1] ^= bw[1] + d.a[2] ^= bw[2] + d.a[3] ^= bw[3] + d.a[4] ^= bw[4] + d.a[5] ^= bw[5] + d.a[6] ^= bw[6] + d.a[7] ^= bw[7] + d.a[8] ^= bw[8] + } + if n >= 104 { + d.a[9] ^= bw[9] + d.a[10] ^= bw[10] + d.a[11] ^= bw[11] + d.a[12] ^= bw[12] + } + if n >= 136 { + d.a[13] ^= bw[13] + d.a[14] ^= bw[14] + d.a[15] ^= bw[15] + d.a[16] ^= bw[16] + } + if n >= 144 { + d.a[17] ^= bw[17] + } + if n >= 168 { + d.a[18] ^= bw[18] + d.a[19] ^= bw[19] + d.a[20] ^= bw[20] + } +} + +func copyOut(d *State, buf []byte) { + ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) + copy(buf, ab[:]) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go new file mode 100644 index 00000000..57a50ff5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go @@ -0,0 +1,205 @@ +// Package fp25519 provides prime field arithmetic over GF(2^255-19). +package fp25519 + +import ( + "errors" + + "github.com/cloudflare/circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 32 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^255-19. +var p = Elt{ + 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, +} + +// P returns the prime modulus 2^255-19. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is +// indicated by returning isQR = true. Otherwise, when x/y is a quadratic +// non-residue, z will have an undetermined value and isQR = false. +func InvSqrt(z, x, y *Elt) (isQR bool) { + sqrtMinusOne := &Elt{ + 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, + 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f, + 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, + 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, + } + t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{} + + Mul(t0, x, y) // t0 = u*v + Sqr(t1, y) // t1 = v^2 + Mul(t2, t0, t1) // t2 = u*v^3 + Sqr(t0, t1) // t0 = v^4 + Mul(t1, t0, t2) // t1 = u*v^7 + + var Tab [4]*Elt + Tab[0] = &Elt{} + Tab[1] = &Elt{} + Tab[2] = t3 + Tab[3] = t1 + + *Tab[0] = *t1 + Sqr(Tab[0], Tab[0]) + Sqr(Tab[1], Tab[0]) + Sqr(Tab[1], Tab[1]) + Mul(Tab[1], Tab[1], Tab[3]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[0], Tab[0]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[1], Tab[0]) + for i := 0; i < 4; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 4; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[0]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 14; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 29; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 59; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + for i := 0; i < 5; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 124; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[2], Tab[2]) + Sqr(Tab[2], Tab[2]) + Mul(Tab[2], Tab[2], Tab[3]) + + Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8 + // Checking whether y z^2 == x + Sqr(t0, z) // t0 = z^2 + Mul(t0, t0, y) // t0 = yz^2 + Sub(t1, t0, x) // t1 = t0-u + Add(t2, t0, x) // t2 = t0+u + if IsZero(t1) { + return true + } else if IsZero(t2) { + Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1) + return true + } else { + return false + } +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + x0, x1, x2 := &Elt{}, &Elt{}, &Elt{} + Sqr(x1, x) + Sqr(x0, x1) + Sqr(x0, x0) + Mul(x0, x0, x) + Mul(z, x0, x1) + Sqr(x1, z) + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 4; i++ { + Sqr(x1, x1) + } + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 9; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + Sqr(x2, x1) + for i := 0; i < 19; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x1) + for i := 0; i < 10; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x0) + Sqr(x0, x2) + for i := 0; i < 49; i++ { + Sqr(x0, x0) + } + Mul(x0, x0, x2) + Sqr(x1, x0) + for i := 0; i < 99; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + for i := 0; i < 50; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x2) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { modp(z) } diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go new file mode 100644 index 00000000..057f0d28 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go @@ -0,0 +1,45 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package fp25519 + +import ( + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } +func modp(z *Elt) { modpAmd64(z) } + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) + +//go:noescape +func modpAmd64(z *Elt) diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h new file mode 100644 index 00000000..b884b584 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h @@ -0,0 +1,351 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define additionLeg(z,x,y) \ + MOVL $38, AX; \ + MOVL $0, DX; \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov, adx +#define additionAdx(z,x,y) \ + MOVL $38, AX; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + CMOVQCS AX, DX ; \ + XORL AX, AX; \ + ADCXQ DX, R8; \ + ADCXQ AX, R9; MOVQ R9, 8+z; \ + ADCXQ AX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + MOVL $38, DX; \ + CMOVQCS DX, AX; \ + ADDQ AX, R8; MOVQ R8, 0+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define subtraction(z,x,y) \ + MOVL $38, AX; \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; MOVQ R8, 0+z; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVL $0,R15; \ + MOVQ 0+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; \ + MOVQ 8+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 8+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; \ + MOVQ 16+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADCXQ R12, AX; MOVQ AX, 16+z; \ + MULXQ 8+x, AX, R9; ADCXQ R13, R8; ADOXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ R14, R9; ADOXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ R15, R10; ADOXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; ADOXQ AX, R11; \ + MOVQ 24+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 24+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; MOVQ R12, 32+z; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; MOVQ R13, 40+z; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; MOVQ R14, 48+z; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; MOVQ R15, 56+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R13, R15; \ + ADCQ R14, R10; MOVQ R10, 16+z; \ + ADCQ AX, R11; MOVQ R11, 24+z; \ + ADCQ $0, DX; MOVQ DX, 32+z; \ + MOVQ 8+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 8+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 16+z, R9; MOVQ R9, R15; \ + ADCQ 24+z, R10; MOVQ R10, 24+z; \ + ADCQ 32+z, R11; MOVQ R11, 32+z; \ + ADCQ $0, DX; MOVQ DX, 40+z; \ + MOVQ 16+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 16+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 24+z, R9; MOVQ R9, R15; \ + ADCQ 32+z, R10; MOVQ R10, 32+z; \ + ADCQ 40+z, R11; MOVQ R11, 40+z; \ + ADCQ $0, DX; MOVQ DX, 48+z; \ + MOVQ 24+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 24+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 32+z, R9; MOVQ R9, 32+z; \ + ADCQ 40+z, R10; MOVQ R10, 40+z; \ + ADCQ 48+z, R11; MOVQ R11, 48+z; \ + ADCQ $0, DX; MOVQ DX, 56+z; + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + MOVQ 0+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R9; MOVQ DX, R10; /* A[0]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \ + MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \ + MOVQ 24+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, CX; MOVQ DX, R13; /* A[3]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \ + \ + ADDQ R14, R10;\ + ADCQ R15, R11; MOVL $0, R15;\ + ADCQ CX, R12;\ + ADCQ AX, R13;\ + ADCQ $0, DX; MOVQ DX, R14;\ + MOVQ 8+x, AX; MULQ 16+x;\ + \ + ADDQ AX, R11;\ + ADCQ DX, R12;\ + ADCQ $0, R13;\ + ADCQ $0, R14;\ + ADCQ $0, R15;\ + \ + SHLQ $1, R14, R15; MOVQ R15, 56+z;\ + SHLQ $1, R13, R14; MOVQ R14, 48+z;\ + SHLQ $1, R12, R13; MOVQ R13, 40+z;\ + SHLQ $1, R11, R12; MOVQ R12, 32+z;\ + SHLQ $1, R10, R11; MOVQ R11, 24+z;\ + SHLQ $1, R9, R10; MOVQ R10, 16+z;\ + SHLQ $1, R9; MOVQ R9, 8+z;\ + \ + MOVQ 0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX, R9;\ + MOVQ 8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\ + MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\ + MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\ + \ + ADDQ 8+z, R9; MOVQ R9, 8+z;\ + ADCQ 16+z, R10; MOVQ R10, 16+z;\ + ADCQ 24+z, R11; MOVQ R11, 24+z;\ + ADCQ 32+z, R12; MOVQ R12, 32+z;\ + ADCQ 40+z, R13; MOVQ R13, 40+z;\ + ADCQ 48+z, R14; MOVQ R14, 48+z;\ + ADCQ 56+z, R15; MOVQ R15, 56+z; + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + MOVQ 0+x, DX; /* A[0] */ \ + MULXQ 8+x, R8, R14; /* A[1]*A[0] */ XORL R15, R15; \ + MULXQ 16+x, R9, R10; /* A[2]*A[0] */ ADCXQ R14, R9; \ + MULXQ 24+x, AX, CX; /* A[3]*A[0] */ ADCXQ AX, R10; \ + MOVQ 24+x, DX; /* A[3] */ \ + MULXQ 8+x, R11, R12; /* A[1]*A[3] */ ADCXQ CX, R11; \ + MULXQ 16+x, AX, R13; /* A[2]*A[3] */ ADCXQ AX, R12; \ + MOVQ 8+x, DX; /* A[1] */ ADCXQ R15, R13; \ + MULXQ 16+x, AX, CX; /* A[2]*A[1] */ MOVL $0, R14; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADCXQ R15, R14; \ + XORL R15, R15; \ + ADOXQ AX, R10; ADCXQ R8, R8; \ + ADOXQ CX, R11; ADCXQ R9, R9; \ + ADOXQ R15, R12; ADCXQ R10, R10; \ + ADOXQ R15, R13; ADCXQ R11, R11; \ + ADOXQ R15, R14; ADCXQ R12, R12; \ + ;;;;;;;;;;;;;;; ADCXQ R13, R13; \ + ;;;;;;;;;;;;;;; ADCXQ R14, R14; \ + MOVQ 0+x, DX; MULXQ DX, AX, CX; /* A[0]^2 */ \ + ;;;;;;;;;;;;;;; MOVQ AX, 0+z; \ + ADDQ CX, R8; MOVQ R8, 8+z; \ + MOVQ 8+x, DX; MULXQ DX, AX, CX; /* A[1]^2 */ \ + ADCQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R10; MOVQ R10, 24+z; \ + MOVQ 16+x, DX; MULXQ DX, AX, CX; /* A[2]^2 */ \ + ADCQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R12; MOVQ R12, 40+z; \ + MOVQ 24+x, DX; MULXQ DX, AX, CX; /* A[3]^2 */ \ + ADCQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R14; MOVQ R14, 56+z; + +// reduceFromDouble finds z congruent to x modulo p such that 0> 63) + // PUT BIT 255 IN CARRY FLAG AND CLEAR + x3 &^= 1 << 63 + + x0, c0 := bits.Add64(x0, cx, 0) + x1, c1 := bits.Add64(x1, 0, c0) + x2, c2 := bits.Add64(x2, 0, c1) + x3, _ = bits.Add64(x3, 0, c2) + + // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19 + // cx = C[255] ? 0 : 19 + cx = uint64(19) &^ (-(x3 >> 63)) + // CLEAR BIT 255 + x3 &^= 1 << 63 + + x0, c0 = bits.Sub64(x0, cx, 0) + x1, c1 = bits.Sub64(x1, 0, c0) + x2, c2 = bits.Sub64(x2, 0, c1) + x3, _ = bits.Sub64(x3, 0, c2) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) +} + +func red64(z *Elt, x0, x1, x2, x3, x4, x5, x6, x7 uint64) { + h0, l0 := bits.Mul64(x4, 38) + h1, l1 := bits.Mul64(x5, 38) + h2, l2 := bits.Mul64(x6, 38) + h3, l3 := bits.Mul64(x7, 38) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + l0, c0 = bits.Add64(l0, x0, 0) + l1, c1 = bits.Add64(l1, x1, c0) + l2, c2 = bits.Add64(l2, x2, c1) + l3, c3 := bits.Add64(l3, x3, c2) + l4, _ = bits.Add64(l4, 0, c3) + + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + z1, c1 := bits.Add64(l1, 0, c0) + z2, c2 := bits.Add64(l2, 0, c1) + z3, c3 := bits.Add64(l3, 0, c2) + z0, _ := bits.Add64(l0, (-c3)&38, 0) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go new file mode 100644 index 00000000..26ca4d01 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go @@ -0,0 +1,13 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package fp25519 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } +func modp(z *Elt) { modpGeneric(z) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp.go b/vendor/github.com/cloudflare/circl/math/fp448/fp.go new file mode 100644 index 00000000..a5e36600 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp.go @@ -0,0 +1,164 @@ +// Package fp448 provides prime field arithmetic over GF(2^448-2^224-1). +package fp448 + +import ( + "errors" + + "github.com/cloudflare/circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 56 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^448-2^224-1. +var p = Elt{ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, +} + +// P returns the prime modulus 2^448-2^224-1. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// IsOne returns true if x is equal to 1. +func IsOne(x *Elt) bool { Modp(x); return *x == Elt{1} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{1} } + +// One returns the 1 element. +func One() (x Elt) { x = Elt{1}; return } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { Sub(z, z, &p) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue. If so, +// isQR = true; otherwise, isQR = false, since x/y is a quadratic non-residue, +// and z = sqrt(-x/y). +func InvSqrt(z, x, y *Elt) (isQR bool) { + // First note that x^(2(k+1)) = x^(p-1)/2 * x = legendre(x) * x + // so that's x if x is a quadratic residue and -x otherwise. + // Next, y^(6k+3) = y^(4k+2) * y^(2k+1) = y^(p-1) * y^((p-1)/2) = legendre(y). + // So the z we compute satisfies z^2 y = x^(2(k+1)) y^(6k+3) = legendre(x)*legendre(y). + // Thus if x and y are quadratic residues, then z is indeed sqrt(x/y). + t0, t1 := &Elt{}, &Elt{} + Mul(t0, x, y) // x*y + Sqr(t1, y) // y^2 + Mul(t1, t0, t1) // x*y^3 + powPminus3div4(z, t1) // (x*y^3)^k + Mul(z, z, t0) // z = x*y*(x*y^3)^k = x^(k+1) * y^(3k+1) + + // Check if x/y is a quadratic residue + Sqr(t0, z) // z^2 + Mul(t0, t0, y) // y*z^2 + Sub(t0, t0, x) // y*z^2-x + return IsZero(t0) +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + // Calculates z = x^(4k+1) = x^(p-3+1) = x^(p-2) = x^-1, where k = (p-3)/4. + t := &Elt{} + powPminus3div4(t, x) // t = x^k + Sqr(t, t) // t = x^2k + Sqr(t, t) // t = x^4k + Mul(z, t, x) // z = x^(4k+1) +} + +// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4. +func powPminus3div4(z, x *Elt) { + x0, x1 := &Elt{}, &Elt{} + Sqr(z, x) + Mul(z, z, x) + Sqr(x0, z) + Mul(x0, x0, x) + Sqr(z, x0) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 11; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 26; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 53; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 110; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + Mul(z, z, x) + for i := 0; i < 223; i++ { + Sqr(z, z) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go new file mode 100644 index 00000000..6a12209a --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go @@ -0,0 +1,43 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package fp448 + +import ( + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } + +/* Functions defined in fp_amd64.s */ + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h new file mode 100644 index 00000000..536fe5bd --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h @@ -0,0 +1,591 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; \ + MOVQ 32+x, AX; MOVQ 32+y, DX; CMOVQNE DX, AX; MOVQ AX, 32+x; \ + MOVQ 40+x, AX; MOVQ 40+y, DX; CMOVQNE DX, AX; MOVQ AX, 40+x; \ + MOVQ 48+x, AX; MOVQ 48+y, DX; CMOVQNE DX, AX; MOVQ AX, 48+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; \ + MOVQ 32+x, AX; MOVQ AX, R8; MOVQ 32+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 32+x; MOVQ DX, 32+y; \ + MOVQ 40+x, AX; MOVQ AX, R8; MOVQ 40+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 40+x; MOVQ DX, 40+y; \ + MOVQ 48+x, AX; MOVQ AX, R8; MOVQ 48+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 48+x; MOVQ DX, 48+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define additionLeg(z,x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ R8, 0+z; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ DX, R11; MOVQ R11, 24+z; \ + ADCQ $0, R12; MOVQ R12, 32+z; \ + ADCQ $0, R13; MOVQ R13, 40+z; \ + ADCQ $0, R14; MOVQ R14, 48+z; + + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, adx +#define additionAdx(z,x,y) \ + MOVL $32, R15; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + MOVQ 32+x, R12; ADCXQ 32+y, R12; \ + MOVQ 40+x, R13; ADCXQ 40+y, R13; \ + MOVQ 48+x, R14; ADCXQ 48+y, R14; \ + ;;;;;;;;;;;;;;; ADCXQ DX, DX; \ + XORL AX, AX; \ + ADCXQ DX, R8; SHLXQ R15, DX, DX; \ + ADCXQ AX, R9; \ + ADCXQ AX, R10; \ + ADCXQ DX, R11; \ + ADCXQ AX, R12; \ + ADCXQ AX, R13; \ + ADCXQ AX, R14; \ + ADCXQ AX, AX; \ + XORL DX, DX; \ + ADCXQ AX, R8; MOVQ R8, 0+z; SHLXQ R15, AX, AX; \ + ADCXQ DX, R9; MOVQ R9, 8+z; \ + ADCXQ DX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + ADCXQ DX, R12; MOVQ R12, 32+z; \ + ADCXQ DX, R13; MOVQ R13, 40+z; \ + ADCXQ DX, R14; MOVQ R14, 48+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define subtraction(z,x,y) \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVQ 32+x, R12; SBBQ 32+y, R12; \ + MOVQ 40+x, R13; SBBQ 40+y, R13; \ + MOVQ 48+x, R14; SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+z; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ DX, R11; MOVQ R11, 24+z; \ + SBBQ $0, R12; MOVQ R12, 32+z; \ + SBBQ $0, R13; MOVQ R13, 40+z; \ + SBBQ $0, R14; MOVQ R14, 48+z; + +// maddBmi2Adx multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64, bmi2, adx +#define maddBmi2Adx(z,x,y,i,r0,r1,r2,r3,r4,r5,r6) \ + MOVQ i+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADOXQ AX, r0; ADCXQ R8, r1; MOVQ r0,i+z; \ + MULXQ 8+x, AX, r0; ADOXQ AX, r1; ADCXQ r0, r2; MOVQ $0, R8; \ + MULXQ 16+x, AX, r0; ADOXQ AX, r2; ADCXQ r0, r3; \ + MULXQ 24+x, AX, r0; ADOXQ AX, r3; ADCXQ r0, r4; \ + MULXQ 32+x, AX, r0; ADOXQ AX, r4; ADCXQ r0, r5; \ + MULXQ 40+x, AX, r0; ADOXQ AX, r5; ADCXQ r0, r6; \ + MULXQ 48+x, AX, r0; ADOXQ AX, r6; ADCXQ R8, r0; \ + ;;;;;;;;;;;;;;;;;;; ADOXQ R8, r0; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVL $0,R15; \ + MOVQ 0+y, DX; XORL AX, AX; MOVQ $0, R8; \ + MULXQ 0+x, AX, R9; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCXQ AX, R13; \ + MULXQ 48+x, AX, R15; ADCXQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R15; \ + maddBmi2Adx(z,x,y, 8, R9,R10,R11,R12,R13,R14,R15) \ + maddBmi2Adx(z,x,y,16,R10,R11,R12,R13,R14,R15, R9) \ + maddBmi2Adx(z,x,y,24,R11,R12,R13,R14,R15, R9,R10) \ + maddBmi2Adx(z,x,y,32,R12,R13,R14,R15, R9,R10,R11) \ + maddBmi2Adx(z,x,y,40,R13,R14,R15, R9,R10,R11,R12) \ + maddBmi2Adx(z,x,y,48,R14,R15, R9,R10,R11,R12,R13) \ + MOVQ R15, 56+z; \ + MOVQ R9, 64+z; \ + MOVQ R10, 72+z; \ + MOVQ R11, 80+z; \ + MOVQ R12, 88+z; \ + MOVQ R13, 96+z; \ + MOVQ R14, 104+z; + +// maddLegacy multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64 +#define maddLegacy(z,x,y,i) \ + MOVQ i+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + ADDQ 0+i+z, R8; MOVQ R8, 0+i+z; \ + ADCQ 8+i+z, R9; MOVQ R9, 8+i+z; \ + ADCQ 16+i+z, R10; MOVQ R10, 16+i+z; \ + ADCQ 24+i+z, R11; MOVQ R11, 24+i+z; \ + ADCQ 32+i+z, R12; MOVQ R12, 32+i+z; \ + ADCQ 40+i+z, R13; MOVQ R13, 40+i+z; \ + ADCQ 48+i+z, R14; MOVQ R14, 48+i+z; \ + ADCQ $0, DX; MOVQ DX, 56+i+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, 0+z; ;;;;;;;;;;;; MOVQ DX, R8; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; MOVQ R9, 16+z; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; MOVQ R10, 24+z; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; MOVQ R11, 32+z; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; MOVQ R12, 40+z; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX,56+z; MOVQ R13, 48+z; \ + maddLegacy(z,x,y, 8) \ + maddLegacy(z,x,y,16) \ + maddLegacy(z,x,y,24) \ + maddLegacy(z,x,y,32) \ + maddLegacy(z,x,y,40) \ + maddLegacy(z,x,y,48) + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, CX; \ + MOVQ CX, AX; MULQ CX; MOVQ AX, 0+z; MOVQ DX, R8; \ + ADDQ CX, CX; ADCQ $0, R15; \ + MOVQ 8+x, AX; MULQ CX; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + \ + MOVQ 8+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9,16+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 8+x, AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 8+x, CX; ADCQ $0, R15; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 24+z; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R9; \ + \ + MOVQ 16+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 32+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 16+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 16+x, CX; ADCQ $0, R15; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 40+z; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX,R10; \ + \ + MOVQ 24+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 48+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 24+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ADDQ 24+x, CX; ADCQ $0, R15; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; MOVQ R14, 56+z; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX,R11; \ + \ + MOVQ 32+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9, 64+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 32+x,AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 32+x, CX; ADCQ $0, R15; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 72+z; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX,R12; \ + \ + XORL R13, R13; \ + XORL R14, R14; \ + MOVQ 40+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 80+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 40+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 40+x, CX; ADCQ $0, R15; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8, R13; ADCQ $0,R14; \ + \ + XORL R9, R9; \ + MOVQ 48+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 96+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 48+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8,R14; ADCQ $0, R9; MOVQ R14, 104+z; + + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, DX; \ + ;;;;;;;;;;;;;; MULXQ DX, AX, R8; MOVQ AX, 0+z; \ + ADDQ DX, DX; ADCQ $0, R15; CLC; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; MOVQ R8, 8+z; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; MOVQ $0, R8;\ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 32+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 40+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 48+x, AX, R14; ADCXQ AX, R13; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R14; \ + \ + MOVQ 8+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 8+x, R8; \ + ADDQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 8+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 16+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 24+z; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; MOVQ $0, R10; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R10, R9; \ + \ + MOVQ 16+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 16+x, R8; \ + ADDQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 16+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 40+z; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; MOVQ $0, R12; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R11,R10; \ + \ + MOVQ 24+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 24+x, R8; \ + ADDQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R8; \ + ADCQ $0, R9; \ + ADDQ 24+x, DX; \ + ADCQ $0, R15; \ + XORL R13, R13; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R14; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; MOVQ R14, 56+z; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; MOVQ $0, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R12,R11; \ + \ + MOVQ 32+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 32+x, R8; \ + ADDQ AX, R9; MOVQ R9, 64+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 32+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 72+z; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R13,R12; \ + \ + MOVQ 40+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 40+x, R8; \ + ADDQ AX, R11; MOVQ R11, 80+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 40+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R14,R13; \ + \ + MOVQ 48+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 48+x, R8; \ + XORL R10, R10; ;;;;;;;;;;;;;; ADOXQ CX, R14; \ + ;;;;;;;;;;;;;; ADCXQ AX, R13; ;;;;;;;;;;;;;; MOVQ R13, 96+z; \ + ;;;;;;;;;;;;;; ADCXQ R8, R14; MOVQ R14, 104+z; + +// reduceFromDoubleLeg finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64 +#define reduceFromDoubleLeg(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + ADDQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCQ $0,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + ADDQ 0+z,R10; \ + ADCQ 8+z,R11; \ + ADCQ 16+z,R12; \ + ADCQ 24+z,R13; \ + ADCQ 32+z,R15; \ + ADCQ 40+z, R8; \ + ADCQ 48+z, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + ADDQ R14,R10; MOVQ $0,R14; \ + ADCQ $0,R11; \ + ADCQ $0,R12; \ + ADCQ AX,R13; \ + ADCQ $0,R15; \ + ADCQ $0, R8; \ + ADCQ $0, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32,AX; \ + ADDQ R14,R10; MOVQ R10, 0+z; \ + ADCQ $0,R11; MOVQ R11, 8+z; \ + ADCQ $0,R12; MOVQ R12,16+z; \ + ADCQ AX,R13; MOVQ R13,24+z; \ + ADCQ $0,R15; MOVQ R15,32+z; \ + ADCQ $0, R8; MOVQ R8,40+z; \ + ADCQ $0, R9; MOVQ R9,48+z; + +// reduceFromDoubleAdx finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64, adx +#define reduceFromDoubleAdx(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + XORL AX,AX; \ + ADCXQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCXQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCXQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCXQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCXQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCXQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCXQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCXQ AX,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + XORL AX,AX; \ + ADCXQ 0+z,R10; \ + ADCXQ 8+z,R11; \ + ADCXQ 16+z,R12; \ + ADCXQ 24+z,R13; \ + ADCXQ 32+z,R15; \ + ADCXQ 40+z, R8; \ + ADCXQ 48+z, R9; \ + ADCXQ AX,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ $0,R14; \ + ADCXQ R14,R11; \ + ADCXQ R14,R12; \ + ADCXQ AX,R13; \ + ADCXQ R14,R15; \ + ADCXQ R14, R8; \ + ADCXQ R14, R9; \ + ADCXQ R14,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ R10, 0+z; MOVQ $0,R14; \ + ADCXQ R14,R11; MOVQ R11, 8+z; \ + ADCXQ R14,R12; MOVQ R12,16+z; \ + ADCXQ AX,R13; MOVQ R13,24+z; \ + ADCXQ R14,R15; MOVQ R15,32+z; \ + ADCXQ R14, R8; MOVQ R8,40+z; \ + ADCXQ R14, R9; MOVQ R9,48+z; + +// addSub calculates two operations: x,y = x+y,x-y +// Uses: AX, DX, R8-R15, FLAGS +#define addSub(x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ 0+x,AX; MOVQ R8, 0+x; MOVQ AX, R8; \ + ADCQ $0, R9; MOVQ 8+x,AX; MOVQ R9, 8+x; MOVQ AX, R9; \ + ADCQ $0, R10; MOVQ 16+x,AX; MOVQ R10, 16+x; MOVQ AX, R10; \ + ADCQ DX, R11; MOVQ 24+x,AX; MOVQ R11, 24+x; MOVQ AX, R11; \ + ADCQ $0, R12; MOVQ 32+x,AX; MOVQ R12, 32+x; MOVQ AX, R12; \ + ADCQ $0, R13; MOVQ 40+x,AX; MOVQ R13, 40+x; MOVQ AX, R13; \ + ADCQ $0, R14; MOVQ 48+x,AX; MOVQ R14, 48+x; MOVQ AX, R14; \ + SUBQ 0+y, R8; \ + SBBQ 8+y, R9; \ + SBBQ 16+y, R10; \ + SBBQ 24+y, R11; \ + SBBQ 32+y, R12; \ + SBBQ 40+y, R13; \ + SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+y; \ + SBBQ $0, R9; MOVQ R9, 8+y; \ + SBBQ $0, R10; MOVQ R10, 16+y; \ + SBBQ DX, R11; MOVQ R11, 24+y; \ + SBBQ $0, R12; MOVQ R12, 32+y; \ + SBBQ $0, R13; MOVQ R13, 40+y; \ + SBBQ $0, R14; MOVQ R14, 48+y; diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s new file mode 100644 index 00000000..435addf5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s @@ -0,0 +1,74 @@ +// +build amd64 + +#include "textflag.h" +#include "fp_amd64.h" + +// func cmovAmd64(x, y *Elt, n uint) +TEXT ·cmovAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cselect(0(DI),0(SI),BX) + RET + +// func cswapAmd64(x, y *Elt, n uint) +TEXT ·cswapAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cswap(0(DI),0(SI),BX) + RET + +// func subAmd64(z, x, y *Elt) +TEXT ·subAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + subtraction(0(DI),0(SI),0(BX)) + RET + +// func addsubAmd64(x, y *Elt) +TEXT ·addsubAmd64(SB),NOSPLIT,$0-16 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + addSub(0(DI),0(SI)) + RET + +#define addLegacy \ + additionLeg(0(DI),0(SI),0(BX)) +#define addBmi2Adx \ + additionAdx(0(DI),0(SI),0(BX)) + +#define mulLegacy \ + integerMulLeg(0(SP),0(SI),0(BX)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define mulBmi2Adx \ + integerMulAdx(0(SP),0(SI),0(BX)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +#define sqrLegacy \ + integerSqrLeg(0(SP),0(SI)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define sqrBmi2Adx \ + integerSqrAdx(0(SP),0(SI)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +// func addAmd64(z, x, y *Elt) +TEXT ·addAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LADD, addLegacy, addBmi2Adx) + +// func mulAmd64(z, x, y *Elt) +TEXT ·mulAmd64(SB),NOSPLIT,$112-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LMUL, mulLegacy, mulBmi2Adx) + +// func sqrAmd64(z, x *Elt) +TEXT ·sqrAmd64(SB),NOSPLIT,$112-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LSQR, sqrLegacy, sqrBmi2Adx) diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go new file mode 100644 index 00000000..47a0b632 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go @@ -0,0 +1,339 @@ +package fp448 + +import ( + "encoding/binary" + "math/bits" +) + +func cmovGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + x0 = (x0 &^ m) | (y0 & m) + x1 = (x1 &^ m) | (y1 & m) + x2 = (x2 &^ m) | (y2 & m) + x3 = (x3 &^ m) | (y3 & m) + x4 = (x4 &^ m) | (y4 & m) + x5 = (x5 &^ m) | (y5 & m) + x6 = (x6 &^ m) | (y6 & m) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) +} + +func cswapGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + t0 := m & (x0 ^ y0) + t1 := m & (x1 ^ y1) + t2 := m & (x2 ^ y2) + t3 := m & (x3 ^ y3) + t4 := m & (x4 ^ y4) + t5 := m & (x5 ^ y5) + t6 := m & (x6 ^ y6) + x0 ^= t0 + x1 ^= t1 + x2 ^= t2 + x3 ^= t3 + x4 ^= t4 + x5 ^= t5 + x6 ^= t6 + y0 ^= t0 + y1 ^= t1 + y2 ^= t2 + y3 ^= t3 + y4 ^= t4 + y5 ^= t5 + y6 ^= t6 + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) + + binary.LittleEndian.PutUint64(y[0*8:1*8], y0) + binary.LittleEndian.PutUint64(y[1*8:2*8], y1) + binary.LittleEndian.PutUint64(y[2*8:3*8], y2) + binary.LittleEndian.PutUint64(y[3*8:4*8], y3) + binary.LittleEndian.PutUint64(y[4*8:5*8], y4) + binary.LittleEndian.PutUint64(y[5*8:6*8], y5) + binary.LittleEndian.PutUint64(y[6*8:7*8], y6) +} + +func addGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Add64(x0, y0, 0) + z1, c1 := bits.Add64(x1, y1, c0) + z2, c2 := bits.Add64(x2, y2, c1) + z3, c3 := bits.Add64(x3, y3, c2) + z4, c4 := bits.Add64(x4, y4, c3) + z5, c5 := bits.Add64(x5, y5, c4) + z6, z7 := bits.Add64(x6, y6, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, z7 = bits.Add64(z6, 0, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, _ = bits.Add64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func subGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Sub64(x0, y0, 0) + z1, c1 := bits.Sub64(x1, y1, c0) + z2, c2 := bits.Sub64(x2, y2, c1) + z3, c3 := bits.Sub64(x3, y3, c2) + z4, c4 := bits.Sub64(x4, y4, c3) + z5, c5 := bits.Sub64(x5, y5, c4) + z6, z7 := bits.Sub64(x6, y6, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, z7 = bits.Sub64(z6, 0, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, _ = bits.Sub64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func addsubGeneric(x, y *Elt) { + z := &Elt{} + addGeneric(z, x, y) + subGeneric(y, x, y) + *x = *z +} + +func mulGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + yy := [7]uint64{y0, y1, y2, y3, y4, y5, y6} + zz := [7]uint64{} + + yi := yy[0] + h0, l0 := bits.Mul64(x0, yi) + h1, l1 := bits.Mul64(x1, yi) + h2, l2 := bits.Mul64(x2, yi) + h3, l3 := bits.Mul64(x3, yi) + h4, l4 := bits.Mul64(x4, yi) + h5, l5 := bits.Mul64(x5, yi) + h6, l6 := bits.Mul64(x6, yi) + + zz[0] = l0 + a0, c0 := bits.Add64(h0, l1, 0) + a1, c1 := bits.Add64(h1, l2, c0) + a2, c2 := bits.Add64(h2, l3, c1) + a3, c3 := bits.Add64(h3, l4, c2) + a4, c4 := bits.Add64(h4, l5, c3) + a5, c5 := bits.Add64(h5, l6, c4) + a6, _ := bits.Add64(h6, 0, c5) + + for i := 1; i < 7; i++ { + yi = yy[i] + h0, l0 = bits.Mul64(x0, yi) + h1, l1 = bits.Mul64(x1, yi) + h2, l2 = bits.Mul64(x2, yi) + h3, l3 = bits.Mul64(x3, yi) + h4, l4 = bits.Mul64(x4, yi) + h5, l5 = bits.Mul64(x5, yi) + h6, l6 = bits.Mul64(x6, yi) + + zz[i], c0 = bits.Add64(a0, l0, 0) + a0, c1 = bits.Add64(a1, l1, c0) + a1, c2 = bits.Add64(a2, l2, c1) + a2, c3 = bits.Add64(a3, l3, c2) + a3, c4 = bits.Add64(a4, l4, c3) + a4, c5 = bits.Add64(a5, l5, c4) + a5, a6 = bits.Add64(a6, l6, c5) + + a0, c0 = bits.Add64(a0, h0, 0) + a1, c1 = bits.Add64(a1, h1, c0) + a2, c2 = bits.Add64(a2, h2, c1) + a3, c3 = bits.Add64(a3, h3, c2) + a4, c4 = bits.Add64(a4, h4, c3) + a5, c5 = bits.Add64(a5, h5, c4) + a6, _ = bits.Add64(a6, h6, c5) + } + red64(z, &zz, &[7]uint64{a0, a1, a2, a3, a4, a5, a6}) +} + +func sqrGeneric(z, x *Elt) { mulGeneric(z, x, x) } + +func red64(z *Elt, l, h *[7]uint64) { + /* (2C13, 2C12, 2C11, 2C10|C10, C9, C8, C7) + (C6,...,C0) */ + h0 := h[0] + h1 := h[1] + h2 := h[2] + h3 := ((h[3] & (0xFFFFFFFF << 32)) << 1) | (h[3] & 0xFFFFFFFF) + h4 := (h[3] >> 63) | (h[4] << 1) + h5 := (h[4] >> 63) | (h[5] << 1) + h6 := (h[5] >> 63) | (h[6] << 1) + h7 := (h[6] >> 63) + + l0, c0 := bits.Add64(h0, l[0], 0) + l1, c1 := bits.Add64(h1, l[1], c0) + l2, c2 := bits.Add64(h2, l[2], c1) + l3, c3 := bits.Add64(h3, l[3], c2) + l4, c4 := bits.Add64(h4, l[4], c3) + l5, c5 := bits.Add64(h5, l[5], c4) + l6, c6 := bits.Add64(h6, l[6], c5) + l7, _ := bits.Add64(h7, 0, c6) + + /* (C10C9, C9C8,C8C7,C7C13,C13C12,C12C11,C11C10) + (C6,...,C0) */ + h0 = (h[3] >> 32) | (h[4] << 32) + h1 = (h[4] >> 32) | (h[5] << 32) + h2 = (h[5] >> 32) | (h[6] << 32) + h3 = (h[6] >> 32) | (h[0] << 32) + h4 = (h[0] >> 32) | (h[1] << 32) + h5 = (h[1] >> 32) | (h[2] << 32) + h6 = (h[2] >> 32) | (h[3] << 32) + + l0, c0 = bits.Add64(l0, h0, 0) + l1, c1 = bits.Add64(l1, h1, c0) + l2, c2 = bits.Add64(l2, h2, c1) + l3, c3 = bits.Add64(l3, h3, c2) + l4, c4 = bits.Add64(l4, h4, c3) + l5, c5 = bits.Add64(l5, h5, c4) + l6, c6 = bits.Add64(l6, h6, c5) + l7, _ = bits.Add64(l7, 0, c6) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, _ = bits.Add64(l6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], l0) + binary.LittleEndian.PutUint64(z[1*8:2*8], l1) + binary.LittleEndian.PutUint64(z[2*8:3*8], l2) + binary.LittleEndian.PutUint64(z[3*8:4*8], l3) + binary.LittleEndian.PutUint64(z[4*8:5*8], l4) + binary.LittleEndian.PutUint64(z[5*8:6*8], l5) + binary.LittleEndian.PutUint64(z[6*8:7*8], l6) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go new file mode 100644 index 00000000..a62225d2 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go @@ -0,0 +1,12 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package fp448 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go b/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go new file mode 100644 index 00000000..2d7afc80 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go @@ -0,0 +1,75 @@ +//go:build gofuzz +// +build gofuzz + +// How to run the fuzzer: +// +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz-build +// $ go-fuzz-build -libfuzzer -func FuzzReduction -o lib.a +// $ clang -fsanitize=fuzzer lib.a -o fu.exe +// $ ./fu.exe +package fp448 + +import ( + "encoding/binary" + "fmt" + "math/big" + + "github.com/cloudflare/circl/internal/conv" +) + +// FuzzReduction is a fuzzer target for red64 function, which reduces t +// (112 bits) to a number t' (56 bits) congruent modulo p448. +func FuzzReduction(data []byte) int { + if len(data) != 2*Size { + return -1 + } + var got, want Elt + var lo, hi [7]uint64 + a := data[:Size] + b := data[Size:] + lo[0] = binary.LittleEndian.Uint64(a[0*8 : 1*8]) + lo[1] = binary.LittleEndian.Uint64(a[1*8 : 2*8]) + lo[2] = binary.LittleEndian.Uint64(a[2*8 : 3*8]) + lo[3] = binary.LittleEndian.Uint64(a[3*8 : 4*8]) + lo[4] = binary.LittleEndian.Uint64(a[4*8 : 5*8]) + lo[5] = binary.LittleEndian.Uint64(a[5*8 : 6*8]) + lo[6] = binary.LittleEndian.Uint64(a[6*8 : 7*8]) + + hi[0] = binary.LittleEndian.Uint64(b[0*8 : 1*8]) + hi[1] = binary.LittleEndian.Uint64(b[1*8 : 2*8]) + hi[2] = binary.LittleEndian.Uint64(b[2*8 : 3*8]) + hi[3] = binary.LittleEndian.Uint64(b[3*8 : 4*8]) + hi[4] = binary.LittleEndian.Uint64(b[4*8 : 5*8]) + hi[5] = binary.LittleEndian.Uint64(b[5*8 : 6*8]) + hi[6] = binary.LittleEndian.Uint64(b[6*8 : 7*8]) + + red64(&got, &lo, &hi) + + t := conv.BytesLe2BigInt(data[:2*Size]) + + two448 := big.NewInt(1) + two448.Lsh(two448, 448) // 2^448 + mask448 := big.NewInt(1) + mask448.Sub(two448, mask448) // 2^448-1 + two224plus1 := big.NewInt(1) + two224plus1.Lsh(two224plus1, 224) + two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 + + var loBig, hiBig big.Int + for t.Cmp(two448) >= 0 { + loBig.And(t, mask448) + hiBig.Rsh(t, 448) + t.Mul(&hiBig, two224plus1) + t.Add(t, &loBig) + } + conv.BigInt2BytesLe(want[:], t) + + if got != want { + fmt.Printf("in: %v\n", conv.BytesLe2BigInt(data[:2*Size])) + fmt.Printf("got: %v\n", got) + fmt.Printf("want: %v\n", want) + panic("error found") + } + return 1 +} diff --git a/vendor/github.com/cloudflare/circl/math/mlsbset/mlsbset.go b/vendor/github.com/cloudflare/circl/math/mlsbset/mlsbset.go new file mode 100644 index 00000000..a43851b8 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/mlsbset/mlsbset.go @@ -0,0 +1,122 @@ +// Package mlsbset provides a constant-time exponentiation method with precomputation. +// +// References: "Efficient and secure algorithms for GLV-based scalar +// multiplication and their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) +// - https://doi.org/10.1007/s13389-014-0085-7 +// - https://eprint.iacr.org/2013/158 +package mlsbset + +import ( + "errors" + "fmt" + "math/big" + + "github.com/cloudflare/circl/internal/conv" +) + +// EltG is a group element. +type EltG interface{} + +// EltP is a precomputed group element. +type EltP interface{} + +// Group defines the operations required by MLSBSet exponentiation method. +type Group interface { + Identity() EltG // Returns the identity of the group. + Sqr(x EltG) // Calculates x = x^2. + Mul(x EltG, y EltP) // Calculates x = x*y. + NewEltP() EltP // Returns an arbitrary precomputed element. + ExtendedEltP() EltP // Returns the precomputed element x^(2^(w*d)). + Lookup(a EltP, v uint, s, u int32) // Sets a = s*T[v][u]. +} + +// Params contains the parameters of the encoding. +type Params struct { + T uint // T is the maximum size (in bits) of exponents. + V uint // V is the number of tables. + W uint // W is the window size. + E uint // E is the number of digits per table. + D uint // D is the number of digits in total. + L uint // L is the length of the code. +} + +// Encoder allows to convert integers into valid powers. +type Encoder struct{ p Params } + +// New produces an encoder of the MLSBSet algorithm. +func New(t, v, w uint) (Encoder, error) { + if !(t > 1 && v >= 1 && w >= 2) { + return Encoder{}, errors.New("t>1, v>=1, w>=2") + } + e := (t + w*v - 1) / (w * v) + d := e * v + l := d * w + return Encoder{Params{t, v, w, e, d, l}}, nil +} + +// Encode converts an odd integer k into a valid power for exponentiation. +func (m Encoder) Encode(k []byte) (*Power, error) { + if len(k) == 0 { + return nil, errors.New("empty slice") + } + if !(len(k) <= int(m.p.L+7)>>3) { + return nil, errors.New("k too big") + } + if k[0]%2 == 0 { + return nil, errors.New("k must be odd") + } + ap := int((m.p.L+7)/8) - len(k) + k = append(k, make([]byte, ap)...) + s := m.signs(k) + b := make([]int32, m.p.L-m.p.D) + c := conv.BytesLe2BigInt(k) + c.Rsh(c, m.p.D) + var bi big.Int + for i := m.p.D; i < m.p.L; i++ { + c0 := int32(c.Bit(0)) + b[i-m.p.D] = s[i%m.p.D] * c0 + bi.SetInt64(int64(b[i-m.p.D] >> 1)) + c.Rsh(c, 1) + c.Sub(c, &bi) + } + carry := int(c.Int64()) + return &Power{m, s, b, carry}, nil +} + +// signs calculates the set of signs. +func (m Encoder) signs(k []byte) []int32 { + s := make([]int32, m.p.D) + s[m.p.D-1] = 1 + for i := uint(1); i < m.p.D; i++ { + ki := int32((k[i>>3] >> (i & 0x7)) & 0x1) + s[i-1] = 2*ki - 1 + } + return s +} + +// GetParams returns the complementary parameters of the encoding. +func (m Encoder) GetParams() Params { return m.p } + +// tableSize returns the size of each table. +func (m Encoder) tableSize() uint { return 1 << (m.p.W - 1) } + +// Elts returns the total number of elements that must be precomputed. +func (m Encoder) Elts() uint { return m.p.V * m.tableSize() } + +// IsExtended returns true if the element x^(2^(wd)) must be calculated. +func (m Encoder) IsExtended() bool { q := m.p.T / (m.p.V * m.p.W); return m.p.T == q*m.p.V*m.p.W } + +// Ops returns the number of squares and multiplications executed during an exponentiation. +func (m Encoder) Ops() (S uint, M uint) { + S = m.p.E + M = m.p.E * m.p.V + if m.IsExtended() { + M++ + } + return +} + +func (m Encoder) String() string { + return fmt.Sprintf("T: %v W: %v V: %v e: %v d: %v l: %v wv|t: %v", + m.p.T, m.p.W, m.p.V, m.p.E, m.p.D, m.p.L, m.IsExtended()) +} diff --git a/vendor/github.com/cloudflare/circl/math/mlsbset/power.go b/vendor/github.com/cloudflare/circl/math/mlsbset/power.go new file mode 100644 index 00000000..3f214c30 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/mlsbset/power.go @@ -0,0 +1,64 @@ +package mlsbset + +import "fmt" + +// Power is a valid exponent produced by the MLSBSet encoding algorithm. +type Power struct { + set Encoder // parameters of code. + s []int32 // set of signs. + b []int32 // set of digits. + c int // carry is {0,1}. +} + +// Exp is calculates x^k, where x is a predetermined element of a group G. +func (p *Power) Exp(G Group) EltG { + a, b := G.Identity(), G.NewEltP() + for e := int(p.set.p.E - 1); e >= 0; e-- { + G.Sqr(a) + for v := uint(0); v < p.set.p.V; v++ { + sgnElt, idElt := p.Digit(v, uint(e)) + G.Lookup(b, v, sgnElt, idElt) + G.Mul(a, b) + } + } + if p.set.IsExtended() && p.c == 1 { + G.Mul(a, G.ExtendedEltP()) + } + return a +} + +// Digit returns the (v,e)-th digit and its sign. +func (p *Power) Digit(v, e uint) (sgn, dig int32) { + sgn = p.bit(0, v, e) + dig = 0 + for i := p.set.p.W - 1; i > 0; i-- { + dig = 2*dig + p.bit(i, v, e) + } + mask := dig >> 31 + dig = (dig + mask) ^ mask + return sgn, dig +} + +// bit returns the (w,v,e)-th bit of the code. +func (p *Power) bit(w, v, e uint) int32 { + if !(w < p.set.p.W && + v < p.set.p.V && + e < p.set.p.E) { + panic(fmt.Errorf("indexes outside (%v,%v,%v)", w, v, e)) + } + if w == 0 { + return p.s[p.set.p.E*v+e] + } + return p.b[p.set.p.D*(w-1)+p.set.p.E*v+e] +} + +func (p *Power) String() string { + dig := "" + for j := uint(0); j < p.set.p.V; j++ { + for i := uint(0); i < p.set.p.E; i++ { + s, d := p.Digit(j, i) + dig += fmt.Sprintf("(%2v,%2v) = %+2v %+2v\n", j, i, s, d) + } + } + return fmt.Sprintf("len: %v\ncarry: %v\ndigits:\n%v", len(p.b)+len(p.s), p.c, dig) +} diff --git a/vendor/github.com/cloudflare/circl/math/wnaf.go b/vendor/github.com/cloudflare/circl/math/wnaf.go new file mode 100644 index 00000000..94a1ec50 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/wnaf.go @@ -0,0 +1,84 @@ +// Package math provides some utility functions for big integers. +package math + +import "math/big" + +// SignedDigit obtains the signed-digit recoding of n and returns a list L of +// digits such that n = sum( L[i]*2^(i*(w-1)) ), and each L[i] is an odd number +// in the set {±1, ±3, ..., ±2^(w-1)-1}. The third parameter ensures that the +// output has ceil(l/(w-1)) digits. +// +// Restrictions: +// - n is odd and n > 0. +// - 1 < w < 32. +// - l >= bit length of n. +// +// References: +// - Alg.6 in "Exponent Recoding and Regular Exponentiation Algorithms" +// by Joye-Tunstall. http://doi.org/10.1007/978-3-642-02384-2_21 +// - Alg.6 in "Selecting Elliptic Curves for Cryptography: An Efficiency and +// Security Analysis" by Bos et al. http://doi.org/10.1007/s13389-015-0097-y +func SignedDigit(n *big.Int, w, l uint) []int32 { + if n.Sign() <= 0 || n.Bit(0) == 0 { + panic("n must be non-zero, odd, and positive") + } + if w <= 1 || w >= 32 { + panic("Verify that 1 < w < 32") + } + if uint(n.BitLen()) > l { + panic("n is too big to fit in l digits") + } + lenN := (l + (w - 1) - 1) / (w - 1) // ceil(l/(w-1)) + L := make([]int32, lenN+1) + var k, v big.Int + k.Set(n) + + var i uint + for i = 0; i < lenN; i++ { + words := k.Bits() + value := int32(words[0] & ((1 << w) - 1)) + value -= int32(1) << (w - 1) + L[i] = value + v.SetInt64(int64(value)) + k.Sub(&k, &v) + k.Rsh(&k, w-1) + } + L[i] = int32(k.Int64()) + return L +} + +// OmegaNAF obtains the window-w Non-Adjacent Form of a positive number n and +// 1 < w < 32. The returned slice L holds n = sum( L[i]*2^i ). +// +// Reference: +// - Alg.9 "Efficient arithmetic on Koblitz curves" by Solinas. +// http://doi.org/10.1023/A:1008306223194 +func OmegaNAF(n *big.Int, w uint) (L []int32) { + if n.Sign() < 0 { + panic("n must be positive") + } + if w <= 1 || w >= 32 { + panic("Verify that 1 < w < 32") + } + + L = make([]int32, n.BitLen()+1) + var k, v big.Int + k.Set(n) + + i := 0 + for ; k.Sign() > 0; i++ { + value := int32(0) + if k.Bit(0) == 1 { + words := k.Bits() + value = int32(words[0] & ((1 << w) - 1)) + if value >= (int32(1) << (w - 1)) { + value -= int32(1) << w + } + v.SetInt64(int64(value)) + k.Sub(&k, &v) + } + L[i] = value + k.Rsh(&k, 1) + } + return L[:i] +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go b/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go new file mode 100644 index 00000000..08ca65d7 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go @@ -0,0 +1,453 @@ +// Package ed25519 implements Ed25519 signature scheme as described in RFC-8032. +// +// This package provides optimized implementations of the three signature +// variants and maintaining closer compatiblilty with crypto/ed25519. +// +// | Scheme Name | Sign Function | Verification | Context | +// |-------------|-------------------|---------------|-------------------| +// | Ed25519 | Sign | Verify | None | +// | Ed25519Ph | SignPh | VerifyPh | Yes, can be empty | +// | Ed25519Ctx | SignWithCtx | VerifyWithCtx | Yes, non-empty | +// | All above | (PrivateKey).Sign | VerifyAny | As above | +// +// Specific functions for sign and verify are defined. A generic signing +// function for all schemes is available through the crypto.Signer interface, +// which is implemented by the PrivateKey type. A correspond all-in-one +// verification method is provided by the VerifyAny function. +// +// Signing with Ed25519Ph or Ed25519Ctx requires a context string for domain +// separation. This parameter is passed using a SignerOptions struct defined +// in this package. While Ed25519Ph accepts an empty context, Ed25519Ctx +// enforces non-empty context strings. +// +// # Compatibility with crypto.ed25519 +// +// These functions are compatible with the “Ed25519” function defined in +// RFC-8032. However, unlike RFC 8032's formulation, this package's private +// key representation includes a public key suffix to make multiple signing +// operations with the same key more efficient. This package refers to the +// RFC-8032 private key as the “seed”. +// +// References +// +// - RFC-8032: https://rfc-editor.org/rfc/rfc8032.txt +// - Ed25519: https://ed25519.cr.yp.to/ +// - EdDSA: High-speed high-security signatures. https://doi.org/10.1007/s13389-012-0027-1 +package ed25519 + +import ( + "bytes" + "crypto" + cryptoRand "crypto/rand" + "crypto/sha512" + "crypto/subtle" + "errors" + "fmt" + "io" + "strconv" + + "github.com/cloudflare/circl/sign" +) + +const ( + // ContextMaxSize is the maximum length (in bytes) allowed for context. + ContextMaxSize = 255 + // PublicKeySize is the size, in bytes, of public keys as used in this package. + PublicKeySize = 32 + // PrivateKeySize is the size, in bytes, of private keys as used in this package. + PrivateKeySize = 64 + // SignatureSize is the size, in bytes, of signatures generated and verified by this package. + SignatureSize = 64 + // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. + SeedSize = 32 +) + +const ( + paramB = 256 / 8 // Size of keys in bytes. +) + +// SignerOptions implements crypto.SignerOpts and augments with parameters +// that are specific to the Ed25519 signature schemes. +type SignerOptions struct { + // Hash must be crypto.Hash(0) for Ed25519/Ed25519ctx, or crypto.SHA512 + // for Ed25519ph. + crypto.Hash + + // Context is an optional domain separation string for Ed25519ph and a + // must for Ed25519ctx. Its length must be less or equal than 255 bytes. + Context string + + // Scheme is an identifier for choosing a signature scheme. The zero value + // is ED25519. + Scheme SchemeID +} + +// SchemeID is an identifier for each signature scheme. +type SchemeID uint + +const ( + ED25519 SchemeID = iota + ED25519Ph + ED25519Ctx +) + +// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. +type PrivateKey []byte + +// Equal reports whether priv and x have the same value. +func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { + xx, ok := x.(PrivateKey) + return ok && subtle.ConstantTimeCompare(priv, xx) == 1 +} + +// Public returns the PublicKey corresponding to priv. +func (priv PrivateKey) Public() crypto.PublicKey { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, priv[SeedSize:]) + return publicKey +} + +// Seed returns the private key seed corresponding to priv. It is provided for +// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds +// in this package. +func (priv PrivateKey) Seed() []byte { + seed := make([]byte, SeedSize) + copy(seed, priv[:SeedSize]) + return seed +} + +func (priv PrivateKey) Scheme() sign.Scheme { return sch } + +func (pub PublicKey) Scheme() sign.Scheme { return sch } + +func (priv PrivateKey) MarshalBinary() (data []byte, err error) { + privateKey := make(PrivateKey, PrivateKeySize) + copy(privateKey, priv) + return privateKey, nil +} + +func (pub PublicKey) MarshalBinary() (data []byte, err error) { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, pub) + return publicKey, nil +} + +// Equal reports whether pub and x have the same value. +func (pub PublicKey) Equal(x crypto.PublicKey) bool { + xx, ok := x.(PublicKey) + return ok && bytes.Equal(pub, xx) +} + +// Sign creates a signature of a message with priv key. +// This function is compatible with crypto.ed25519 and also supports the +// three signature variants defined in RFC-8032, namely Ed25519 (or pure +// EdDSA), Ed25519Ph, and Ed25519Ctx. +// The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx +// variant. This can be achieved by passing crypto.Hash(0) as the value for +// opts. +// The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. +// This can be achieved by passing crypto.SHA512 as the value for opts. +// Use a SignerOptions struct (defined in this package) to pass a context +// string for signing. +func (priv PrivateKey) Sign( + rand io.Reader, + message []byte, + opts crypto.SignerOpts, +) (signature []byte, err error) { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): + return Sign(priv, message), nil + case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: + return SignPh(priv, message, ctx), nil + case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: + return SignWithCtx(priv, message, ctx), nil + default: + return nil, errors.New("ed25519: bad hash algorithm") + } +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { + if rand == nil { + rand = cryptoRand.Reader + } + + seed := make([]byte, SeedSize) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + + return publicKey, privateKey, nil +} + +// NewKeyFromSeed calculates a private key from a seed. It will panic if +// len(seed) is not SeedSize. This function is provided for interoperability +// with RFC 8032. RFC 8032's private keys correspond to seeds in this +// package. +func NewKeyFromSeed(seed []byte) PrivateKey { + privateKey := make(PrivateKey, PrivateKeySize) + newKeyFromSeed(privateKey, seed) + return privateKey +} + +func newKeyFromSeed(privateKey, seed []byte) { + if l := len(seed); l != SeedSize { + panic("ed25519: bad seed length: " + strconv.Itoa(l)) + } + var P pointR1 + k := sha512.Sum512(seed) + clamp(k[:]) + reduceModOrder(k[:paramB], false) + P.fixedMult(k[:paramB]) + copy(privateKey[:SeedSize], seed) + _ = P.ToBytes(privateKey[SeedSize:]) +} + +func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { + if l := len(privateKey); l != PrivateKeySize { + panic("ed25519: bad private key length: " + strconv.Itoa(l)) + } + + H := sha512.New() + var PHM []byte + + if preHash { + _, _ = H.Write(message) + PHM = H.Sum(nil) + H.Reset() + } else { + PHM = message + } + + // 1. Hash the 32-byte private key using SHA-512. + _, _ = H.Write(privateKey[:SeedSize]) + h := H.Sum(nil) + clamp(h[:]) + prefix, s := h[paramB:], h[:paramB] + + // 2. Compute SHA-512(dom2(F, C) || prefix || PH(M)) + H.Reset() + + writeDom(H, ctx, preHash) + + _, _ = H.Write(prefix) + _, _ = H.Write(PHM) + r := H.Sum(nil) + reduceModOrder(r[:], true) + + // 3. Compute the point [r]B. + var P pointR1 + P.fixedMult(r[:paramB]) + R := (&[paramB]byte{})[:] + if err := P.ToBytes(R); err != nil { + panic(err) + } + + // 4. Compute SHA512(dom2(F, C) || R || A || PH(M)). + H.Reset() + + writeDom(H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(privateKey[SeedSize:]) + _, _ = H.Write(PHM) + hRAM := H.Sum(nil) + + reduceModOrder(hRAM[:], true) + + // 5. Compute S = (r + k * s) mod order. + S := (&[paramB]byte{})[:] + calculateS(S, r[:paramB], hRAM[:paramB], s) + + // 6. The signature is the concatenation of R and S. + copy(signature[:paramB], R[:]) + copy(signature[paramB:], S[:]) +} + +// Sign signs the message with privateKey and returns a signature. +// This function supports the signature variant defined in RFC-8032: Ed25519, +// also known as the pure version of EdDSA. +// It will panic if len(privateKey) is not PrivateKeySize. +func Sign(privateKey PrivateKey, message []byte) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(""), false) + return signature +} + +// SignPh creates a signature of a message with private key and context. +// This function supports the signature variant defined in RFC-8032: Ed25519ph, +// meaning it internally hashes the message using SHA-512, and optionally +// accepts a context string. +// It will panic if len(privateKey) is not PrivateKeySize. +// Context could be passed to this function, which length should be no more than +// ContextMaxSize=255. It can be empty. +func SignPh(privateKey PrivateKey, message []byte, ctx string) []byte { + if len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed25519: bad context length: %v", len(ctx))) + } + + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(ctx), true) + return signature +} + +// SignWithCtx creates a signature of a message with private key and context. +// This function supports the signature variant defined in RFC-8032: Ed25519ctx, +// meaning it accepts a non-empty context string. +// It will panic if len(privateKey) is not PrivateKeySize. +// Context must be passed to this function, which length should be no more than +// ContextMaxSize=255 and cannot be empty. +func SignWithCtx(privateKey PrivateKey, message []byte, ctx string) []byte { + if len(ctx) == 0 || len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed25519: bad context length: %v > %v", len(ctx), ContextMaxSize)) + } + + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(ctx), false) + return signature +} + +func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { + if len(public) != PublicKeySize || + len(signature) != SignatureSize || + !isLessThanOrder(signature[paramB:]) { + return false + } + + var P pointR1 + if ok := P.FromBytes(public); !ok { + return false + } + + H := sha512.New() + var PHM []byte + + if preHash { + _, _ = H.Write(message) + PHM = H.Sum(nil) + H.Reset() + } else { + PHM = message + } + + R := signature[:paramB] + + writeDom(H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(public) + _, _ = H.Write(PHM) + hRAM := H.Sum(nil) + reduceModOrder(hRAM[:], true) + + var Q pointR1 + encR := (&[paramB]byte{})[:] + P.neg() + Q.doubleMult(&P, signature[paramB:], hRAM[:paramB]) + _ = Q.ToBytes(encR) + return bytes.Equal(R, encR) +} + +// VerifyAny returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports all the three signature variants defined in RFC-8032, +// namely Ed25519 (or pure EdDSA), Ed25519Ph, and Ed25519Ctx. +// The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx +// variant. This can be achieved by passing crypto.Hash(0) as the value for opts. +// The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. +// This can be achieved by passing crypto.SHA512 as the value for opts. +// Use a SignerOptions struct to pass a context string for signing. +func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): + return Verify(public, message, signature) + case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: + return VerifyPh(public, message, signature, ctx) + case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: + return VerifyWithCtx(public, message, signature, ctx) + default: + return false + } +} + +// Verify returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed25519, +// also known as the pure version of EdDSA. +func Verify(public PublicKey, message, signature []byte) bool { + return verify(public, message, signature, []byte(""), false) +} + +// VerifyPh returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed25519ph, +// meaning it internally hashes the message using SHA-512. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), true) +} + +// VerifyWithCtx returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded, or when context is +// not provided. +// This function supports the signature variant defined in RFC-8032: Ed25519ctx, +// meaning it does not handle prehashed messages. Non-empty context string must be +// provided, and must not be more than 255 of length. +func VerifyWithCtx(public PublicKey, message, signature []byte, ctx string) bool { + if len(ctx) == 0 || len(ctx) > ContextMaxSize { + return false + } + + return verify(public, message, signature, []byte(ctx), false) +} + +func clamp(k []byte) { + k[0] &= 248 + k[paramB-1] = (k[paramB-1] & 127) | 64 +} + +// isLessThanOrder returns true if 0 <= x < order. +func isLessThanOrder(x []byte) bool { + i := len(order) - 1 + for i > 0 && x[i] == order[i] { + i-- + } + return x[i] < order[i] +} + +func writeDom(h io.Writer, ctx []byte, preHash bool) { + dom2 := "SigEd25519 no Ed25519 collisions" + + if len(ctx) > 0 { + _, _ = h.Write([]byte(dom2)) + if preHash { + _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) + } else { + _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) + } + _, _ = h.Write(ctx) + } else if preHash { + _, _ = h.Write([]byte(dom2)) + _, _ = h.Write([]byte{0x01, 0x00}) + } +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go b/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go new file mode 100644 index 00000000..10efafdc --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go @@ -0,0 +1,175 @@ +package ed25519 + +import ( + "encoding/binary" + "math/bits" +) + +var order = [paramB]byte{ + 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, + 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, +} + +// isLessThan returns true if 0 <= x < y, and assumes that slices have the same length. +func isLessThan(x, y []byte) bool { + i := len(x) - 1 + for i > 0 && x[i] == y[i] { + i-- + } + return x[i] < y[i] +} + +// reduceModOrder calculates k = k mod order of the curve. +func reduceModOrder(k []byte, is512Bit bool) { + var X [((2 * paramB) * 8) / 64]uint64 + numWords := len(k) >> 3 + for i := 0; i < numWords; i++ { + X[i] = binary.LittleEndian.Uint64(k[i*8 : (i+1)*8]) + } + red512(&X, is512Bit) + for i := 0; i < numWords; i++ { + binary.LittleEndian.PutUint64(k[i*8:(i+1)*8], X[i]) + } +} + +// red512 calculates x = x mod Order of the curve. +func red512(x *[8]uint64, full bool) { + // Implementation of Algs.(14.47)+(14.52) of Handbook of Applied + // Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone. + const ( + ell0 = uint64(0x5812631a5cf5d3ed) + ell1 = uint64(0x14def9dea2f79cd6) + ell160 = uint64(0x812631a5cf5d3ed0) + ell161 = uint64(0x4def9dea2f79cd65) + ell162 = uint64(0x0000000000000001) + ) + + var c0, c1, c2, c3 uint64 + r0, r1, r2, r3, r4 := x[0], x[1], x[2], x[3], uint64(0) + + if full { + q0, q1, q2, q3 := x[4], x[5], x[6], x[7] + + for i := 0; i < 3; i++ { + h0, s0 := bits.Mul64(q0, ell160) + h1, s1 := bits.Mul64(q1, ell160) + h2, s2 := bits.Mul64(q2, ell160) + h3, s3 := bits.Mul64(q3, ell160) + + s1, c0 = bits.Add64(h0, s1, 0) + s2, c1 = bits.Add64(h1, s2, c0) + s3, c2 = bits.Add64(h2, s3, c1) + s4, _ := bits.Add64(h3, 0, c2) + + h0, l0 := bits.Mul64(q0, ell161) + h1, l1 := bits.Mul64(q1, ell161) + h2, l2 := bits.Mul64(q2, ell161) + h3, l3 := bits.Mul64(q3, ell161) + + l1, c0 = bits.Add64(h0, l1, 0) + l2, c1 = bits.Add64(h1, l2, c0) + l3, c2 = bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + s1, c0 = bits.Add64(s1, l0, 0) + s2, c1 = bits.Add64(s2, l1, c0) + s3, c2 = bits.Add64(s3, l2, c1) + s4, c3 = bits.Add64(s4, l3, c2) + s5, s6 := bits.Add64(l4, 0, c3) + + s2, c0 = bits.Add64(s2, q0, 0) + s3, c1 = bits.Add64(s3, q1, c0) + s4, c2 = bits.Add64(s4, q2, c1) + s5, c3 = bits.Add64(s5, q3, c2) + s6, s7 := bits.Add64(s6, 0, c3) + + q := q0 | q1 | q2 | q3 + m := -((q | -q) >> 63) // if q=0 then m=0...0 else m=1..1 + s0 &= m + s1 &= m + s2 &= m + s3 &= m + q0, q1, q2, q3 = s4, s5, s6, s7 + + if (i+1)%2 == 0 { + r0, c0 = bits.Add64(r0, s0, 0) + r1, c1 = bits.Add64(r1, s1, c0) + r2, c2 = bits.Add64(r2, s2, c1) + r3, c3 = bits.Add64(r3, s3, c2) + r4, _ = bits.Add64(r4, 0, c3) + } else { + r0, c0 = bits.Sub64(r0, s0, 0) + r1, c1 = bits.Sub64(r1, s1, c0) + r2, c2 = bits.Sub64(r2, s2, c1) + r3, c3 = bits.Sub64(r3, s3, c2) + r4, _ = bits.Sub64(r4, 0, c3) + } + } + + m := -(r4 >> 63) + r0, c0 = bits.Add64(r0, m&ell160, 0) + r1, c1 = bits.Add64(r1, m&ell161, c0) + r2, c2 = bits.Add64(r2, m&ell162, c1) + r3, c3 = bits.Add64(r3, 0, c2) + r4, _ = bits.Add64(r4, m&1, c3) + x[4], x[5], x[6], x[7] = 0, 0, 0, 0 + } + + q0 := (r4 << 4) | (r3 >> 60) + r3 &= (uint64(1) << 60) - 1 + + h0, s0 := bits.Mul64(ell0, q0) + h1, s1 := bits.Mul64(ell1, q0) + s1, c0 = bits.Add64(h0, s1, 0) + s2, _ := bits.Add64(h1, 0, c0) + + r0, c0 = bits.Sub64(r0, s0, 0) + r1, c1 = bits.Sub64(r1, s1, c0) + r2, c2 = bits.Sub64(r2, s2, c1) + r3, _ = bits.Sub64(r3, 0, c2) + + x[0], x[1], x[2], x[3] = r0, r1, r2, r3 +} + +// calculateS performs s = r+k*a mod Order of the curve. +func calculateS(s, r, k, a []byte) { + K := [4]uint64{ + binary.LittleEndian.Uint64(k[0*8 : 1*8]), + binary.LittleEndian.Uint64(k[1*8 : 2*8]), + binary.LittleEndian.Uint64(k[2*8 : 3*8]), + binary.LittleEndian.Uint64(k[3*8 : 4*8]), + } + S := [8]uint64{ + binary.LittleEndian.Uint64(r[0*8 : 1*8]), + binary.LittleEndian.Uint64(r[1*8 : 2*8]), + binary.LittleEndian.Uint64(r[2*8 : 3*8]), + binary.LittleEndian.Uint64(r[3*8 : 4*8]), + } + var c3 uint64 + for i := range K { + ai := binary.LittleEndian.Uint64(a[i*8 : (i+1)*8]) + + h0, l0 := bits.Mul64(K[0], ai) + h1, l1 := bits.Mul64(K[1], ai) + h2, l2 := bits.Mul64(K[2], ai) + h3, l3 := bits.Mul64(K[3], ai) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + S[i+0], c0 = bits.Add64(S[i+0], l0, 0) + S[i+1], c1 = bits.Add64(S[i+1], l1, c0) + S[i+2], c2 = bits.Add64(S[i+2], l2, c1) + S[i+3], c3 = bits.Add64(S[i+3], l3, c2) + S[i+4], _ = bits.Add64(S[i+4], l4, c3) + } + red512(&S, true) + binary.LittleEndian.PutUint64(s[0*8:1*8], S[0]) + binary.LittleEndian.PutUint64(s[1*8:2*8], S[1]) + binary.LittleEndian.PutUint64(s[2*8:3*8], S[2]) + binary.LittleEndian.PutUint64(s[3*8:4*8], S[3]) +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go b/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go new file mode 100644 index 00000000..3216aae3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go @@ -0,0 +1,180 @@ +package ed25519 + +import ( + "crypto/subtle" + "encoding/binary" + "math/bits" + + "github.com/cloudflare/circl/internal/conv" + "github.com/cloudflare/circl/math" + fp "github.com/cloudflare/circl/math/fp25519" +) + +var paramD = fp.Elt{ + 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, + 0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00, + 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c, + 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52, +} + +// mLSBRecoding parameters. +const ( + fxT = 257 + fxV = 2 + fxW = 3 + fx2w1 = 1 << (uint(fxW) - 1) + numWords64 = (paramB * 8 / 64) +) + +// mLSBRecoding is the odd-only modified LSB-set. +// +// Reference: +// +// "Efficient and secure algorithms for GLV-based scalar multiplication and +// their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) +// http://doi.org/10.1007/s13389-014-0085-7. +func mLSBRecoding(L []int8, k []byte) { + const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) + const dd = ee * fxV + const ll = dd * fxW + if len(L) == (ll + 1) { + var m [numWords64 + 1]uint64 + for i := 0; i < numWords64; i++ { + m[i] = binary.LittleEndian.Uint64(k[8*i : 8*i+8]) + } + condAddOrderN(&m) + L[dd-1] = 1 + for i := 0; i < dd-1; i++ { + kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1 + L[i] = int8(kip1<<1) - 1 + } + { // right-shift by d + right := uint(dd % 64) + left := uint(64) - right + lim := ((numWords64+1)*64 - dd) / 64 + j := dd / 64 + for i := 0; i < lim; i++ { + m[i] = (m[i+j] >> right) | (m[i+j+1] << left) + } + m[lim] = m[lim+j] >> right + } + for i := dd; i < ll; i++ { + L[i] = L[i%dd] * int8(m[0]&0x1) + div2subY(m[:], int64(L[i]>>1), numWords64) + } + L[ll] = int8(m[0]) + } +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} + +// condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged. +func condAddOrderN(x *[numWords64 + 1]uint64) { + isOdd := (x[0] & 0x1) - 1 + c := uint64(0) + for i := 0; i < numWords64; i++ { + orderWord := binary.LittleEndian.Uint64(order[8*i : 8*i+8]) + o := isOdd & orderWord + x0, c0 := bits.Add64(x[i], o, c) + x[i] = x0 + c = c0 + } + x[numWords64], _ = bits.Add64(x[numWords64], 0, c) +} + +// div2subY update x = (x/2) - y. +func div2subY(x []uint64, y int64, l int) { + s := uint64(y >> 63) + for i := 0; i < l-1; i++ { + x[i] = (x[i] >> 1) | (x[i+1] << 63) + } + x[l-1] = (x[l-1] >> 1) + + b := uint64(0) + x0, b0 := bits.Sub64(x[0], uint64(y), b) + x[0] = x0 + b = b0 + for i := 1; i < l-1; i++ { + x0, b0 := bits.Sub64(x[i], s, b) + x[i] = x0 + b = b0 + } + x[l-1], _ = bits.Sub64(x[l-1], s, b) +} + +func (P *pointR1) fixedMult(scalar []byte) { + if len(scalar) != paramB { + panic("wrong scalar size") + } + const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) + const dd = ee * fxV + const ll = dd * fxW + + L := make([]int8, ll+1) + mLSBRecoding(L[:], scalar) + S := &pointR3{} + P.SetIdentity() + for ii := ee - 1; ii >= 0; ii-- { + P.double() + for j := 0; j < fxV; j++ { + dig := L[fxW*dd-j*ee+ii-ee] + for i := (fxW-1)*dd - j*ee + ii - ee; i >= (2*dd - j*ee + ii - ee); i = i - dd { + dig = 2*dig + L[i] + } + idx := absolute(int32(dig)) + sig := L[dd-j*ee+ii-ee] + Tabj := &tabSign[fxV-j-1] + for k := 0; k < fx2w1; k++ { + S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx)) + } + S.cneg(subtle.ConstantTimeEq(int32(sig), -1)) + P.mixAdd(S) + } + } +} + +const ( + omegaFix = 7 + omegaVar = 5 +) + +// doubleMult returns P=mG+nQ. +func (P *pointR1) doubleMult(Q *pointR1, m, n []byte) { + nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m), omegaFix) + nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n), omegaVar) + + if len(nafFix) > len(nafVar) { + nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) + } else if len(nafFix) < len(nafVar) { + nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) + } + + var TabQ [1 << (omegaVar - 2)]pointR2 + Q.oddMultiples(TabQ[:]) + P.SetIdentity() + for i := len(nafFix) - 1; i >= 0; i-- { + P.double() + // Generator point + if nafFix[i] != 0 { + idxM := absolute(nafFix[i]) >> 1 + R := tabVerif[idxM] + if nafFix[i] < 0 { + R.neg() + } + P.mixAdd(&R) + } + // Variable input point + if nafVar[i] != 0 { + idxN := absolute(nafVar[i]) >> 1 + S := TabQ[idxN] + if nafVar[i] < 0 { + S.neg() + } + P.add(&S) + } + } +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/point.go b/vendor/github.com/cloudflare/circl/sign/ed25519/point.go new file mode 100644 index 00000000..374a6950 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/point.go @@ -0,0 +1,195 @@ +package ed25519 + +import fp "github.com/cloudflare/circl/math/fp25519" + +type ( + pointR1 struct{ x, y, z, ta, tb fp.Elt } + pointR2 struct { + pointR3 + z2 fp.Elt + } +) +type pointR3 struct{ addYX, subYX, dt2 fp.Elt } + +func (P *pointR1) neg() { + fp.Neg(&P.x, &P.x) + fp.Neg(&P.ta, &P.ta) +} + +func (P *pointR1) SetIdentity() { + P.x = fp.Elt{} + fp.SetOne(&P.y) + fp.SetOne(&P.z) + P.ta = fp.Elt{} + P.tb = fp.Elt{} +} + +func (P *pointR1) toAffine() { + fp.Inv(&P.z, &P.z) + fp.Mul(&P.x, &P.x, &P.z) + fp.Mul(&P.y, &P.y, &P.z) + fp.Modp(&P.x) + fp.Modp(&P.y) + fp.SetOne(&P.z) + P.ta = P.x + P.tb = P.y +} + +func (P *pointR1) ToBytes(k []byte) error { + P.toAffine() + var x [fp.Size]byte + err := fp.ToBytes(k[:fp.Size], &P.y) + if err != nil { + return err + } + err = fp.ToBytes(x[:], &P.x) + if err != nil { + return err + } + b := x[0] & 1 + k[paramB-1] = k[paramB-1] | (b << 7) + return nil +} + +func (P *pointR1) FromBytes(k []byte) bool { + if len(k) != paramB { + panic("wrong size") + } + signX := k[paramB-1] >> 7 + copy(P.y[:], k[:fp.Size]) + P.y[fp.Size-1] &= 0x7F + p := fp.P() + if !isLessThan(P.y[:], p[:]) { + return false + } + + one, u, v := &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + fp.SetOne(one) + fp.Sqr(u, &P.y) // u = y^2 + fp.Mul(v, u, ¶mD) // v = dy^2 + fp.Sub(u, u, one) // u = y^2-1 + fp.Add(v, v, one) // v = dy^2+1 + isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) + if !isQR { + return false + } + fp.Modp(&P.x) // x = x mod p + if fp.IsZero(&P.x) && signX == 1 { + return false + } + if signX != (P.x[0] & 1) { + fp.Neg(&P.x, &P.x) + } + P.ta = P.x + P.tb = P.y + fp.SetOne(&P.z) + return true +} + +// double calculates 2P for curves with A=-1. +func (P *pointR1) double() { + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Add(h, a, b) // H = A+B + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, h) // E = (x+y)^2-A-B + fp.Sub(g, b, a) // G = B-A + fp.Sub(f, c, g) // F = C-G + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *pointR1) mixAdd(Q *pointR3) { + fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 + P.coreAddition(Q) +} + +func (P *pointR1) add(Q *pointR2) { + fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 + P.coreAddition(&Q.pointR3) +} + +// coreAddition calculates P=P+Q for curves with A=-1. +func (P *pointR1) coreAddition(Q *pointR3) { + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 + a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb + fp.Mul(c, Pta, Ptb) // t1 = ta*tb + fp.Sub(h, Py, Px) // y1-x1 + fp.Add(b, Py, Px) // y1+x1 + fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) + fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) + fp.Mul(c, c, dt2) // C = 2*D*t1*t2 + fp.Sub(e, b, a) // E = B-A + fp.Add(h, b, a) // H = B+A + fp.Sub(f, d, c) // F = D-C + fp.Add(g, d, c) // G = D+C + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *pointR1) oddMultiples(T []pointR2) { + var R pointR2 + n := len(T) + T[0].fromR1(P) + _2P := *P + _2P.double() + R.fromR1(&_2P) + for i := 1; i < n; i++ { + P.add(&R) + T[i].fromR1(P) + } +} + +func (P *pointR1) isEqual(Q *pointR1) bool { + l, r := &fp.Elt{}, &fp.Elt{} + fp.Mul(l, &P.x, &Q.z) + fp.Mul(r, &Q.x, &P.z) + fp.Sub(l, l, r) + b := fp.IsZero(l) + fp.Mul(l, &P.y, &Q.z) + fp.Mul(r, &Q.y, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + fp.Mul(l, &P.ta, &P.tb) + fp.Mul(l, l, &Q.z) + fp.Mul(r, &Q.ta, &Q.tb) + fp.Mul(r, r, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + return b +} + +func (P *pointR3) neg() { + P.addYX, P.subYX = P.subYX, P.addYX + fp.Neg(&P.dt2, &P.dt2) +} + +func (P *pointR2) fromR1(Q *pointR1) { + fp.Add(&P.addYX, &Q.y, &Q.x) + fp.Sub(&P.subYX, &Q.y, &Q.x) + fp.Mul(&P.dt2, &Q.ta, &Q.tb) + fp.Mul(&P.dt2, &P.dt2, ¶mD) + fp.Add(&P.dt2, &P.dt2, &P.dt2) + fp.Add(&P.z2, &Q.z, &Q.z) +} + +func (P *pointR3) cneg(b int) { + t := &fp.Elt{} + fp.Cswap(&P.addYX, &P.subYX, uint(b)) + fp.Neg(t, &P.dt2) + fp.Cmov(&P.dt2, t, uint(b)) +} + +func (P *pointR3) cmov(Q *pointR3, b int) { + fp.Cmov(&P.addYX, &Q.addYX, uint(b)) + fp.Cmov(&P.subYX, &Q.subYX, uint(b)) + fp.Cmov(&P.dt2, &Q.dt2, uint(b)) +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey.go b/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey.go new file mode 100644 index 00000000..c3505b67 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey.go @@ -0,0 +1,9 @@ +//go:build go1.13 +// +build go1.13 + +package ed25519 + +import cryptoEd25519 "crypto/ed25519" + +// PublicKey is the type of Ed25519 public keys. +type PublicKey cryptoEd25519.PublicKey diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey112.go b/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey112.go new file mode 100644 index 00000000..d57d86ef --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/pubkey112.go @@ -0,0 +1,7 @@ +//go:build !go1.13 +// +build !go1.13 + +package ed25519 + +// PublicKey is the type of Ed25519 public keys. +type PublicKey []byte diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/signapi.go b/vendor/github.com/cloudflare/circl/sign/ed25519/signapi.go new file mode 100644 index 00000000..e4520f52 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/signapi.go @@ -0,0 +1,87 @@ +package ed25519 + +import ( + "crypto/rand" + "encoding/asn1" + + "github.com/cloudflare/circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed25519" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0x0807 } +func (*scheme) SupportsContext() bool { return false } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 101, 112} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + return Sign(priv, message) +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil { + if opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + } + return Verify(pub, message, signature) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + return publicKey, privateKey +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) < PublicKeySize { + return nil, sign.ErrPubKeySize + } + pub := make(PublicKey, PublicKeySize) + copy(pub, buf[:PublicKeySize]) + return pub, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) < PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + priv := make(PrivateKey, PrivateKeySize) + copy(priv, buf[:PrivateKeySize]) + return priv, nil +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go b/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go new file mode 100644 index 00000000..8763b426 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go @@ -0,0 +1,213 @@ +package ed25519 + +import fp "github.com/cloudflare/circl/math/fp25519" + +var tabSign = [fxV][fx2w1]pointR3{ + { + pointR3{ + addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, + subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, + dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, + }, + { + addYX: fp.Elt{0x7c, 0xb0, 0x9e, 0xe6, 0xc5, 0xbf, 0xfa, 0x13, 0x8e, 0x0d, 0x22, 0xde, 0xc8, 0xd1, 0xce, 0x52, 0x02, 0xd5, 0x62, 0x31, 0x71, 0x0e, 0x8e, 0x9d, 0xb0, 0xd6, 0x00, 0xa5, 0x5a, 0x0e, 0xce, 0x72}, + subYX: fp.Elt{0x1a, 0x8e, 0x5c, 0xdc, 0xa4, 0xb3, 0x6c, 0x51, 0x18, 0xa0, 0x09, 0x80, 0x9a, 0x46, 0x33, 0xd5, 0xe0, 0x3c, 0x4d, 0x3b, 0xfc, 0x49, 0xa2, 0x43, 0x29, 0xe1, 0x29, 0xa9, 0x93, 0xea, 0x7c, 0x35}, + dt2: fp.Elt{0x08, 0x46, 0x6f, 0x68, 0x7f, 0x0b, 0x7c, 0x9e, 0xad, 0xba, 0x07, 0x61, 0x74, 0x83, 0x2f, 0xfc, 0x26, 0xd6, 0x09, 0xb9, 0x00, 0x34, 0x36, 0x4f, 0x01, 0xf3, 0x48, 0xdb, 0x43, 0xba, 0x04, 0x44}, + }, + { + addYX: fp.Elt{0x4c, 0xda, 0x0d, 0x13, 0x66, 0xfd, 0x82, 0x84, 0x9f, 0x75, 0x5b, 0xa2, 0x17, 0xfe, 0x34, 0xbf, 0x1f, 0xcb, 0xba, 0x90, 0x55, 0x80, 0x83, 0xfd, 0x63, 0xb9, 0x18, 0xf8, 0x5b, 0x5d, 0x94, 0x1e}, + subYX: fp.Elt{0xb9, 0xdb, 0x6c, 0x04, 0x88, 0x22, 0xd8, 0x79, 0x83, 0x2f, 0x8d, 0x65, 0x6b, 0xd2, 0xab, 0x1b, 0xdd, 0x65, 0xe5, 0x93, 0x63, 0xf8, 0xa2, 0xd8, 0x3c, 0xf1, 0x4b, 0xc5, 0x99, 0xd1, 0xf2, 0x12}, + dt2: fp.Elt{0x05, 0x4c, 0xb8, 0x3b, 0xfe, 0xf5, 0x9f, 0x2e, 0xd1, 0xb2, 0xb8, 0xff, 0xfe, 0x6d, 0xd9, 0x37, 0xe0, 0xae, 0xb4, 0x5a, 0x51, 0x80, 0x7e, 0x9b, 0x1d, 0xd1, 0x8d, 0x8c, 0x56, 0xb1, 0x84, 0x35}, + }, + { + addYX: fp.Elt{0x39, 0x71, 0x43, 0x34, 0xe3, 0x42, 0x45, 0xa1, 0xf2, 0x68, 0x71, 0xa7, 0xe8, 0x23, 0xfd, 0x9f, 0x86, 0x48, 0xff, 0xe5, 0x96, 0x74, 0xcf, 0x05, 0x49, 0xe2, 0xb3, 0x6c, 0x17, 0x77, 0x2f, 0x6d}, + subYX: fp.Elt{0x73, 0x3f, 0xc1, 0xc7, 0x6a, 0x66, 0xa1, 0x20, 0xdd, 0x11, 0xfb, 0x7a, 0x6e, 0xa8, 0x51, 0xb8, 0x3f, 0x9d, 0xa2, 0x97, 0x84, 0xb5, 0xc7, 0x90, 0x7c, 0xab, 0x48, 0xd6, 0x84, 0xa3, 0xd5, 0x1a}, + dt2: fp.Elt{0x63, 0x27, 0x3c, 0x49, 0x4b, 0xfc, 0x22, 0xf2, 0x0b, 0x50, 0xc2, 0x0f, 0xb4, 0x1f, 0x31, 0x0c, 0x2f, 0x53, 0xab, 0xaa, 0x75, 0x6f, 0xe0, 0x69, 0x39, 0x56, 0xe0, 0x3b, 0xb7, 0xa8, 0xbf, 0x45}, + }, + }, + { + { + addYX: fp.Elt{0x00, 0x45, 0xd9, 0x0d, 0x58, 0x03, 0xfc, 0x29, 0x93, 0xec, 0xbb, 0x6f, 0xa4, 0x7a, 0xd2, 0xec, 0xf8, 0xa7, 0xe2, 0xc2, 0x5f, 0x15, 0x0a, 0x13, 0xd5, 0xa1, 0x06, 0xb7, 0x1a, 0x15, 0x6b, 0x41}, + subYX: fp.Elt{0x85, 0x8c, 0xb2, 0x17, 0xd6, 0x3b, 0x0a, 0xd3, 0xea, 0x3b, 0x77, 0x39, 0xb7, 0x77, 0xd3, 0xc5, 0xbf, 0x5c, 0x6a, 0x1e, 0x8c, 0xe7, 0xc6, 0xc6, 0xc4, 0xb7, 0x2a, 0x8b, 0xf7, 0xb8, 0x61, 0x0d}, + dt2: fp.Elt{0xb0, 0x36, 0xc1, 0xe9, 0xef, 0xd7, 0xa8, 0x56, 0x20, 0x4b, 0xe4, 0x58, 0xcd, 0xe5, 0x07, 0xbd, 0xab, 0xe0, 0x57, 0x1b, 0xda, 0x2f, 0xe6, 0xaf, 0xd2, 0xe8, 0x77, 0x42, 0xf7, 0x2a, 0x1a, 0x19}, + }, + { + addYX: fp.Elt{0x6a, 0x6d, 0x6d, 0xd1, 0xfa, 0xf5, 0x03, 0x30, 0xbd, 0x6d, 0xc2, 0xc8, 0xf5, 0x38, 0x80, 0x4f, 0xb2, 0xbe, 0xa1, 0x76, 0x50, 0x1a, 0x73, 0xf2, 0x78, 0x2b, 0x8e, 0x3a, 0x1e, 0x34, 0x47, 0x7b}, + subYX: fp.Elt{0xc3, 0x2c, 0x36, 0xdc, 0xc5, 0x45, 0xbc, 0xef, 0x1b, 0x64, 0xd6, 0x65, 0x28, 0xe9, 0xda, 0x84, 0x13, 0xbe, 0x27, 0x8e, 0x3f, 0x98, 0x2a, 0x37, 0xee, 0x78, 0x97, 0xd6, 0xc0, 0x6f, 0xb4, 0x53}, + dt2: fp.Elt{0x58, 0x5d, 0xa7, 0xa3, 0x68, 0xbb, 0x20, 0x30, 0x2e, 0x03, 0xe9, 0xb1, 0xd4, 0x90, 0x72, 0xe3, 0x71, 0xb2, 0x36, 0x3e, 0x73, 0xa0, 0x2e, 0x3d, 0xd1, 0x85, 0x33, 0x62, 0x4e, 0xa7, 0x7b, 0x31}, + }, + { + addYX: fp.Elt{0xbf, 0xc4, 0x38, 0x53, 0xfb, 0x68, 0xa9, 0x77, 0xce, 0x55, 0xf9, 0x05, 0xcb, 0xeb, 0xfb, 0x8c, 0x46, 0xc2, 0x32, 0x7c, 0xf0, 0xdb, 0xd7, 0x2c, 0x62, 0x8e, 0xdd, 0x54, 0x75, 0xcf, 0x3f, 0x33}, + subYX: fp.Elt{0x49, 0x50, 0x1f, 0x4e, 0x6e, 0x55, 0x55, 0xde, 0x8c, 0x4e, 0x77, 0x96, 0x38, 0x3b, 0xfe, 0xb6, 0x43, 0x3c, 0x86, 0x69, 0xc2, 0x72, 0x66, 0x1f, 0x6b, 0xf9, 0x87, 0xbc, 0x4f, 0x37, 0x3e, 0x3c}, + dt2: fp.Elt{0xd2, 0x2f, 0x06, 0x6b, 0x08, 0x07, 0x69, 0x77, 0xc0, 0x94, 0xcc, 0xae, 0x43, 0x00, 0x59, 0x6e, 0xa3, 0x63, 0xa8, 0xdd, 0xfa, 0x24, 0x18, 0xd0, 0x35, 0xc7, 0x78, 0xf7, 0x0d, 0xd4, 0x5a, 0x1e}, + }, + { + addYX: fp.Elt{0x45, 0xc1, 0x17, 0x51, 0xf8, 0xed, 0x7e, 0xc7, 0xa9, 0x1a, 0x11, 0x6e, 0x2d, 0xef, 0x0b, 0xd5, 0x3f, 0x98, 0xb0, 0xa3, 0x9d, 0x65, 0xf1, 0xcd, 0x53, 0x4a, 0x8a, 0x18, 0x70, 0x0a, 0x7f, 0x23}, + subYX: fp.Elt{0xdd, 0xef, 0xbe, 0x3a, 0x31, 0xe0, 0xbc, 0xbe, 0x6d, 0x5d, 0x79, 0x87, 0xd6, 0xbe, 0x68, 0xe3, 0x59, 0x76, 0x8c, 0x86, 0x0e, 0x7a, 0x92, 0x13, 0x14, 0x8f, 0x67, 0xb3, 0xcb, 0x1a, 0x76, 0x76}, + dt2: fp.Elt{0x56, 0x7a, 0x1c, 0x9d, 0xca, 0x96, 0xf9, 0xf9, 0x03, 0x21, 0xd4, 0xe8, 0xb3, 0xd5, 0xe9, 0x52, 0xc8, 0x54, 0x1e, 0x1b, 0x13, 0xb6, 0xfd, 0x47, 0x7d, 0x02, 0x32, 0x33, 0x27, 0xe2, 0x1f, 0x19}, + }, + }, +} + +var tabVerif = [1 << (omegaFix - 2)]pointR3{ + { /* 1P */ + addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, + subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, + dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, + }, + { /* 3P */ + addYX: fp.Elt{0x30, 0x97, 0xee, 0x4c, 0xa8, 0xb0, 0x25, 0xaf, 0x8a, 0x4b, 0x86, 0xe8, 0x30, 0x84, 0x5a, 0x02, 0x32, 0x67, 0x01, 0x9f, 0x02, 0x50, 0x1b, 0xc1, 0xf4, 0xf8, 0x80, 0x9a, 0x1b, 0x4e, 0x16, 0x7a}, + subYX: fp.Elt{0x65, 0xd2, 0xfc, 0xa4, 0xe8, 0x1f, 0x61, 0x56, 0x7d, 0xba, 0xc1, 0xe5, 0xfd, 0x53, 0xd3, 0x3b, 0xbd, 0xd6, 0x4b, 0x21, 0x1a, 0xf3, 0x31, 0x81, 0x62, 0xda, 0x5b, 0x55, 0x87, 0x15, 0xb9, 0x2a}, + dt2: fp.Elt{0x89, 0xd8, 0xd0, 0x0d, 0x3f, 0x93, 0xae, 0x14, 0x62, 0xda, 0x35, 0x1c, 0x22, 0x23, 0x94, 0x58, 0x4c, 0xdb, 0xf2, 0x8c, 0x45, 0xe5, 0x70, 0xd1, 0xc6, 0xb4, 0xb9, 0x12, 0xaf, 0x26, 0x28, 0x5a}, + }, + { /* 5P */ + addYX: fp.Elt{0x33, 0xbb, 0xa5, 0x08, 0x44, 0xbc, 0x12, 0xa2, 0x02, 0xed, 0x5e, 0xc7, 0xc3, 0x48, 0x50, 0x8d, 0x44, 0xec, 0xbf, 0x5a, 0x0c, 0xeb, 0x1b, 0xdd, 0xeb, 0x06, 0xe2, 0x46, 0xf1, 0xcc, 0x45, 0x29}, + subYX: fp.Elt{0xba, 0xd6, 0x47, 0xa4, 0xc3, 0x82, 0x91, 0x7f, 0xb7, 0x29, 0x27, 0x4b, 0xd1, 0x14, 0x00, 0xd5, 0x87, 0xa0, 0x64, 0xb8, 0x1c, 0xf1, 0x3c, 0xe3, 0xf3, 0x55, 0x1b, 0xeb, 0x73, 0x7e, 0x4a, 0x15}, + dt2: fp.Elt{0x85, 0x82, 0x2a, 0x81, 0xf1, 0xdb, 0xbb, 0xbc, 0xfc, 0xd1, 0xbd, 0xd0, 0x07, 0x08, 0x0e, 0x27, 0x2d, 0xa7, 0xbd, 0x1b, 0x0b, 0x67, 0x1b, 0xb4, 0x9a, 0xb6, 0x3b, 0x6b, 0x69, 0xbe, 0xaa, 0x43}, + }, + { /* 7P */ + addYX: fp.Elt{0xbf, 0xa3, 0x4e, 0x94, 0xd0, 0x5c, 0x1a, 0x6b, 0xd2, 0xc0, 0x9d, 0xb3, 0x3a, 0x35, 0x70, 0x74, 0x49, 0x2e, 0x54, 0x28, 0x82, 0x52, 0xb2, 0x71, 0x7e, 0x92, 0x3c, 0x28, 0x69, 0xea, 0x1b, 0x46}, + subYX: fp.Elt{0xb1, 0x21, 0x32, 0xaa, 0x9a, 0x2c, 0x6f, 0xba, 0xa7, 0x23, 0xba, 0x3b, 0x53, 0x21, 0xa0, 0x6c, 0x3a, 0x2c, 0x19, 0x92, 0x4f, 0x76, 0xea, 0x9d, 0xe0, 0x17, 0x53, 0x2e, 0x5d, 0xdd, 0x6e, 0x1d}, + dt2: fp.Elt{0xa2, 0xb3, 0xb8, 0x01, 0xc8, 0x6d, 0x83, 0xf1, 0x9a, 0xa4, 0x3e, 0x05, 0x47, 0x5f, 0x03, 0xb3, 0xf3, 0xad, 0x77, 0x58, 0xba, 0x41, 0x9c, 0x52, 0xa7, 0x90, 0x0f, 0x6a, 0x1c, 0xbb, 0x9f, 0x7a}, + }, + { /* 9P */ + addYX: fp.Elt{0x2f, 0x63, 0xa8, 0xa6, 0x8a, 0x67, 0x2e, 0x9b, 0xc5, 0x46, 0xbc, 0x51, 0x6f, 0x9e, 0x50, 0xa6, 0xb5, 0xf5, 0x86, 0xc6, 0xc9, 0x33, 0xb2, 0xce, 0x59, 0x7f, 0xdd, 0x8a, 0x33, 0xed, 0xb9, 0x34}, + subYX: fp.Elt{0x64, 0x80, 0x9d, 0x03, 0x7e, 0x21, 0x6e, 0xf3, 0x9b, 0x41, 0x20, 0xf5, 0xb6, 0x81, 0xa0, 0x98, 0x44, 0xb0, 0x5e, 0xe7, 0x08, 0xc6, 0xcb, 0x96, 0x8f, 0x9c, 0xdc, 0xfa, 0x51, 0x5a, 0xc0, 0x49}, + dt2: fp.Elt{0x1b, 0xaf, 0x45, 0x90, 0xbf, 0xe8, 0xb4, 0x06, 0x2f, 0xd2, 0x19, 0xa7, 0xe8, 0x83, 0xff, 0xe2, 0x16, 0xcf, 0xd4, 0x93, 0x29, 0xfc, 0xf6, 0xaa, 0x06, 0x8b, 0x00, 0x1b, 0x02, 0x72, 0xc1, 0x73}, + }, + { /* 11P */ + addYX: fp.Elt{0xde, 0x2a, 0x80, 0x8a, 0x84, 0x00, 0xbf, 0x2f, 0x27, 0x2e, 0x30, 0x02, 0xcf, 0xfe, 0xd9, 0xe5, 0x06, 0x34, 0x70, 0x17, 0x71, 0x84, 0x3e, 0x11, 0xaf, 0x8f, 0x6d, 0x54, 0xe2, 0xaa, 0x75, 0x42}, + subYX: fp.Elt{0x48, 0x43, 0x86, 0x49, 0x02, 0x5b, 0x5f, 0x31, 0x81, 0x83, 0x08, 0x77, 0x69, 0xb3, 0xd6, 0x3e, 0x95, 0xeb, 0x8d, 0x6a, 0x55, 0x75, 0xa0, 0xa3, 0x7f, 0xc7, 0xd5, 0x29, 0x80, 0x59, 0xab, 0x18}, + dt2: fp.Elt{0xe9, 0x89, 0x60, 0xfd, 0xc5, 0x2c, 0x2b, 0xd8, 0xa4, 0xe4, 0x82, 0x32, 0xa1, 0xb4, 0x1e, 0x03, 0x22, 0x86, 0x1a, 0xb5, 0x99, 0x11, 0x31, 0x44, 0x48, 0xf9, 0x3d, 0xb5, 0x22, 0x55, 0xc6, 0x3d}, + }, + { /* 13P */ + addYX: fp.Elt{0x6d, 0x7f, 0x00, 0xa2, 0x22, 0xc2, 0x70, 0xbf, 0xdb, 0xde, 0xbc, 0xb5, 0x9a, 0xb3, 0x84, 0xbf, 0x07, 0xba, 0x07, 0xfb, 0x12, 0x0e, 0x7a, 0x53, 0x41, 0xf2, 0x46, 0xc3, 0xee, 0xd7, 0x4f, 0x23}, + subYX: fp.Elt{0x93, 0xbf, 0x7f, 0x32, 0x3b, 0x01, 0x6f, 0x50, 0x6b, 0x6f, 0x77, 0x9b, 0xc9, 0xeb, 0xfc, 0xae, 0x68, 0x59, 0xad, 0xaa, 0x32, 0xb2, 0x12, 0x9d, 0xa7, 0x24, 0x60, 0x17, 0x2d, 0x88, 0x67, 0x02}, + dt2: fp.Elt{0x78, 0xa3, 0x2e, 0x73, 0x19, 0xa1, 0x60, 0x53, 0x71, 0xd4, 0x8d, 0xdf, 0xb1, 0xe6, 0x37, 0x24, 0x33, 0xe5, 0xa7, 0x91, 0xf8, 0x37, 0xef, 0xa2, 0x63, 0x78, 0x09, 0xaa, 0xfd, 0xa6, 0x7b, 0x49}, + }, + { /* 15P */ + addYX: fp.Elt{0xa0, 0xea, 0xcf, 0x13, 0x03, 0xcc, 0xce, 0x24, 0x6d, 0x24, 0x9c, 0x18, 0x8d, 0xc2, 0x48, 0x86, 0xd0, 0xd4, 0xf2, 0xc1, 0xfa, 0xbd, 0xbd, 0x2d, 0x2b, 0xe7, 0x2d, 0xf1, 0x17, 0x29, 0xe2, 0x61}, + subYX: fp.Elt{0x0b, 0xcf, 0x8c, 0x46, 0x86, 0xcd, 0x0b, 0x04, 0xd6, 0x10, 0x99, 0x2a, 0xa4, 0x9b, 0x82, 0xd3, 0x92, 0x51, 0xb2, 0x07, 0x08, 0x30, 0x08, 0x75, 0xbf, 0x5e, 0xd0, 0x18, 0x42, 0xcd, 0xb5, 0x43}, + dt2: fp.Elt{0x16, 0xb5, 0xd0, 0x9b, 0x2f, 0x76, 0x9a, 0x5d, 0xee, 0xde, 0x3f, 0x37, 0x4e, 0xaf, 0x38, 0xeb, 0x70, 0x42, 0xd6, 0x93, 0x7d, 0x5a, 0x2e, 0x03, 0x42, 0xd8, 0xe4, 0x0a, 0x21, 0x61, 0x1d, 0x51}, + }, + { /* 17P */ + addYX: fp.Elt{0x81, 0x9d, 0x0e, 0x95, 0xef, 0x76, 0xc6, 0x92, 0x4f, 0x04, 0xd7, 0xc0, 0xcd, 0x20, 0x46, 0xa5, 0x48, 0x12, 0x8f, 0x6f, 0x64, 0x36, 0x9b, 0xaa, 0xe3, 0x55, 0xb8, 0xdd, 0x24, 0x59, 0x32, 0x6d}, + subYX: fp.Elt{0x87, 0xde, 0x20, 0x44, 0x48, 0x86, 0x13, 0x08, 0xb4, 0xed, 0x92, 0xb5, 0x16, 0xf0, 0x1c, 0x8a, 0x25, 0x2d, 0x94, 0x29, 0x27, 0x4e, 0xfa, 0x39, 0x10, 0x28, 0x48, 0xe2, 0x6f, 0xfe, 0xa7, 0x71}, + dt2: fp.Elt{0x54, 0xc8, 0xc8, 0xa5, 0xb8, 0x82, 0x71, 0x6c, 0x03, 0x2a, 0x5f, 0xfe, 0x79, 0x14, 0xfd, 0x33, 0x0c, 0x8d, 0x77, 0x83, 0x18, 0x59, 0xcf, 0x72, 0xa9, 0xea, 0x9e, 0x55, 0xb6, 0xc4, 0x46, 0x47}, + }, + { /* 19P */ + addYX: fp.Elt{0x2b, 0x9a, 0xc6, 0x6d, 0x3c, 0x7b, 0x77, 0xd3, 0x17, 0xf6, 0x89, 0x6f, 0x27, 0xb2, 0xfa, 0xde, 0xb5, 0x16, 0x3a, 0xb5, 0xf7, 0x1c, 0x65, 0x45, 0xb7, 0x9f, 0xfe, 0x34, 0xde, 0x51, 0x9a, 0x5c}, + subYX: fp.Elt{0x47, 0x11, 0x74, 0x64, 0xc8, 0x46, 0x85, 0x34, 0x49, 0xc8, 0xfc, 0x0e, 0xdd, 0xae, 0x35, 0x7d, 0x32, 0xa3, 0x72, 0x06, 0x76, 0x9a, 0x93, 0xff, 0xd6, 0xe6, 0xb5, 0x7d, 0x49, 0x63, 0x96, 0x21}, + dt2: fp.Elt{0x67, 0x0e, 0xf1, 0x79, 0xcf, 0xf1, 0x10, 0xf5, 0x5b, 0x51, 0x58, 0xe6, 0xa1, 0xda, 0xdd, 0xff, 0x77, 0x22, 0x14, 0x10, 0x17, 0xa7, 0xc3, 0x09, 0xbb, 0x23, 0x82, 0x60, 0x3c, 0x50, 0x04, 0x48}, + }, + { /* 21P */ + addYX: fp.Elt{0xc7, 0x7f, 0xa3, 0x2c, 0xd0, 0x9e, 0x24, 0xc4, 0xab, 0xac, 0x15, 0xa6, 0xe3, 0xa0, 0x59, 0xa0, 0x23, 0x0e, 0x6e, 0xc9, 0xd7, 0x6e, 0xa9, 0x88, 0x6d, 0x69, 0x50, 0x16, 0xa5, 0x98, 0x33, 0x55}, + subYX: fp.Elt{0x75, 0xd1, 0x36, 0x3a, 0xd2, 0x21, 0x68, 0x3b, 0x32, 0x9e, 0x9b, 0xe9, 0xa7, 0x0a, 0xb4, 0xbb, 0x47, 0x8a, 0x83, 0x20, 0xe4, 0x5c, 0x9e, 0x5d, 0x5e, 0x4c, 0xde, 0x58, 0x88, 0x09, 0x1e, 0x77}, + dt2: fp.Elt{0xdf, 0x1e, 0x45, 0x78, 0xd2, 0xf5, 0x12, 0x9a, 0xcb, 0x9c, 0x89, 0x85, 0x79, 0x5d, 0xda, 0x3a, 0x08, 0x95, 0xa5, 0x9f, 0x2d, 0x4a, 0x7f, 0x47, 0x11, 0xa6, 0xf5, 0x8f, 0xd6, 0xd1, 0x5e, 0x5a}, + }, + { /* 23P */ + addYX: fp.Elt{0x83, 0x0e, 0x15, 0xfe, 0x2a, 0x12, 0x95, 0x11, 0xd8, 0x35, 0x4b, 0x7e, 0x25, 0x9a, 0x20, 0xcf, 0x20, 0x1e, 0x71, 0x1e, 0x29, 0xf8, 0x87, 0x73, 0xf0, 0x92, 0xbf, 0xd8, 0x97, 0xb8, 0xac, 0x44}, + subYX: fp.Elt{0x59, 0x73, 0x52, 0x58, 0xc5, 0xe0, 0xe5, 0xba, 0x7e, 0x9d, 0xdb, 0xca, 0x19, 0x5c, 0x2e, 0x39, 0xe9, 0xab, 0x1c, 0xda, 0x1e, 0x3c, 0x65, 0x28, 0x44, 0xdc, 0xef, 0x5f, 0x13, 0x60, 0x9b, 0x01}, + dt2: fp.Elt{0x83, 0x4b, 0x13, 0x5e, 0x14, 0x68, 0x60, 0x1e, 0x16, 0x4c, 0x30, 0x24, 0x4f, 0xe6, 0xf5, 0xc4, 0xd7, 0x3e, 0x1a, 0xfc, 0xa8, 0x88, 0x6e, 0x50, 0x92, 0x2f, 0xad, 0xe6, 0xfd, 0x49, 0x0c, 0x15}, + }, + { /* 25P */ + addYX: fp.Elt{0x38, 0x11, 0x47, 0x09, 0x95, 0xf2, 0x7b, 0x8e, 0x51, 0xa6, 0x75, 0x4f, 0x39, 0xef, 0x6f, 0x5d, 0xad, 0x08, 0xa7, 0x25, 0xc4, 0x79, 0xaf, 0x10, 0x22, 0x99, 0xb9, 0x5b, 0x07, 0x5a, 0x2b, 0x6b}, + subYX: fp.Elt{0x68, 0xa8, 0xdc, 0x9c, 0x3c, 0x86, 0x49, 0xb8, 0xd0, 0x4a, 0x71, 0xb8, 0xdb, 0x44, 0x3f, 0xc8, 0x8d, 0x16, 0x36, 0x0c, 0x56, 0xe3, 0x3e, 0xfe, 0xc1, 0xfb, 0x05, 0x1e, 0x79, 0xd7, 0xa6, 0x78}, + dt2: fp.Elt{0x76, 0xb9, 0xa0, 0x47, 0x4b, 0x70, 0xbf, 0x58, 0xd5, 0x48, 0x17, 0x74, 0x55, 0xb3, 0x01, 0xa6, 0x90, 0xf5, 0x42, 0xd5, 0xb1, 0x1f, 0x2b, 0xaa, 0x00, 0x5d, 0xd5, 0x4a, 0xfc, 0x7f, 0x5c, 0x72}, + }, + { /* 27P */ + addYX: fp.Elt{0xb2, 0x99, 0xcf, 0xd1, 0x15, 0x67, 0x42, 0xe4, 0x34, 0x0d, 0xa2, 0x02, 0x11, 0xd5, 0x52, 0x73, 0x9f, 0x10, 0x12, 0x8b, 0x7b, 0x15, 0xd1, 0x23, 0xa3, 0xf3, 0xb1, 0x7c, 0x27, 0xc9, 0x4c, 0x79}, + subYX: fp.Elt{0xc0, 0x98, 0xd0, 0x1c, 0xf7, 0x2b, 0x80, 0x91, 0x66, 0x63, 0x5e, 0xed, 0xa4, 0x6c, 0x41, 0xfe, 0x4c, 0x99, 0x02, 0x49, 0x71, 0x5d, 0x58, 0xdf, 0xe7, 0xfa, 0x55, 0xf8, 0x25, 0x46, 0xd5, 0x4c}, + dt2: fp.Elt{0x53, 0x50, 0xac, 0xc2, 0x26, 0xc4, 0xf6, 0x4a, 0x58, 0x72, 0xf6, 0x32, 0xad, 0xed, 0x9a, 0xbc, 0x21, 0x10, 0x31, 0x0a, 0xf1, 0x32, 0xd0, 0x2a, 0x85, 0x8e, 0xcc, 0x6f, 0x7b, 0x35, 0x08, 0x70}, + }, + { /* 29P */ + addYX: fp.Elt{0x01, 0x3f, 0x77, 0x38, 0x27, 0x67, 0x88, 0x0b, 0xfb, 0xcc, 0xfb, 0x95, 0xfa, 0xc8, 0xcc, 0xb8, 0xb6, 0x29, 0xad, 0xb9, 0xa3, 0xd5, 0x2d, 0x8d, 0x6a, 0x0f, 0xad, 0x51, 0x98, 0x7e, 0xef, 0x06}, + subYX: fp.Elt{0x34, 0x4a, 0x58, 0x82, 0xbb, 0x9f, 0x1b, 0xd0, 0x2b, 0x79, 0xb4, 0xd2, 0x63, 0x64, 0xab, 0x47, 0x02, 0x62, 0x53, 0x48, 0x9c, 0x63, 0x31, 0xb6, 0x28, 0xd4, 0xd6, 0x69, 0x36, 0x2a, 0xa9, 0x13}, + dt2: fp.Elt{0xe5, 0x7d, 0x57, 0xc0, 0x1c, 0x77, 0x93, 0xca, 0x5c, 0xdc, 0x35, 0x50, 0x1e, 0xe4, 0x40, 0x75, 0x71, 0xe0, 0x02, 0xd8, 0x01, 0x0f, 0x68, 0x24, 0x6a, 0xf8, 0x2a, 0x8a, 0xdf, 0x6d, 0x29, 0x3c}, + }, + { /* 31P */ + addYX: fp.Elt{0x13, 0xa7, 0x14, 0xd9, 0xf9, 0x15, 0xad, 0xae, 0x12, 0xf9, 0x8f, 0x8c, 0xf9, 0x7b, 0x2f, 0xa9, 0x30, 0xd7, 0x53, 0x9f, 0x17, 0x23, 0xf8, 0xaf, 0xba, 0x77, 0x0c, 0x49, 0x93, 0xd3, 0x99, 0x7a}, + subYX: fp.Elt{0x41, 0x25, 0x1f, 0xbb, 0x2e, 0x4d, 0xeb, 0xfc, 0x1f, 0xb9, 0xad, 0x40, 0xc7, 0x10, 0x95, 0xb8, 0x05, 0xad, 0xa1, 0xd0, 0x7d, 0xa3, 0x71, 0xfc, 0x7b, 0x71, 0x47, 0x07, 0x70, 0x2c, 0x89, 0x0a}, + dt2: fp.Elt{0xe8, 0xa3, 0xbd, 0x36, 0x24, 0xed, 0x52, 0x8f, 0x94, 0x07, 0xe8, 0x57, 0x41, 0xc8, 0xa8, 0x77, 0xe0, 0x9c, 0x2f, 0x26, 0x63, 0x65, 0xa9, 0xa5, 0xd2, 0xf7, 0x02, 0x83, 0xd2, 0x62, 0x67, 0x28}, + }, + { /* 33P */ + addYX: fp.Elt{0x25, 0x5b, 0xe3, 0x3c, 0x09, 0x36, 0x78, 0x4e, 0x97, 0xaa, 0x6b, 0xb2, 0x1d, 0x18, 0xe1, 0x82, 0x3f, 0xb8, 0xc7, 0xcb, 0xd3, 0x92, 0xc1, 0x0c, 0x3a, 0x9d, 0x9d, 0x6a, 0x04, 0xda, 0xf1, 0x32}, + subYX: fp.Elt{0xbd, 0xf5, 0x2e, 0xce, 0x2b, 0x8e, 0x55, 0x7c, 0x63, 0xbc, 0x47, 0x67, 0xb4, 0x6c, 0x98, 0xe4, 0xb8, 0x89, 0xbb, 0x3b, 0x9f, 0x17, 0x4a, 0x15, 0x7a, 0x76, 0xf1, 0xd6, 0xa3, 0xf2, 0x86, 0x76}, + dt2: fp.Elt{0x6a, 0x7c, 0x59, 0x6d, 0xa6, 0x12, 0x8d, 0xaa, 0x2b, 0x85, 0xd3, 0x04, 0x03, 0x93, 0x11, 0x8f, 0x22, 0xb0, 0x09, 0xc2, 0x73, 0xdc, 0x91, 0x3f, 0xa6, 0x28, 0xad, 0xa9, 0xf8, 0x05, 0x13, 0x56}, + }, + { /* 35P */ + addYX: fp.Elt{0xd1, 0xae, 0x92, 0xec, 0x8d, 0x97, 0x0c, 0x10, 0xe5, 0x73, 0x6d, 0x4d, 0x43, 0xd5, 0x43, 0xca, 0x48, 0xba, 0x47, 0xd8, 0x22, 0x1b, 0x13, 0x83, 0x2c, 0x4d, 0x5d, 0xe3, 0x53, 0xec, 0xaa}, + subYX: fp.Elt{0xd5, 0xc0, 0xb0, 0xe7, 0x28, 0xcc, 0x22, 0x67, 0x53, 0x5c, 0x07, 0xdb, 0xbb, 0xe9, 0x9d, 0x70, 0x61, 0x0a, 0x01, 0xd7, 0xa7, 0x8d, 0xf6, 0xca, 0x6c, 0xcc, 0x57, 0x2c, 0xef, 0x1a, 0x0a, 0x03}, + dt2: fp.Elt{0xaa, 0xd2, 0x3a, 0x00, 0x73, 0xf7, 0xb1, 0x7b, 0x08, 0x66, 0x21, 0x2b, 0x80, 0x29, 0x3f, 0x0b, 0x3e, 0xd2, 0x0e, 0x52, 0x86, 0xdc, 0x21, 0x78, 0x80, 0x54, 0x06, 0x24, 0x1c, 0x9c, 0xbe, 0x20}, + }, + { /* 37P */ + addYX: fp.Elt{0xa6, 0x73, 0x96, 0x24, 0xd8, 0x87, 0x53, 0xe1, 0x93, 0xe4, 0x46, 0xf5, 0x2d, 0xbc, 0x43, 0x59, 0xb5, 0x63, 0x6f, 0xc3, 0x81, 0x9a, 0x7f, 0x1c, 0xde, 0xc1, 0x0a, 0x1f, 0x36, 0xb3, 0x0a, 0x75}, + subYX: fp.Elt{0x60, 0x5e, 0x02, 0xe2, 0x4a, 0xe4, 0xe0, 0x20, 0x38, 0xb9, 0xdc, 0xcb, 0x2f, 0x3b, 0x3b, 0xb0, 0x1c, 0x0d, 0x5a, 0xf9, 0x9c, 0x63, 0x5d, 0x10, 0x11, 0xe3, 0x67, 0x50, 0x54, 0x4c, 0x76, 0x69}, + dt2: fp.Elt{0x37, 0x10, 0xf8, 0xa2, 0x83, 0x32, 0x8a, 0x1e, 0xf1, 0xcb, 0x7f, 0xbd, 0x23, 0xda, 0x2e, 0x6f, 0x63, 0x25, 0x2e, 0xac, 0x5b, 0xd1, 0x2f, 0xb7, 0x40, 0x50, 0x07, 0xb7, 0x3f, 0x6b, 0xf9, 0x54}, + }, + { /* 39P */ + addYX: fp.Elt{0x79, 0x92, 0x66, 0x29, 0x04, 0xf2, 0xad, 0x0f, 0x4a, 0x72, 0x7d, 0x7d, 0x04, 0xa2, 0xdd, 0x3a, 0xf1, 0x60, 0x57, 0x8c, 0x82, 0x94, 0x3d, 0x6f, 0x9e, 0x53, 0xb7, 0x2b, 0xc5, 0xe9, 0x7f, 0x3d}, + subYX: fp.Elt{0xcd, 0x1e, 0xb1, 0x16, 0xc6, 0xaf, 0x7d, 0x17, 0x79, 0x64, 0x57, 0xfa, 0x9c, 0x4b, 0x76, 0x89, 0x85, 0xe7, 0xec, 0xe6, 0x10, 0xa1, 0xa8, 0xb7, 0xf0, 0xdb, 0x85, 0xbe, 0x9f, 0x83, 0xe6, 0x78}, + dt2: fp.Elt{0x6b, 0x85, 0xb8, 0x37, 0xf7, 0x2d, 0x33, 0x70, 0x8a, 0x17, 0x1a, 0x04, 0x43, 0x5d, 0xd0, 0x75, 0x22, 0x9e, 0xe5, 0xa0, 0x4a, 0xf7, 0x0f, 0x32, 0x42, 0x82, 0x08, 0x50, 0xf3, 0x68, 0xf2, 0x70}, + }, + { /* 41P */ + addYX: fp.Elt{0x47, 0x5f, 0x80, 0xb1, 0x83, 0x45, 0x86, 0x66, 0x19, 0x7c, 0xdd, 0x60, 0xd1, 0xc5, 0x35, 0xf5, 0x06, 0xb0, 0x4c, 0x1e, 0xb7, 0x4e, 0x87, 0xe9, 0xd9, 0x89, 0xd8, 0xfa, 0x5c, 0x34, 0x0d, 0x7c}, + subYX: fp.Elt{0x55, 0xf3, 0xdc, 0x70, 0x20, 0x11, 0x24, 0x23, 0x17, 0xe1, 0xfc, 0xe7, 0x7e, 0xc9, 0x0c, 0x38, 0x98, 0xb6, 0x52, 0x35, 0xed, 0xde, 0x1d, 0xb3, 0xb9, 0xc4, 0xb8, 0x39, 0xc0, 0x56, 0x4e, 0x40}, + dt2: fp.Elt{0x8a, 0x33, 0x78, 0x8c, 0x4b, 0x1f, 0x1f, 0x59, 0xe1, 0xb5, 0xe0, 0x67, 0xb1, 0x6a, 0x36, 0xa0, 0x44, 0x3d, 0x5f, 0xb4, 0x52, 0x41, 0xbc, 0x5c, 0x77, 0xc7, 0xae, 0x2a, 0x76, 0x54, 0xd7, 0x20}, + }, + { /* 43P */ + addYX: fp.Elt{0x58, 0xb7, 0x3b, 0xc7, 0x6f, 0xc3, 0x8f, 0x5e, 0x9a, 0xbb, 0x3c, 0x36, 0xa5, 0x43, 0xe5, 0xac, 0x22, 0xc9, 0x3b, 0x90, 0x7d, 0x4a, 0x93, 0xa9, 0x62, 0xec, 0xce, 0xf3, 0x46, 0x1e, 0x8f, 0x2b}, + subYX: fp.Elt{0x43, 0xf5, 0xb9, 0x35, 0xb1, 0xfe, 0x74, 0x9d, 0x6c, 0x95, 0x8c, 0xde, 0xf1, 0x7d, 0xb3, 0x84, 0xa9, 0x8b, 0x13, 0x57, 0x07, 0x2b, 0x32, 0xe9, 0xe1, 0x4c, 0x0b, 0x79, 0xa8, 0xad, 0xb8, 0x38}, + dt2: fp.Elt{0x5d, 0xf9, 0x51, 0xdf, 0x9c, 0x4a, 0xc0, 0xb5, 0xac, 0xde, 0x1f, 0xcb, 0xae, 0x52, 0x39, 0x2b, 0xda, 0x66, 0x8b, 0x32, 0x8b, 0x6d, 0x10, 0x1d, 0x53, 0x19, 0xba, 0xce, 0x32, 0xeb, 0x9a, 0x04}, + }, + { /* 45P */ + addYX: fp.Elt{0x31, 0x79, 0xfc, 0x75, 0x0b, 0x7d, 0x50, 0xaa, 0xd3, 0x25, 0x67, 0x7a, 0x4b, 0x92, 0xef, 0x0f, 0x30, 0x39, 0x6b, 0x39, 0x2b, 0x54, 0x82, 0x1d, 0xfc, 0x74, 0xf6, 0x30, 0x75, 0xe1, 0x5e, 0x79}, + subYX: fp.Elt{0x7e, 0xfe, 0xdc, 0x63, 0x3c, 0x7d, 0x76, 0xd7, 0x40, 0x6e, 0x85, 0x97, 0x48, 0x59, 0x9c, 0x20, 0x13, 0x7c, 0x4f, 0xe1, 0x61, 0x68, 0x67, 0xb6, 0xfc, 0x25, 0xd6, 0xc8, 0xe0, 0x65, 0xc6, 0x51}, + dt2: fp.Elt{0x81, 0xbd, 0xec, 0x52, 0x0a, 0x5b, 0x4a, 0x25, 0xe7, 0xaf, 0x34, 0xe0, 0x6e, 0x1f, 0x41, 0x5d, 0x31, 0x4a, 0xee, 0xca, 0x0d, 0x4d, 0xa2, 0xe6, 0x77, 0x44, 0xc5, 0x9d, 0xf4, 0x9b, 0xd1, 0x6c}, + }, + { /* 47P */ + addYX: fp.Elt{0x86, 0xc3, 0xaf, 0x65, 0x21, 0x61, 0xfe, 0x1f, 0x10, 0x1b, 0xd5, 0xb8, 0x88, 0x2a, 0x2a, 0x08, 0xaa, 0x0b, 0x99, 0x20, 0x7e, 0x62, 0xf6, 0x76, 0xe7, 0x43, 0x9e, 0x42, 0xa7, 0xb3, 0x01, 0x5e}, + subYX: fp.Elt{0xa3, 0x9c, 0x17, 0x52, 0x90, 0x61, 0x87, 0x7e, 0x85, 0x9f, 0x2c, 0x0b, 0x06, 0x0a, 0x1d, 0x57, 0x1e, 0x71, 0x99, 0x84, 0xa8, 0xba, 0xa2, 0x80, 0x38, 0xe6, 0xb2, 0x40, 0xdb, 0xf3, 0x20, 0x75}, + dt2: fp.Elt{0xa1, 0x57, 0x93, 0xd3, 0xe3, 0x0b, 0xb5, 0x3d, 0xa5, 0x94, 0x9e, 0x59, 0xdd, 0x6c, 0x7b, 0x96, 0x6e, 0x1e, 0x31, 0xdf, 0x64, 0x9a, 0x30, 0x1a, 0x86, 0xc9, 0xf3, 0xce, 0x9c, 0x2c, 0x09, 0x71}, + }, + { /* 49P */ + addYX: fp.Elt{0xcf, 0x1d, 0x05, 0x74, 0xac, 0xd8, 0x6b, 0x85, 0x1e, 0xaa, 0xb7, 0x55, 0x08, 0xa4, 0xf6, 0x03, 0xeb, 0x3c, 0x74, 0xc9, 0xcb, 0xe7, 0x4a, 0x3a, 0xde, 0xab, 0x37, 0x71, 0xbb, 0xa5, 0x73, 0x41}, + subYX: fp.Elt{0x8c, 0x91, 0x64, 0x03, 0x3f, 0x52, 0xd8, 0x53, 0x1c, 0x6b, 0xab, 0x3f, 0xf4, 0x04, 0xb4, 0xa2, 0xa4, 0xe5, 0x81, 0x66, 0x9e, 0x4a, 0x0b, 0x08, 0xa7, 0x7b, 0x25, 0xd0, 0x03, 0x5b, 0xa1, 0x0e}, + dt2: fp.Elt{0x8a, 0x21, 0xf9, 0xf0, 0x31, 0x6e, 0xc5, 0x17, 0x08, 0x47, 0xfc, 0x1a, 0x2b, 0x6e, 0x69, 0x5a, 0x76, 0xf1, 0xb2, 0xf4, 0x68, 0x16, 0x93, 0xf7, 0x67, 0x3a, 0x4e, 0x4a, 0x61, 0x65, 0xc5, 0x5f}, + }, + { /* 51P */ + addYX: fp.Elt{0x8e, 0x98, 0x90, 0x77, 0xe6, 0xe1, 0x92, 0x48, 0x22, 0xd7, 0x5c, 0x1c, 0x0f, 0x95, 0xd5, 0x01, 0xed, 0x3e, 0x92, 0xe5, 0x9a, 0x81, 0xb0, 0xe3, 0x1b, 0x65, 0x46, 0x9d, 0x40, 0xc7, 0x14, 0x32}, + subYX: fp.Elt{0xe5, 0x7a, 0x6d, 0xc4, 0x0d, 0x57, 0x6e, 0x13, 0x8f, 0xdc, 0xf8, 0x54, 0xcc, 0xaa, 0xd0, 0x0f, 0x86, 0xad, 0x0d, 0x31, 0x03, 0x9f, 0x54, 0x59, 0xa1, 0x4a, 0x45, 0x4c, 0x41, 0x1c, 0x71, 0x62}, + dt2: fp.Elt{0x70, 0x17, 0x65, 0x06, 0x74, 0x82, 0x29, 0x13, 0x36, 0x94, 0x27, 0x8a, 0x66, 0xa0, 0xa4, 0x3b, 0x3c, 0x22, 0x5d, 0x18, 0xec, 0xb8, 0xb6, 0xd9, 0x3c, 0x83, 0xcb, 0x3e, 0x07, 0x94, 0xea, 0x5b}, + }, + { /* 53P */ + addYX: fp.Elt{0xf8, 0xd2, 0x43, 0xf3, 0x63, 0xce, 0x70, 0xb4, 0xf1, 0xe8, 0x43, 0x05, 0x8f, 0xba, 0x67, 0x00, 0x6f, 0x7b, 0x11, 0xa2, 0xa1, 0x51, 0xda, 0x35, 0x2f, 0xbd, 0xf1, 0x44, 0x59, 0x78, 0xd0, 0x4a}, + subYX: fp.Elt{0xe4, 0x9b, 0xc8, 0x12, 0x09, 0xbf, 0x1d, 0x64, 0x9c, 0x57, 0x6e, 0x7d, 0x31, 0x8b, 0xf3, 0xac, 0x65, 0xb0, 0x97, 0xf6, 0x02, 0x9e, 0xfe, 0xab, 0xec, 0x1e, 0xf6, 0x48, 0xc1, 0xd5, 0xac, 0x3a}, + dt2: fp.Elt{0x01, 0x83, 0x31, 0xc3, 0x34, 0x3b, 0x8e, 0x85, 0x26, 0x68, 0x31, 0x07, 0x47, 0xc0, 0x99, 0xdc, 0x8c, 0xa8, 0x9d, 0xd3, 0x2e, 0x5b, 0x08, 0x34, 0x3d, 0x85, 0x02, 0xd9, 0xb1, 0x0c, 0xff, 0x3a}, + }, + { /* 55P */ + addYX: fp.Elt{0x05, 0x35, 0xc5, 0xf4, 0x0b, 0x43, 0x26, 0x92, 0x83, 0x22, 0x1f, 0x26, 0x13, 0x9c, 0xe4, 0x68, 0xc6, 0x27, 0xd3, 0x8f, 0x78, 0x33, 0xef, 0x09, 0x7f, 0x9e, 0xd9, 0x2b, 0x73, 0x9f, 0xcf, 0x2c}, + subYX: fp.Elt{0x5e, 0x40, 0x20, 0x3a, 0xeb, 0xc7, 0xc5, 0x87, 0xc9, 0x56, 0xad, 0xed, 0xef, 0x11, 0xe3, 0x8e, 0xf9, 0xd5, 0x29, 0xad, 0x48, 0x2e, 0x25, 0x29, 0x1d, 0x25, 0xcd, 0xf4, 0x86, 0x7e, 0x0e, 0x11}, + dt2: fp.Elt{0xe4, 0xf5, 0x03, 0xd6, 0x9e, 0xd8, 0xc0, 0x57, 0x0c, 0x20, 0xb0, 0xf0, 0x28, 0x86, 0x88, 0x12, 0xb7, 0x3b, 0x2e, 0xa0, 0x09, 0x27, 0x17, 0x53, 0x37, 0x3a, 0x69, 0xb9, 0xe0, 0x57, 0xc5, 0x05}, + }, + { /* 57P */ + addYX: fp.Elt{0xb0, 0x0e, 0xc2, 0x89, 0xb0, 0xbb, 0x76, 0xf7, 0x5c, 0xd8, 0x0f, 0xfa, 0xf6, 0x5b, 0xf8, 0x61, 0xfb, 0x21, 0x44, 0x63, 0x4e, 0x3f, 0xb9, 0xb6, 0x05, 0x12, 0x86, 0x41, 0x08, 0xef, 0x9f, 0x28}, + subYX: fp.Elt{0x6f, 0x7e, 0xc9, 0x1f, 0x31, 0xce, 0xf9, 0xd8, 0xae, 0xfd, 0xf9, 0x11, 0x30, 0x26, 0x3f, 0x7a, 0xdd, 0x25, 0xed, 0x8b, 0xa0, 0x7e, 0x5b, 0xe1, 0x5a, 0x87, 0xe9, 0x8f, 0x17, 0x4c, 0x15, 0x6e}, + dt2: fp.Elt{0xbf, 0x9a, 0xd6, 0xfe, 0x36, 0x63, 0x61, 0xcf, 0x4f, 0xc9, 0x35, 0x83, 0xe7, 0xe4, 0x16, 0x9b, 0xe7, 0x7f, 0x3a, 0x75, 0x65, 0x97, 0x78, 0x13, 0x19, 0xa3, 0x5c, 0xa9, 0x42, 0xf6, 0xfb, 0x6a}, + }, + { /* 59P */ + addYX: fp.Elt{0xcc, 0xa8, 0x13, 0xf9, 0x70, 0x50, 0xe5, 0x5d, 0x61, 0xf5, 0x0c, 0x2b, 0x7b, 0x16, 0x1d, 0x7d, 0x89, 0xd4, 0xea, 0x90, 0xb6, 0x56, 0x29, 0xda, 0xd9, 0x1e, 0x80, 0xdb, 0xce, 0x93, 0xc0, 0x12}, + subYX: fp.Elt{0xc1, 0xd2, 0xf5, 0x62, 0x0c, 0xde, 0xa8, 0x7d, 0x9a, 0x7b, 0x0e, 0xb0, 0xa4, 0x3d, 0xfc, 0x98, 0xe0, 0x70, 0xad, 0x0d, 0xda, 0x6a, 0xeb, 0x7d, 0xc4, 0x38, 0x50, 0xb9, 0x51, 0xb8, 0xb4, 0x0d}, + dt2: fp.Elt{0x0f, 0x19, 0xb8, 0x08, 0x93, 0x7f, 0x14, 0xfc, 0x10, 0xe3, 0x1a, 0xa1, 0xa0, 0x9d, 0x96, 0x06, 0xfd, 0xd7, 0xc7, 0xda, 0x72, 0x55, 0xe7, 0xce, 0xe6, 0x5c, 0x63, 0xc6, 0x99, 0x87, 0xaa, 0x33}, + }, + { /* 61P */ + addYX: fp.Elt{0xb1, 0x6c, 0x15, 0xfc, 0x88, 0xf5, 0x48, 0x83, 0x27, 0x6d, 0x0a, 0x1a, 0x9b, 0xba, 0xa2, 0x6d, 0xb6, 0x5a, 0xca, 0x87, 0x5c, 0x2d, 0x26, 0xe2, 0xa6, 0x89, 0xd5, 0xc8, 0xc1, 0xd0, 0x2c, 0x21}, + subYX: fp.Elt{0xf2, 0x5c, 0x08, 0xbd, 0x1e, 0xf5, 0x0f, 0xaf, 0x1f, 0x3f, 0xd3, 0x67, 0x89, 0x1a, 0xf5, 0x78, 0x3c, 0x03, 0x60, 0x50, 0xe1, 0xbf, 0xc2, 0x6e, 0x86, 0x1a, 0xe2, 0xe8, 0x29, 0x6f, 0x3c, 0x23}, + dt2: fp.Elt{0x81, 0xc7, 0x18, 0x7f, 0x10, 0xd5, 0xf4, 0xd2, 0x28, 0x9d, 0x7e, 0x52, 0xf2, 0xcd, 0x2e, 0x12, 0x41, 0x33, 0x3d, 0x3d, 0x2a, 0x86, 0x0a, 0xa7, 0xe3, 0x4c, 0x91, 0x11, 0x89, 0x77, 0xb7, 0x1d}, + }, + { /* 63P */ + addYX: fp.Elt{0xb6, 0x1a, 0x70, 0xdd, 0x69, 0x47, 0x39, 0xb3, 0xa5, 0x8d, 0xcf, 0x19, 0xd4, 0xde, 0xb8, 0xe2, 0x52, 0xc8, 0x2a, 0xfd, 0x61, 0x41, 0xdf, 0x15, 0xbe, 0x24, 0x7d, 0x01, 0x8a, 0xca, 0xe2, 0x7a}, + subYX: fp.Elt{0x6f, 0xc2, 0x6b, 0x7c, 0x39, 0x52, 0xf3, 0xdd, 0x13, 0x01, 0xd5, 0x53, 0xcc, 0xe2, 0x97, 0x7a, 0x30, 0xa3, 0x79, 0xbf, 0x3a, 0xf4, 0x74, 0x7c, 0xfc, 0xad, 0xe2, 0x26, 0xad, 0x97, 0xad, 0x31}, + dt2: fp.Elt{0x62, 0xb9, 0x20, 0x09, 0xed, 0x17, 0xe8, 0xb7, 0x9d, 0xda, 0x19, 0x3f, 0xcc, 0x18, 0x85, 0x1e, 0x64, 0x0a, 0x56, 0x25, 0x4f, 0xc1, 0x91, 0xe4, 0x83, 0x2c, 0x62, 0xa6, 0x53, 0xfc, 0xd1, 0x1e}, + }, +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed448/ed448.go b/vendor/github.com/cloudflare/circl/sign/ed448/ed448.go new file mode 100644 index 00000000..324bd8f3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed448/ed448.go @@ -0,0 +1,411 @@ +// Package ed448 implements Ed448 signature scheme as described in RFC-8032. +// +// This package implements two signature variants. +// +// | Scheme Name | Sign Function | Verification | Context | +// |-------------|-------------------|---------------|-------------------| +// | Ed448 | Sign | Verify | Yes, can be empty | +// | Ed448Ph | SignPh | VerifyPh | Yes, can be empty | +// | All above | (PrivateKey).Sign | VerifyAny | As above | +// +// Specific functions for sign and verify are defined. A generic signing +// function for all schemes is available through the crypto.Signer interface, +// which is implemented by the PrivateKey type. A correspond all-in-one +// verification method is provided by the VerifyAny function. +// +// Both schemes require a context string for domain separation. This parameter +// is passed using a SignerOptions struct defined in this package. +// +// References: +// +// - RFC8032: https://rfc-editor.org/rfc/rfc8032.txt +// - EdDSA for more curves: https://eprint.iacr.org/2015/677 +// - High-speed high-security signatures: https://doi.org/10.1007/s13389-012-0027-1 +package ed448 + +import ( + "bytes" + "crypto" + cryptoRand "crypto/rand" + "crypto/subtle" + "errors" + "fmt" + "io" + "strconv" + + "github.com/cloudflare/circl/ecc/goldilocks" + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/sign" +) + +const ( + // ContextMaxSize is the maximum length (in bytes) allowed for context. + ContextMaxSize = 255 + // PublicKeySize is the length in bytes of Ed448 public keys. + PublicKeySize = 57 + // PrivateKeySize is the length in bytes of Ed448 private keys. + PrivateKeySize = 114 + // SignatureSize is the length in bytes of signatures. + SignatureSize = 114 + // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. + SeedSize = 57 +) + +const ( + paramB = 456 / 8 // Size of keys in bytes. + hashSize = 2 * paramB // Size of the hash function's output. +) + +// SignerOptions implements crypto.SignerOpts and augments with parameters +// that are specific to the Ed448 signature schemes. +type SignerOptions struct { + // Hash must be crypto.Hash(0) for both Ed448 and Ed448Ph. + crypto.Hash + + // Context is an optional domain separation string for signing. + // Its length must be less or equal than 255 bytes. + Context string + + // Scheme is an identifier for choosing a signature scheme. + Scheme SchemeID +} + +// SchemeID is an identifier for each signature scheme. +type SchemeID uint + +const ( + ED448 SchemeID = iota + ED448Ph +) + +// PublicKey is the type of Ed448 public keys. +type PublicKey []byte + +// Equal reports whether pub and x have the same value. +func (pub PublicKey) Equal(x crypto.PublicKey) bool { + xx, ok := x.(PublicKey) + return ok && bytes.Equal(pub, xx) +} + +// PrivateKey is the type of Ed448 private keys. It implements crypto.Signer. +type PrivateKey []byte + +// Equal reports whether priv and x have the same value. +func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { + xx, ok := x.(PrivateKey) + return ok && subtle.ConstantTimeCompare(priv, xx) == 1 +} + +// Public returns the PublicKey corresponding to priv. +func (priv PrivateKey) Public() crypto.PublicKey { + publicKey := make([]byte, PublicKeySize) + copy(publicKey, priv[SeedSize:]) + return PublicKey(publicKey) +} + +// Seed returns the private key seed corresponding to priv. It is provided for +// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds +// in this package. +func (priv PrivateKey) Seed() []byte { + seed := make([]byte, SeedSize) + copy(seed, priv[:SeedSize]) + return seed +} + +func (priv PrivateKey) Scheme() sign.Scheme { return sch } + +func (pub PublicKey) Scheme() sign.Scheme { return sch } + +func (priv PrivateKey) MarshalBinary() (data []byte, err error) { + privateKey := make(PrivateKey, PrivateKeySize) + copy(privateKey, priv) + return privateKey, nil +} + +func (pub PublicKey) MarshalBinary() (data []byte, err error) { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, pub) + return publicKey, nil +} + +// Sign creates a signature of a message given a key pair. +// This function supports all the two signature variants defined in RFC-8032, +// namely Ed448 (or pure EdDSA) and Ed448Ph. +// The opts.HashFunc() must return zero to the specify Ed448 variant. This can +// be achieved by passing crypto.Hash(0) as the value for opts. +// Use an Options struct to pass a bool indicating that the ed448Ph variant +// should be used. +// The struct can also be optionally used to pass a context string for signing. +func (priv PrivateKey) Sign( + rand io.Reader, + message []byte, + opts crypto.SignerOpts, +) (signature []byte, err error) { + var ctx string + var scheme SchemeID + + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): + return Sign(priv, message, ctx), nil + case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): + return SignPh(priv, message, ctx), nil + default: + return nil, errors.New("ed448: bad hash algorithm") + } +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { + if rand == nil { + rand = cryptoRand.Reader + } + + seed := make(PrivateKey, SeedSize) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + + privateKey := NewKeyFromSeed(seed) + publicKey := make([]byte, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + + return publicKey, privateKey, nil +} + +// NewKeyFromSeed calculates a private key from a seed. It will panic if +// len(seed) is not SeedSize. This function is provided for interoperability +// with RFC 8032. RFC 8032's private keys correspond to seeds in this +// package. +func NewKeyFromSeed(seed []byte) PrivateKey { + privateKey := make([]byte, PrivateKeySize) + newKeyFromSeed(privateKey, seed) + return privateKey +} + +func newKeyFromSeed(privateKey, seed []byte) { + if l := len(seed); l != SeedSize { + panic("ed448: bad seed length: " + strconv.Itoa(l)) + } + + var h [hashSize]byte + H := sha3.NewShake256() + _, _ = H.Write(seed) + _, _ = H.Read(h[:]) + s := &goldilocks.Scalar{} + deriveSecretScalar(s, h[:paramB]) + + copy(privateKey[:SeedSize], seed) + _ = goldilocks.Curve{}.ScalarBaseMult(s).ToBytes(privateKey[SeedSize:]) +} + +func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { + if len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed448: bad context length: " + strconv.Itoa(len(ctx)))) + } + + H := sha3.NewShake256() + var PHM []byte + + if preHash { + var h [64]byte + _, _ = H.Write(message) + _, _ = H.Read(h[:]) + PHM = h[:] + H.Reset() + } else { + PHM = message + } + + // 1. Hash the 57-byte private key using SHAKE256(x, 114). + var h [hashSize]byte + _, _ = H.Write(privateKey[:SeedSize]) + _, _ = H.Read(h[:]) + s := &goldilocks.Scalar{} + deriveSecretScalar(s, h[:paramB]) + prefix := h[paramB:] + + // 2. Compute SHAKE256(dom4(F, C) || prefix || PH(M), 114). + var rPM [hashSize]byte + H.Reset() + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(prefix) + _, _ = H.Write(PHM) + _, _ = H.Read(rPM[:]) + + // 3. Compute the point [r]B. + r := &goldilocks.Scalar{} + r.FromBytes(rPM[:]) + R := (&[paramB]byte{})[:] + if err := (goldilocks.Curve{}.ScalarBaseMult(r).ToBytes(R)); err != nil { + panic(err) + } + // 4. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114) + var hRAM [hashSize]byte + H.Reset() + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(privateKey[SeedSize:]) + _, _ = H.Write(PHM) + _, _ = H.Read(hRAM[:]) + + // 5. Compute S = (r + k * s) mod order. + k := &goldilocks.Scalar{} + k.FromBytes(hRAM[:]) + S := &goldilocks.Scalar{} + S.Mul(k, s) + S.Add(S, r) + + // 6. The signature is the concatenation of R and S. + copy(signature[:paramB], R[:]) + copy(signature[paramB:], S[:]) +} + +// Sign signs the message with privateKey and returns a signature. +// This function supports the signature variant defined in RFC-8032: Ed448, +// also known as the pure version of EdDSA. +// It will panic if len(privateKey) is not PrivateKeySize. +func Sign(priv PrivateKey, message []byte, ctx string) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, priv, message, []byte(ctx), false) + return signature +} + +// SignPh creates a signature of a message given a keypair. +// This function supports the signature variant defined in RFC-8032: Ed448ph, +// meaning it internally hashes the message using SHAKE-256. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func SignPh(priv PrivateKey, message []byte, ctx string) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, priv, message, []byte(ctx), true) + return signature +} + +func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { + if len(public) != PublicKeySize || + len(signature) != SignatureSize || + len(ctx) > ContextMaxSize || + !isLessThanOrder(signature[paramB:]) { + return false + } + + P, err := goldilocks.FromBytes(public) + if err != nil { + return false + } + + H := sha3.NewShake256() + var PHM []byte + + if preHash { + var h [64]byte + _, _ = H.Write(message) + _, _ = H.Read(h[:]) + PHM = h[:] + H.Reset() + } else { + PHM = message + } + + var hRAM [hashSize]byte + R := signature[:paramB] + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(public) + _, _ = H.Write(PHM) + _, _ = H.Read(hRAM[:]) + + k := &goldilocks.Scalar{} + k.FromBytes(hRAM[:]) + S := &goldilocks.Scalar{} + S.FromBytes(signature[paramB:]) + + encR := (&[paramB]byte{})[:] + P.Neg() + _ = goldilocks.Curve{}.CombinedMult(S, k, P).ToBytes(encR) + return bytes.Equal(R, encR) +} + +// VerifyAny returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports all the two signature variants defined in RFC-8032, +// namely Ed448 (or pure EdDSA) and Ed448Ph. +// The opts.HashFunc() must return zero, this can be achieved by passing +// crypto.Hash(0) as the value for opts. +// Use a SignerOptions struct to pass a context string for signing. +func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): + return Verify(public, message, signature, ctx) + case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): + return VerifyPh(public, message, signature, ctx) + default: + return false + } +} + +// Verify returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed448, +// also known as the pure version of EdDSA. +func Verify(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), false) +} + +// VerifyPh returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed448ph, +// meaning it internally hashes the message using SHAKE-256. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), true) +} + +func deriveSecretScalar(s *goldilocks.Scalar, h []byte) { + h[0] &= 0xFC // The two least significant bits of the first octet are cleared, + h[paramB-1] = 0x00 // all eight bits the last octet are cleared, and + h[paramB-2] |= 0x80 // the highest bit of the second to last octet is set. + s.FromBytes(h[:paramB]) +} + +// isLessThanOrder returns true if 0 <= x < order and if the last byte of x is zero. +func isLessThanOrder(x []byte) bool { + order := goldilocks.Curve{}.Order() + i := len(order) - 1 + for i > 0 && x[i] == order[i] { + i-- + } + return x[paramB-1] == 0 && x[i] < order[i] +} + +func writeDom(h io.Writer, ctx []byte, preHash bool) { + dom4 := "SigEd448" + _, _ = h.Write([]byte(dom4)) + + if preHash { + _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) + } else { + _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) + } + _, _ = h.Write(ctx) +} diff --git a/vendor/github.com/cloudflare/circl/sign/ed448/signapi.go b/vendor/github.com/cloudflare/circl/sign/ed448/signapi.go new file mode 100644 index 00000000..22da8bc0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/ed448/signapi.go @@ -0,0 +1,87 @@ +package ed448 + +import ( + "crypto/rand" + "encoding/asn1" + + "github.com/cloudflare/circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed448" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0x0808 } +func (*scheme) SupportsContext() bool { return true } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 101, 113} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + ctx := "" + if opts != nil { + ctx = opts.Context + } + return Sign(priv, message, ctx) +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + ctx := "" + if opts != nil { + ctx = opts.Context + } + return Verify(pub, message, signature, ctx) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + return publicKey, privateKey +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) < PublicKeySize { + return nil, sign.ErrPubKeySize + } + pub := make(PublicKey, PublicKeySize) + copy(pub, buf[:PublicKeySize]) + return pub, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) < PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + priv := make(PrivateKey, PrivateKeySize) + copy(priv, buf[:PrivateKeySize]) + return priv, nil +} diff --git a/vendor/github.com/cloudflare/circl/sign/sign.go b/vendor/github.com/cloudflare/circl/sign/sign.go new file mode 100644 index 00000000..13b20fa4 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/sign/sign.go @@ -0,0 +1,110 @@ +// Package sign provides unified interfaces for signature schemes. +// +// A register of schemes is available in the package +// +// github.com/cloudflare/circl/sign/schemes +package sign + +import ( + "crypto" + "encoding" + "errors" +) + +type SignatureOpts struct { + // If non-empty, includes the given context in the signature if supported + // and will cause an error during signing otherwise. + Context string +} + +// A public key is used to verify a signature set by the corresponding private +// key. +type PublicKey interface { + // Returns the signature scheme for this public key. + Scheme() Scheme + Equal(crypto.PublicKey) bool + encoding.BinaryMarshaler + crypto.PublicKey +} + +// A private key allows one to create signatures. +type PrivateKey interface { + // Returns the signature scheme for this private key. + Scheme() Scheme + Equal(crypto.PrivateKey) bool + // For compatibility with Go standard library + crypto.Signer + crypto.PrivateKey + encoding.BinaryMarshaler +} + +// A Scheme represents a specific instance of a signature scheme. +type Scheme interface { + // Name of the scheme. + Name() string + + // GenerateKey creates a new key-pair. + GenerateKey() (PublicKey, PrivateKey, error) + + // Creates a signature using the PrivateKey on the given message and + // returns the signature. opts are additional options which can be nil. + // + // Panics if key is nil or wrong type or opts context is not supported. + Sign(sk PrivateKey, message []byte, opts *SignatureOpts) []byte + + // Checks whether the given signature is a valid signature set by + // the private key corresponding to the given public key on the + // given message. opts are additional options which can be nil. + // + // Panics if key is nil or wrong type or opts context is not supported. + Verify(pk PublicKey, message []byte, signature []byte, opts *SignatureOpts) bool + + // Deterministically derives a keypair from a seed. If you're unsure, + // you're better off using GenerateKey(). + // + // Panics if seed is not of length SeedSize(). + DeriveKey(seed []byte) (PublicKey, PrivateKey) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPublicKey([]byte) (PublicKey, error) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) + + // Size of binary marshalled public keys. + PublicKeySize() int + + // Size of binary marshalled public keys. + PrivateKeySize() int + + // Size of signatures. + SignatureSize() int + + // Size of seeds. + SeedSize() int + + // Returns whether contexts are supported. + SupportsContext() bool +} + +var ( + // ErrTypeMismatch is the error used if types of, for instance, private + // and public keys don't match. + ErrTypeMismatch = errors.New("types mismatch") + + // ErrSeedSize is the error used if the provided seed is of the wrong + // size. + ErrSeedSize = errors.New("wrong seed size") + + // ErrPubKeySize is the error used if the provided public key is of + // the wrong size. + ErrPubKeySize = errors.New("wrong size for public key") + + // ErrPrivKeySize is the error used if the provided private key is of + // the wrong size. + ErrPrivKeySize = errors.New("wrong size for private key") + + // ErrContextNotSupported is the error used if a context is not + // supported. + ErrContextNotSupported = errors.New("context not supported") +) diff --git a/vendor/github.com/hashicorp/vault/LICENSE b/vendor/github.com/hashicorp/vault/LICENSE index e87a115e..f4f97ee5 100644 --- a/vendor/github.com/hashicorp/vault/LICENSE +++ b/vendor/github.com/hashicorp/vault/LICENSE @@ -1,3 +1,5 @@ +Copyright (c) 2015 HashiCorp, Inc. + Mozilla Public License, version 2.0 1. Definitions diff --git a/vendor/github.com/hashicorp/vault/helper/pgpkeys/encrypt_decrypt.go b/vendor/github.com/hashicorp/vault/helper/pgpkeys/encrypt_decrypt.go index eef4c5ed..554013d6 100644 --- a/vendor/github.com/hashicorp/vault/helper/pgpkeys/encrypt_decrypt.go +++ b/vendor/github.com/hashicorp/vault/helper/pgpkeys/encrypt_decrypt.go @@ -5,9 +5,8 @@ import ( "encoding/base64" "fmt" - "github.com/hashicorp/errwrap" - "github.com/keybase/go-crypto/openpgp" - "github.com/keybase/go-crypto/openpgp/packet" + "github.com/ProtonMail/go-crypto/openpgp" + "github.com/ProtonMail/go-crypto/openpgp/packet" ) // EncryptShares takes an ordered set of byte slices to encrypt and the @@ -29,11 +28,11 @@ func EncryptShares(input [][]byte, pgpKeys []string) ([]string, [][]byte, error) ctBuf := bytes.NewBuffer(nil) pt, err := openpgp.Encrypt(ctBuf, []*openpgp.Entity{entity}, nil, nil, nil) if err != nil { - return nil, nil, errwrap.Wrapf("error setting up encryption for PGP message: {{err}}", err) + return nil, nil, fmt.Errorf("error setting up encryption for PGP message: %w", err) } _, err = pt.Write(input[i]) if err != nil { - return nil, nil, errwrap.Wrapf("error encrypting PGP message: {{err}}", err) + return nil, nil, fmt.Errorf("error encrypting PGP message: %w", err) } pt.Close() encryptedShares = append(encryptedShares, ctBuf.Bytes()) @@ -73,11 +72,11 @@ func GetEntities(pgpKeys []string) ([]*openpgp.Entity, error) { for _, keystring := range pgpKeys { data, err := base64.StdEncoding.DecodeString(keystring) if err != nil { - return nil, errwrap.Wrapf("error decoding given PGP key: {{err}}", err) + return nil, fmt.Errorf("error decoding given PGP key: %w", err) } entity, err := openpgp.ReadEntity(packet.NewReader(bytes.NewBuffer(data))) if err != nil { - return nil, errwrap.Wrapf("error parsing given PGP key: {{err}}", err) + return nil, fmt.Errorf("error parsing given PGP key: %w", err) } ret = append(ret, entity) } @@ -92,23 +91,23 @@ func GetEntities(pgpKeys []string) ([]*openpgp.Entity, error) { func DecryptBytes(encodedCrypt, privKey string) (*bytes.Buffer, error) { privKeyBytes, err := base64.StdEncoding.DecodeString(privKey) if err != nil { - return nil, errwrap.Wrapf("error decoding base64 private key: {{err}}", err) + return nil, fmt.Errorf("error decoding base64 private key: %w", err) } cryptBytes, err := base64.StdEncoding.DecodeString(encodedCrypt) if err != nil { - return nil, errwrap.Wrapf("error decoding base64 crypted bytes: {{err}}", err) + return nil, fmt.Errorf("error decoding base64 crypted bytes: %w", err) } entity, err := openpgp.ReadEntity(packet.NewReader(bytes.NewBuffer(privKeyBytes))) if err != nil { - return nil, errwrap.Wrapf("error parsing private key: {{err}}", err) + return nil, fmt.Errorf("error parsing private key: %w", err) } entityList := &openpgp.EntityList{entity} md, err := openpgp.ReadMessage(bytes.NewBuffer(cryptBytes), entityList, nil, nil) if err != nil { - return nil, errwrap.Wrapf("error decrypting the messages: {{err}}", err) + return nil, fmt.Errorf("error decrypting the messages: %w", err) } ptBuf := bytes.NewBuffer(nil) diff --git a/vendor/github.com/hashicorp/vault/helper/pgpkeys/flag.go b/vendor/github.com/hashicorp/vault/helper/pgpkeys/flag.go index 4d5fd969..e107bc99 100644 --- a/vendor/github.com/hashicorp/vault/helper/pgpkeys/flag.go +++ b/vendor/github.com/hashicorp/vault/helper/pgpkeys/flag.go @@ -8,8 +8,7 @@ import ( "os" "strings" - "github.com/hashicorp/errwrap" - "github.com/keybase/go-crypto/openpgp" + "github.com/ProtonMail/go-crypto/openpgp" ) // PubKeyFileFlag implements flag.Value and command.Example to receive exactly @@ -128,7 +127,7 @@ func ReadPGPFile(path string) (string, error) { serializedEntity := bytes.NewBuffer(nil) err = entityList[0].Serialize(serializedEntity) if err != nil { - return "", errwrap.Wrapf(fmt.Sprintf("error serializing entity for file %q: {{err}}", path), err) + return "", fmt.Errorf("error serializing entity for file %q: %w", path, err) } return base64.StdEncoding.EncodeToString(serializedEntity.Bytes()), nil @@ -139,5 +138,4 @@ func ReadPGPFile(path string) (string, error) { return buf.String(), nil } return base64.StdEncoding.EncodeToString(buf.Bytes()), nil - } diff --git a/vendor/github.com/hashicorp/vault/helper/pgpkeys/keybase.go b/vendor/github.com/hashicorp/vault/helper/pgpkeys/keybase.go index 21572350..b2571b45 100644 --- a/vendor/github.com/hashicorp/vault/helper/pgpkeys/keybase.go +++ b/vendor/github.com/hashicorp/vault/helper/pgpkeys/keybase.go @@ -6,10 +6,9 @@ import ( "fmt" "strings" - "github.com/hashicorp/errwrap" + "github.com/ProtonMail/go-crypto/openpgp" cleanhttp "github.com/hashicorp/go-cleanhttp" "github.com/hashicorp/vault/sdk/helper/jsonutil" - "github.com/keybase/go-crypto/openpgp" ) const ( @@ -102,7 +101,7 @@ func FetchKeybasePubkeys(input []string) (map[string]string, error) { serializedEntity.Reset() err = entityList[0].Serialize(serializedEntity) if err != nil { - return nil, errwrap.Wrapf(fmt.Sprintf("error serializing entity for user %q: {{err}}", usernames[i]), err) + return nil, fmt.Errorf("error serializing entity for user %q: %w", usernames[i], err) } // The API returns values in the same ordering requested, so this should properly match diff --git a/vendor/golang.org/x/crypto/argon2/argon2.go b/vendor/golang.org/x/crypto/argon2/argon2.go new file mode 100644 index 00000000..29f0a2de --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/argon2.go @@ -0,0 +1,283 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package argon2 implements the key derivation function Argon2. +// Argon2 was selected as the winner of the Password Hashing Competition and can +// be used to derive cryptographic keys from passwords. +// +// For a detailed specification of Argon2 see [1]. +// +// If you aren't sure which function you need, use Argon2id (IDKey) and +// the parameter recommendations for your scenario. +// +// # Argon2i +// +// Argon2i (implemented by Key) is the side-channel resistant version of Argon2. +// It uses data-independent memory access, which is preferred for password +// hashing and password-based key derivation. Argon2i requires more passes over +// memory than Argon2id to protect from trade-off attacks. The recommended +// parameters (taken from [2]) for non-interactive operations are time=3 and to +// use the maximum available memory. +// +// # Argon2id +// +// Argon2id (implemented by IDKey) is a hybrid version of Argon2 combining +// Argon2i and Argon2d. It uses data-independent memory access for the first +// half of the first iteration over the memory and data-dependent memory access +// for the rest. Argon2id is side-channel resistant and provides better brute- +// force cost savings due to time-memory tradeoffs than Argon2i. The recommended +// parameters for non-interactive operations (taken from [2]) are time=1 and to +// use the maximum available memory. +// +// [1] https://github.com/P-H-C/phc-winner-argon2/blob/master/argon2-specs.pdf +// [2] https://tools.ietf.org/html/draft-irtf-cfrg-argon2-03#section-9.3 +package argon2 + +import ( + "encoding/binary" + "sync" + + "golang.org/x/crypto/blake2b" +) + +// The Argon2 version implemented by this package. +const Version = 0x13 + +const ( + argon2d = iota + argon2i + argon2id +) + +// Key derives a key from the password, salt, and cost parameters using Argon2i +// returning a byte slice of length keyLen that can be used as cryptographic +// key. The CPU cost and parallelism degree must be greater than zero. +// +// For example, you can get a derived key for e.g. AES-256 (which needs a +// 32-byte key) by doing: +// +// key := argon2.Key([]byte("some password"), salt, 3, 32*1024, 4, 32) +// +// The draft RFC recommends[2] time=3, and memory=32*1024 is a sensible number. +// If using that amount of memory (32 MB) is not possible in some contexts then +// the time parameter can be increased to compensate. +// +// The time parameter specifies the number of passes over the memory and the +// memory parameter specifies the size of the memory in KiB. For example +// memory=32*1024 sets the memory cost to ~32 MB. The number of threads can be +// adjusted to the number of available CPUs. The cost parameters should be +// increased as memory latency and CPU parallelism increases. Remember to get a +// good random salt. +func Key(password, salt []byte, time, memory uint32, threads uint8, keyLen uint32) []byte { + return deriveKey(argon2i, password, salt, nil, nil, time, memory, threads, keyLen) +} + +// IDKey derives a key from the password, salt, and cost parameters using +// Argon2id returning a byte slice of length keyLen that can be used as +// cryptographic key. The CPU cost and parallelism degree must be greater than +// zero. +// +// For example, you can get a derived key for e.g. AES-256 (which needs a +// 32-byte key) by doing: +// +// key := argon2.IDKey([]byte("some password"), salt, 1, 64*1024, 4, 32) +// +// The draft RFC recommends[2] time=1, and memory=64*1024 is a sensible number. +// If using that amount of memory (64 MB) is not possible in some contexts then +// the time parameter can be increased to compensate. +// +// The time parameter specifies the number of passes over the memory and the +// memory parameter specifies the size of the memory in KiB. For example +// memory=64*1024 sets the memory cost to ~64 MB. The number of threads can be +// adjusted to the numbers of available CPUs. The cost parameters should be +// increased as memory latency and CPU parallelism increases. Remember to get a +// good random salt. +func IDKey(password, salt []byte, time, memory uint32, threads uint8, keyLen uint32) []byte { + return deriveKey(argon2id, password, salt, nil, nil, time, memory, threads, keyLen) +} + +func deriveKey(mode int, password, salt, secret, data []byte, time, memory uint32, threads uint8, keyLen uint32) []byte { + if time < 1 { + panic("argon2: number of rounds too small") + } + if threads < 1 { + panic("argon2: parallelism degree too low") + } + h0 := initHash(password, salt, secret, data, time, memory, uint32(threads), keyLen, mode) + + memory = memory / (syncPoints * uint32(threads)) * (syncPoints * uint32(threads)) + if memory < 2*syncPoints*uint32(threads) { + memory = 2 * syncPoints * uint32(threads) + } + B := initBlocks(&h0, memory, uint32(threads)) + processBlocks(B, time, memory, uint32(threads), mode) + return extractKey(B, memory, uint32(threads), keyLen) +} + +const ( + blockLength = 128 + syncPoints = 4 +) + +type block [blockLength]uint64 + +func initHash(password, salt, key, data []byte, time, memory, threads, keyLen uint32, mode int) [blake2b.Size + 8]byte { + var ( + h0 [blake2b.Size + 8]byte + params [24]byte + tmp [4]byte + ) + + b2, _ := blake2b.New512(nil) + binary.LittleEndian.PutUint32(params[0:4], threads) + binary.LittleEndian.PutUint32(params[4:8], keyLen) + binary.LittleEndian.PutUint32(params[8:12], memory) + binary.LittleEndian.PutUint32(params[12:16], time) + binary.LittleEndian.PutUint32(params[16:20], uint32(Version)) + binary.LittleEndian.PutUint32(params[20:24], uint32(mode)) + b2.Write(params[:]) + binary.LittleEndian.PutUint32(tmp[:], uint32(len(password))) + b2.Write(tmp[:]) + b2.Write(password) + binary.LittleEndian.PutUint32(tmp[:], uint32(len(salt))) + b2.Write(tmp[:]) + b2.Write(salt) + binary.LittleEndian.PutUint32(tmp[:], uint32(len(key))) + b2.Write(tmp[:]) + b2.Write(key) + binary.LittleEndian.PutUint32(tmp[:], uint32(len(data))) + b2.Write(tmp[:]) + b2.Write(data) + b2.Sum(h0[:0]) + return h0 +} + +func initBlocks(h0 *[blake2b.Size + 8]byte, memory, threads uint32) []block { + var block0 [1024]byte + B := make([]block, memory) + for lane := uint32(0); lane < threads; lane++ { + j := lane * (memory / threads) + binary.LittleEndian.PutUint32(h0[blake2b.Size+4:], lane) + + binary.LittleEndian.PutUint32(h0[blake2b.Size:], 0) + blake2bHash(block0[:], h0[:]) + for i := range B[j+0] { + B[j+0][i] = binary.LittleEndian.Uint64(block0[i*8:]) + } + + binary.LittleEndian.PutUint32(h0[blake2b.Size:], 1) + blake2bHash(block0[:], h0[:]) + for i := range B[j+1] { + B[j+1][i] = binary.LittleEndian.Uint64(block0[i*8:]) + } + } + return B +} + +func processBlocks(B []block, time, memory, threads uint32, mode int) { + lanes := memory / threads + segments := lanes / syncPoints + + processSegment := func(n, slice, lane uint32, wg *sync.WaitGroup) { + var addresses, in, zero block + if mode == argon2i || (mode == argon2id && n == 0 && slice < syncPoints/2) { + in[0] = uint64(n) + in[1] = uint64(lane) + in[2] = uint64(slice) + in[3] = uint64(memory) + in[4] = uint64(time) + in[5] = uint64(mode) + } + + index := uint32(0) + if n == 0 && slice == 0 { + index = 2 // we have already generated the first two blocks + if mode == argon2i || mode == argon2id { + in[6]++ + processBlock(&addresses, &in, &zero) + processBlock(&addresses, &addresses, &zero) + } + } + + offset := lane*lanes + slice*segments + index + var random uint64 + for index < segments { + prev := offset - 1 + if index == 0 && slice == 0 { + prev += lanes // last block in lane + } + if mode == argon2i || (mode == argon2id && n == 0 && slice < syncPoints/2) { + if index%blockLength == 0 { + in[6]++ + processBlock(&addresses, &in, &zero) + processBlock(&addresses, &addresses, &zero) + } + random = addresses[index%blockLength] + } else { + random = B[prev][0] + } + newOffset := indexAlpha(random, lanes, segments, threads, n, slice, lane, index) + processBlockXOR(&B[offset], &B[prev], &B[newOffset]) + index, offset = index+1, offset+1 + } + wg.Done() + } + + for n := uint32(0); n < time; n++ { + for slice := uint32(0); slice < syncPoints; slice++ { + var wg sync.WaitGroup + for lane := uint32(0); lane < threads; lane++ { + wg.Add(1) + go processSegment(n, slice, lane, &wg) + } + wg.Wait() + } + } + +} + +func extractKey(B []block, memory, threads, keyLen uint32) []byte { + lanes := memory / threads + for lane := uint32(0); lane < threads-1; lane++ { + for i, v := range B[(lane*lanes)+lanes-1] { + B[memory-1][i] ^= v + } + } + + var block [1024]byte + for i, v := range B[memory-1] { + binary.LittleEndian.PutUint64(block[i*8:], v) + } + key := make([]byte, keyLen) + blake2bHash(key, block[:]) + return key +} + +func indexAlpha(rand uint64, lanes, segments, threads, n, slice, lane, index uint32) uint32 { + refLane := uint32(rand>>32) % threads + if n == 0 && slice == 0 { + refLane = lane + } + m, s := 3*segments, ((slice+1)%syncPoints)*segments + if lane == refLane { + m += index + } + if n == 0 { + m, s = slice*segments, 0 + if slice == 0 || lane == refLane { + m += index + } + } + if index == 0 || lane == refLane { + m-- + } + return phi(rand, uint64(m), uint64(s), refLane, lanes) +} + +func phi(rand, m, s uint64, lane, lanes uint32) uint32 { + p := rand & 0xFFFFFFFF + p = (p * p) >> 32 + p = (p * m) >> 32 + return lane*lanes + uint32((s+m-(p+1))%uint64(lanes)) +} diff --git a/vendor/golang.org/x/crypto/argon2/blake2b.go b/vendor/golang.org/x/crypto/argon2/blake2b.go new file mode 100644 index 00000000..10f46948 --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/blake2b.go @@ -0,0 +1,53 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package argon2 + +import ( + "encoding/binary" + "hash" + + "golang.org/x/crypto/blake2b" +) + +// blake2bHash computes an arbitrary long hash value of in +// and writes the hash to out. +func blake2bHash(out []byte, in []byte) { + var b2 hash.Hash + if n := len(out); n < blake2b.Size { + b2, _ = blake2b.New(n, nil) + } else { + b2, _ = blake2b.New512(nil) + } + + var buffer [blake2b.Size]byte + binary.LittleEndian.PutUint32(buffer[:4], uint32(len(out))) + b2.Write(buffer[:4]) + b2.Write(in) + + if len(out) <= blake2b.Size { + b2.Sum(out[:0]) + return + } + + outLen := len(out) + b2.Sum(buffer[:0]) + b2.Reset() + copy(out, buffer[:32]) + out = out[32:] + for len(out) > blake2b.Size { + b2.Write(buffer[:]) + b2.Sum(buffer[:0]) + copy(out, buffer[:32]) + out = out[32:] + b2.Reset() + } + + if outLen%blake2b.Size > 0 { // outLen > 64 + r := ((outLen + 31) / 32) - 2 // ⌈τ /32⌉-2 + b2, _ = blake2b.New(outLen-32*r, nil) + } + b2.Write(buffer[:]) + b2.Sum(out[:0]) +} diff --git a/vendor/golang.org/x/crypto/argon2/blamka_amd64.go b/vendor/golang.org/x/crypto/argon2/blamka_amd64.go new file mode 100644 index 00000000..a014ac92 --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/blamka_amd64.go @@ -0,0 +1,61 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && gc && !purego +// +build amd64,gc,!purego + +package argon2 + +import "golang.org/x/sys/cpu" + +func init() { + useSSE4 = cpu.X86.HasSSE41 +} + +//go:noescape +func mixBlocksSSE2(out, a, b, c *block) + +//go:noescape +func xorBlocksSSE2(out, a, b, c *block) + +//go:noescape +func blamkaSSE4(b *block) + +func processBlockSSE(out, in1, in2 *block, xor bool) { + var t block + mixBlocksSSE2(&t, in1, in2, &t) + if useSSE4 { + blamkaSSE4(&t) + } else { + for i := 0; i < blockLength; i += 16 { + blamkaGeneric( + &t[i+0], &t[i+1], &t[i+2], &t[i+3], + &t[i+4], &t[i+5], &t[i+6], &t[i+7], + &t[i+8], &t[i+9], &t[i+10], &t[i+11], + &t[i+12], &t[i+13], &t[i+14], &t[i+15], + ) + } + for i := 0; i < blockLength/8; i += 2 { + blamkaGeneric( + &t[i], &t[i+1], &t[16+i], &t[16+i+1], + &t[32+i], &t[32+i+1], &t[48+i], &t[48+i+1], + &t[64+i], &t[64+i+1], &t[80+i], &t[80+i+1], + &t[96+i], &t[96+i+1], &t[112+i], &t[112+i+1], + ) + } + } + if xor { + xorBlocksSSE2(out, in1, in2, &t) + } else { + mixBlocksSSE2(out, in1, in2, &t) + } +} + +func processBlock(out, in1, in2 *block) { + processBlockSSE(out, in1, in2, false) +} + +func processBlockXOR(out, in1, in2 *block) { + processBlockSSE(out, in1, in2, true) +} diff --git a/vendor/golang.org/x/crypto/argon2/blamka_amd64.s b/vendor/golang.org/x/crypto/argon2/blamka_amd64.s new file mode 100644 index 00000000..b2cc0515 --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/blamka_amd64.s @@ -0,0 +1,244 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && gc && !purego +// +build amd64,gc,!purego + +#include "textflag.h" + +DATA ·c40<>+0x00(SB)/8, $0x0201000706050403 +DATA ·c40<>+0x08(SB)/8, $0x0a09080f0e0d0c0b +GLOBL ·c40<>(SB), (NOPTR+RODATA), $16 + +DATA ·c48<>+0x00(SB)/8, $0x0100070605040302 +DATA ·c48<>+0x08(SB)/8, $0x09080f0e0d0c0b0a +GLOBL ·c48<>(SB), (NOPTR+RODATA), $16 + +#define SHUFFLE(v2, v3, v4, v5, v6, v7, t1, t2) \ + MOVO v4, t1; \ + MOVO v5, v4; \ + MOVO t1, v5; \ + MOVO v6, t1; \ + PUNPCKLQDQ v6, t2; \ + PUNPCKHQDQ v7, v6; \ + PUNPCKHQDQ t2, v6; \ + PUNPCKLQDQ v7, t2; \ + MOVO t1, v7; \ + MOVO v2, t1; \ + PUNPCKHQDQ t2, v7; \ + PUNPCKLQDQ v3, t2; \ + PUNPCKHQDQ t2, v2; \ + PUNPCKLQDQ t1, t2; \ + PUNPCKHQDQ t2, v3 + +#define SHUFFLE_INV(v2, v3, v4, v5, v6, v7, t1, t2) \ + MOVO v4, t1; \ + MOVO v5, v4; \ + MOVO t1, v5; \ + MOVO v2, t1; \ + PUNPCKLQDQ v2, t2; \ + PUNPCKHQDQ v3, v2; \ + PUNPCKHQDQ t2, v2; \ + PUNPCKLQDQ v3, t2; \ + MOVO t1, v3; \ + MOVO v6, t1; \ + PUNPCKHQDQ t2, v3; \ + PUNPCKLQDQ v7, t2; \ + PUNPCKHQDQ t2, v6; \ + PUNPCKLQDQ t1, t2; \ + PUNPCKHQDQ t2, v7 + +#define HALF_ROUND(v0, v1, v2, v3, v4, v5, v6, v7, t0, c40, c48) \ + MOVO v0, t0; \ + PMULULQ v2, t0; \ + PADDQ v2, v0; \ + PADDQ t0, v0; \ + PADDQ t0, v0; \ + PXOR v0, v6; \ + PSHUFD $0xB1, v6, v6; \ + MOVO v4, t0; \ + PMULULQ v6, t0; \ + PADDQ v6, v4; \ + PADDQ t0, v4; \ + PADDQ t0, v4; \ + PXOR v4, v2; \ + PSHUFB c40, v2; \ + MOVO v0, t0; \ + PMULULQ v2, t0; \ + PADDQ v2, v0; \ + PADDQ t0, v0; \ + PADDQ t0, v0; \ + PXOR v0, v6; \ + PSHUFB c48, v6; \ + MOVO v4, t0; \ + PMULULQ v6, t0; \ + PADDQ v6, v4; \ + PADDQ t0, v4; \ + PADDQ t0, v4; \ + PXOR v4, v2; \ + MOVO v2, t0; \ + PADDQ v2, t0; \ + PSRLQ $63, v2; \ + PXOR t0, v2; \ + MOVO v1, t0; \ + PMULULQ v3, t0; \ + PADDQ v3, v1; \ + PADDQ t0, v1; \ + PADDQ t0, v1; \ + PXOR v1, v7; \ + PSHUFD $0xB1, v7, v7; \ + MOVO v5, t0; \ + PMULULQ v7, t0; \ + PADDQ v7, v5; \ + PADDQ t0, v5; \ + PADDQ t0, v5; \ + PXOR v5, v3; \ + PSHUFB c40, v3; \ + MOVO v1, t0; \ + PMULULQ v3, t0; \ + PADDQ v3, v1; \ + PADDQ t0, v1; \ + PADDQ t0, v1; \ + PXOR v1, v7; \ + PSHUFB c48, v7; \ + MOVO v5, t0; \ + PMULULQ v7, t0; \ + PADDQ v7, v5; \ + PADDQ t0, v5; \ + PADDQ t0, v5; \ + PXOR v5, v3; \ + MOVO v3, t0; \ + PADDQ v3, t0; \ + PSRLQ $63, v3; \ + PXOR t0, v3 + +#define LOAD_MSG_0(block, off) \ + MOVOU 8*(off+0)(block), X0; \ + MOVOU 8*(off+2)(block), X1; \ + MOVOU 8*(off+4)(block), X2; \ + MOVOU 8*(off+6)(block), X3; \ + MOVOU 8*(off+8)(block), X4; \ + MOVOU 8*(off+10)(block), X5; \ + MOVOU 8*(off+12)(block), X6; \ + MOVOU 8*(off+14)(block), X7 + +#define STORE_MSG_0(block, off) \ + MOVOU X0, 8*(off+0)(block); \ + MOVOU X1, 8*(off+2)(block); \ + MOVOU X2, 8*(off+4)(block); \ + MOVOU X3, 8*(off+6)(block); \ + MOVOU X4, 8*(off+8)(block); \ + MOVOU X5, 8*(off+10)(block); \ + MOVOU X6, 8*(off+12)(block); \ + MOVOU X7, 8*(off+14)(block) + +#define LOAD_MSG_1(block, off) \ + MOVOU 8*off+0*8(block), X0; \ + MOVOU 8*off+16*8(block), X1; \ + MOVOU 8*off+32*8(block), X2; \ + MOVOU 8*off+48*8(block), X3; \ + MOVOU 8*off+64*8(block), X4; \ + MOVOU 8*off+80*8(block), X5; \ + MOVOU 8*off+96*8(block), X6; \ + MOVOU 8*off+112*8(block), X7 + +#define STORE_MSG_1(block, off) \ + MOVOU X0, 8*off+0*8(block); \ + MOVOU X1, 8*off+16*8(block); \ + MOVOU X2, 8*off+32*8(block); \ + MOVOU X3, 8*off+48*8(block); \ + MOVOU X4, 8*off+64*8(block); \ + MOVOU X5, 8*off+80*8(block); \ + MOVOU X6, 8*off+96*8(block); \ + MOVOU X7, 8*off+112*8(block) + +#define BLAMKA_ROUND_0(block, off, t0, t1, c40, c48) \ + LOAD_MSG_0(block, off); \ + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, t0, c40, c48); \ + SHUFFLE(X2, X3, X4, X5, X6, X7, t0, t1); \ + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, t0, c40, c48); \ + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, t0, t1); \ + STORE_MSG_0(block, off) + +#define BLAMKA_ROUND_1(block, off, t0, t1, c40, c48) \ + LOAD_MSG_1(block, off); \ + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, t0, c40, c48); \ + SHUFFLE(X2, X3, X4, X5, X6, X7, t0, t1); \ + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, t0, c40, c48); \ + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, t0, t1); \ + STORE_MSG_1(block, off) + +// func blamkaSSE4(b *block) +TEXT ·blamkaSSE4(SB), 4, $0-8 + MOVQ b+0(FP), AX + + MOVOU ·c40<>(SB), X10 + MOVOU ·c48<>(SB), X11 + + BLAMKA_ROUND_0(AX, 0, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 16, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 32, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 48, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 64, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 80, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 96, X8, X9, X10, X11) + BLAMKA_ROUND_0(AX, 112, X8, X9, X10, X11) + + BLAMKA_ROUND_1(AX, 0, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 2, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 4, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 6, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 8, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 10, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 12, X8, X9, X10, X11) + BLAMKA_ROUND_1(AX, 14, X8, X9, X10, X11) + RET + +// func mixBlocksSSE2(out, a, b, c *block) +TEXT ·mixBlocksSSE2(SB), 4, $0-32 + MOVQ out+0(FP), DX + MOVQ a+8(FP), AX + MOVQ b+16(FP), BX + MOVQ a+24(FP), CX + MOVQ $128, BP + +loop: + MOVOU 0(AX), X0 + MOVOU 0(BX), X1 + MOVOU 0(CX), X2 + PXOR X1, X0 + PXOR X2, X0 + MOVOU X0, 0(DX) + ADDQ $16, AX + ADDQ $16, BX + ADDQ $16, CX + ADDQ $16, DX + SUBQ $2, BP + JA loop + RET + +// func xorBlocksSSE2(out, a, b, c *block) +TEXT ·xorBlocksSSE2(SB), 4, $0-32 + MOVQ out+0(FP), DX + MOVQ a+8(FP), AX + MOVQ b+16(FP), BX + MOVQ a+24(FP), CX + MOVQ $128, BP + +loop: + MOVOU 0(AX), X0 + MOVOU 0(BX), X1 + MOVOU 0(CX), X2 + MOVOU 0(DX), X3 + PXOR X1, X0 + PXOR X2, X0 + PXOR X3, X0 + MOVOU X0, 0(DX) + ADDQ $16, AX + ADDQ $16, BX + ADDQ $16, CX + ADDQ $16, DX + SUBQ $2, BP + JA loop + RET diff --git a/vendor/golang.org/x/crypto/argon2/blamka_generic.go b/vendor/golang.org/x/crypto/argon2/blamka_generic.go new file mode 100644 index 00000000..a481b224 --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/blamka_generic.go @@ -0,0 +1,163 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package argon2 + +var useSSE4 bool + +func processBlockGeneric(out, in1, in2 *block, xor bool) { + var t block + for i := range t { + t[i] = in1[i] ^ in2[i] + } + for i := 0; i < blockLength; i += 16 { + blamkaGeneric( + &t[i+0], &t[i+1], &t[i+2], &t[i+3], + &t[i+4], &t[i+5], &t[i+6], &t[i+7], + &t[i+8], &t[i+9], &t[i+10], &t[i+11], + &t[i+12], &t[i+13], &t[i+14], &t[i+15], + ) + } + for i := 0; i < blockLength/8; i += 2 { + blamkaGeneric( + &t[i], &t[i+1], &t[16+i], &t[16+i+1], + &t[32+i], &t[32+i+1], &t[48+i], &t[48+i+1], + &t[64+i], &t[64+i+1], &t[80+i], &t[80+i+1], + &t[96+i], &t[96+i+1], &t[112+i], &t[112+i+1], + ) + } + if xor { + for i := range t { + out[i] ^= in1[i] ^ in2[i] ^ t[i] + } + } else { + for i := range t { + out[i] = in1[i] ^ in2[i] ^ t[i] + } + } +} + +func blamkaGeneric(t00, t01, t02, t03, t04, t05, t06, t07, t08, t09, t10, t11, t12, t13, t14, t15 *uint64) { + v00, v01, v02, v03 := *t00, *t01, *t02, *t03 + v04, v05, v06, v07 := *t04, *t05, *t06, *t07 + v08, v09, v10, v11 := *t08, *t09, *t10, *t11 + v12, v13, v14, v15 := *t12, *t13, *t14, *t15 + + v00 += v04 + 2*uint64(uint32(v00))*uint64(uint32(v04)) + v12 ^= v00 + v12 = v12>>32 | v12<<32 + v08 += v12 + 2*uint64(uint32(v08))*uint64(uint32(v12)) + v04 ^= v08 + v04 = v04>>24 | v04<<40 + + v00 += v04 + 2*uint64(uint32(v00))*uint64(uint32(v04)) + v12 ^= v00 + v12 = v12>>16 | v12<<48 + v08 += v12 + 2*uint64(uint32(v08))*uint64(uint32(v12)) + v04 ^= v08 + v04 = v04>>63 | v04<<1 + + v01 += v05 + 2*uint64(uint32(v01))*uint64(uint32(v05)) + v13 ^= v01 + v13 = v13>>32 | v13<<32 + v09 += v13 + 2*uint64(uint32(v09))*uint64(uint32(v13)) + v05 ^= v09 + v05 = v05>>24 | v05<<40 + + v01 += v05 + 2*uint64(uint32(v01))*uint64(uint32(v05)) + v13 ^= v01 + v13 = v13>>16 | v13<<48 + v09 += v13 + 2*uint64(uint32(v09))*uint64(uint32(v13)) + v05 ^= v09 + v05 = v05>>63 | v05<<1 + + v02 += v06 + 2*uint64(uint32(v02))*uint64(uint32(v06)) + v14 ^= v02 + v14 = v14>>32 | v14<<32 + v10 += v14 + 2*uint64(uint32(v10))*uint64(uint32(v14)) + v06 ^= v10 + v06 = v06>>24 | v06<<40 + + v02 += v06 + 2*uint64(uint32(v02))*uint64(uint32(v06)) + v14 ^= v02 + v14 = v14>>16 | v14<<48 + v10 += v14 + 2*uint64(uint32(v10))*uint64(uint32(v14)) + v06 ^= v10 + v06 = v06>>63 | v06<<1 + + v03 += v07 + 2*uint64(uint32(v03))*uint64(uint32(v07)) + v15 ^= v03 + v15 = v15>>32 | v15<<32 + v11 += v15 + 2*uint64(uint32(v11))*uint64(uint32(v15)) + v07 ^= v11 + v07 = v07>>24 | v07<<40 + + v03 += v07 + 2*uint64(uint32(v03))*uint64(uint32(v07)) + v15 ^= v03 + v15 = v15>>16 | v15<<48 + v11 += v15 + 2*uint64(uint32(v11))*uint64(uint32(v15)) + v07 ^= v11 + v07 = v07>>63 | v07<<1 + + v00 += v05 + 2*uint64(uint32(v00))*uint64(uint32(v05)) + v15 ^= v00 + v15 = v15>>32 | v15<<32 + v10 += v15 + 2*uint64(uint32(v10))*uint64(uint32(v15)) + v05 ^= v10 + v05 = v05>>24 | v05<<40 + + v00 += v05 + 2*uint64(uint32(v00))*uint64(uint32(v05)) + v15 ^= v00 + v15 = v15>>16 | v15<<48 + v10 += v15 + 2*uint64(uint32(v10))*uint64(uint32(v15)) + v05 ^= v10 + v05 = v05>>63 | v05<<1 + + v01 += v06 + 2*uint64(uint32(v01))*uint64(uint32(v06)) + v12 ^= v01 + v12 = v12>>32 | v12<<32 + v11 += v12 + 2*uint64(uint32(v11))*uint64(uint32(v12)) + v06 ^= v11 + v06 = v06>>24 | v06<<40 + + v01 += v06 + 2*uint64(uint32(v01))*uint64(uint32(v06)) + v12 ^= v01 + v12 = v12>>16 | v12<<48 + v11 += v12 + 2*uint64(uint32(v11))*uint64(uint32(v12)) + v06 ^= v11 + v06 = v06>>63 | v06<<1 + + v02 += v07 + 2*uint64(uint32(v02))*uint64(uint32(v07)) + v13 ^= v02 + v13 = v13>>32 | v13<<32 + v08 += v13 + 2*uint64(uint32(v08))*uint64(uint32(v13)) + v07 ^= v08 + v07 = v07>>24 | v07<<40 + + v02 += v07 + 2*uint64(uint32(v02))*uint64(uint32(v07)) + v13 ^= v02 + v13 = v13>>16 | v13<<48 + v08 += v13 + 2*uint64(uint32(v08))*uint64(uint32(v13)) + v07 ^= v08 + v07 = v07>>63 | v07<<1 + + v03 += v04 + 2*uint64(uint32(v03))*uint64(uint32(v04)) + v14 ^= v03 + v14 = v14>>32 | v14<<32 + v09 += v14 + 2*uint64(uint32(v09))*uint64(uint32(v14)) + v04 ^= v09 + v04 = v04>>24 | v04<<40 + + v03 += v04 + 2*uint64(uint32(v03))*uint64(uint32(v04)) + v14 ^= v03 + v14 = v14>>16 | v14<<48 + v09 += v14 + 2*uint64(uint32(v09))*uint64(uint32(v14)) + v04 ^= v09 + v04 = v04>>63 | v04<<1 + + *t00, *t01, *t02, *t03 = v00, v01, v02, v03 + *t04, *t05, *t06, *t07 = v04, v05, v06, v07 + *t08, *t09, *t10, *t11 = v08, v09, v10, v11 + *t12, *t13, *t14, *t15 = v12, v13, v14, v15 +} diff --git a/vendor/golang.org/x/crypto/argon2/blamka_ref.go b/vendor/golang.org/x/crypto/argon2/blamka_ref.go new file mode 100644 index 00000000..167c59d2 --- /dev/null +++ b/vendor/golang.org/x/crypto/argon2/blamka_ref.go @@ -0,0 +1,16 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !amd64 || purego || !gc +// +build !amd64 purego !gc + +package argon2 + +func processBlock(out, in1, in2 *block) { + processBlockGeneric(out, in1, in2, false) +} + +func processBlockXOR(out, in1, in2 *block) { + processBlockGeneric(out, in1, in2, true) +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2b.go b/vendor/golang.org/x/crypto/blake2b/blake2b.go new file mode 100644 index 00000000..d2e98d42 --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2b.go @@ -0,0 +1,291 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package blake2b implements the BLAKE2b hash algorithm defined by RFC 7693 +// and the extendable output function (XOF) BLAKE2Xb. +// +// BLAKE2b is optimized for 64-bit platforms—including NEON-enabled ARMs—and +// produces digests of any size between 1 and 64 bytes. +// For a detailed specification of BLAKE2b see https://blake2.net/blake2.pdf +// and for BLAKE2Xb see https://blake2.net/blake2x.pdf +// +// If you aren't sure which function you need, use BLAKE2b (Sum512 or New512). +// If you need a secret-key MAC (message authentication code), use the New512 +// function with a non-nil key. +// +// BLAKE2X is a construction to compute hash values larger than 64 bytes. It +// can produce hash values between 0 and 4 GiB. +package blake2b + +import ( + "encoding/binary" + "errors" + "hash" +) + +const ( + // The blocksize of BLAKE2b in bytes. + BlockSize = 128 + // The hash size of BLAKE2b-512 in bytes. + Size = 64 + // The hash size of BLAKE2b-384 in bytes. + Size384 = 48 + // The hash size of BLAKE2b-256 in bytes. + Size256 = 32 +) + +var ( + useAVX2 bool + useAVX bool + useSSE4 bool +) + +var ( + errKeySize = errors.New("blake2b: invalid key size") + errHashSize = errors.New("blake2b: invalid hash size") +) + +var iv = [8]uint64{ + 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, + 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179, +} + +// Sum512 returns the BLAKE2b-512 checksum of the data. +func Sum512(data []byte) [Size]byte { + var sum [Size]byte + checkSum(&sum, Size, data) + return sum +} + +// Sum384 returns the BLAKE2b-384 checksum of the data. +func Sum384(data []byte) [Size384]byte { + var sum [Size]byte + var sum384 [Size384]byte + checkSum(&sum, Size384, data) + copy(sum384[:], sum[:Size384]) + return sum384 +} + +// Sum256 returns the BLAKE2b-256 checksum of the data. +func Sum256(data []byte) [Size256]byte { + var sum [Size]byte + var sum256 [Size256]byte + checkSum(&sum, Size256, data) + copy(sum256[:], sum[:Size256]) + return sum256 +} + +// New512 returns a new hash.Hash computing the BLAKE2b-512 checksum. A non-nil +// key turns the hash into a MAC. The key must be between zero and 64 bytes long. +func New512(key []byte) (hash.Hash, error) { return newDigest(Size, key) } + +// New384 returns a new hash.Hash computing the BLAKE2b-384 checksum. A non-nil +// key turns the hash into a MAC. The key must be between zero and 64 bytes long. +func New384(key []byte) (hash.Hash, error) { return newDigest(Size384, key) } + +// New256 returns a new hash.Hash computing the BLAKE2b-256 checksum. A non-nil +// key turns the hash into a MAC. The key must be between zero and 64 bytes long. +func New256(key []byte) (hash.Hash, error) { return newDigest(Size256, key) } + +// New returns a new hash.Hash computing the BLAKE2b checksum with a custom length. +// A non-nil key turns the hash into a MAC. The key must be between zero and 64 bytes long. +// The hash size can be a value between 1 and 64 but it is highly recommended to use +// values equal or greater than: +// - 32 if BLAKE2b is used as a hash function (The key is zero bytes long). +// - 16 if BLAKE2b is used as a MAC function (The key is at least 16 bytes long). +// When the key is nil, the returned hash.Hash implements BinaryMarshaler +// and BinaryUnmarshaler for state (de)serialization as documented by hash.Hash. +func New(size int, key []byte) (hash.Hash, error) { return newDigest(size, key) } + +func newDigest(hashSize int, key []byte) (*digest, error) { + if hashSize < 1 || hashSize > Size { + return nil, errHashSize + } + if len(key) > Size { + return nil, errKeySize + } + d := &digest{ + size: hashSize, + keyLen: len(key), + } + copy(d.key[:], key) + d.Reset() + return d, nil +} + +func checkSum(sum *[Size]byte, hashSize int, data []byte) { + h := iv + h[0] ^= uint64(hashSize) | (1 << 16) | (1 << 24) + var c [2]uint64 + + if length := len(data); length > BlockSize { + n := length &^ (BlockSize - 1) + if length == n { + n -= BlockSize + } + hashBlocks(&h, &c, 0, data[:n]) + data = data[n:] + } + + var block [BlockSize]byte + offset := copy(block[:], data) + remaining := uint64(BlockSize - offset) + if c[0] < remaining { + c[1]-- + } + c[0] -= remaining + + hashBlocks(&h, &c, 0xFFFFFFFFFFFFFFFF, block[:]) + + for i, v := range h[:(hashSize+7)/8] { + binary.LittleEndian.PutUint64(sum[8*i:], v) + } +} + +type digest struct { + h [8]uint64 + c [2]uint64 + size int + block [BlockSize]byte + offset int + + key [BlockSize]byte + keyLen int +} + +const ( + magic = "b2b" + marshaledSize = len(magic) + 8*8 + 2*8 + 1 + BlockSize + 1 +) + +func (d *digest) MarshalBinary() ([]byte, error) { + if d.keyLen != 0 { + return nil, errors.New("crypto/blake2b: cannot marshal MACs") + } + b := make([]byte, 0, marshaledSize) + b = append(b, magic...) + for i := 0; i < 8; i++ { + b = appendUint64(b, d.h[i]) + } + b = appendUint64(b, d.c[0]) + b = appendUint64(b, d.c[1]) + // Maximum value for size is 64 + b = append(b, byte(d.size)) + b = append(b, d.block[:]...) + b = append(b, byte(d.offset)) + return b, nil +} + +func (d *digest) UnmarshalBinary(b []byte) error { + if len(b) < len(magic) || string(b[:len(magic)]) != magic { + return errors.New("crypto/blake2b: invalid hash state identifier") + } + if len(b) != marshaledSize { + return errors.New("crypto/blake2b: invalid hash state size") + } + b = b[len(magic):] + for i := 0; i < 8; i++ { + b, d.h[i] = consumeUint64(b) + } + b, d.c[0] = consumeUint64(b) + b, d.c[1] = consumeUint64(b) + d.size = int(b[0]) + b = b[1:] + copy(d.block[:], b[:BlockSize]) + b = b[BlockSize:] + d.offset = int(b[0]) + return nil +} + +func (d *digest) BlockSize() int { return BlockSize } + +func (d *digest) Size() int { return d.size } + +func (d *digest) Reset() { + d.h = iv + d.h[0] ^= uint64(d.size) | (uint64(d.keyLen) << 8) | (1 << 16) | (1 << 24) + d.offset, d.c[0], d.c[1] = 0, 0, 0 + if d.keyLen > 0 { + d.block = d.key + d.offset = BlockSize + } +} + +func (d *digest) Write(p []byte) (n int, err error) { + n = len(p) + + if d.offset > 0 { + remaining := BlockSize - d.offset + if n <= remaining { + d.offset += copy(d.block[d.offset:], p) + return + } + copy(d.block[d.offset:], p[:remaining]) + hashBlocks(&d.h, &d.c, 0, d.block[:]) + d.offset = 0 + p = p[remaining:] + } + + if length := len(p); length > BlockSize { + nn := length &^ (BlockSize - 1) + if length == nn { + nn -= BlockSize + } + hashBlocks(&d.h, &d.c, 0, p[:nn]) + p = p[nn:] + } + + if len(p) > 0 { + d.offset += copy(d.block[:], p) + } + + return +} + +func (d *digest) Sum(sum []byte) []byte { + var hash [Size]byte + d.finalize(&hash) + return append(sum, hash[:d.size]...) +} + +func (d *digest) finalize(hash *[Size]byte) { + var block [BlockSize]byte + copy(block[:], d.block[:d.offset]) + remaining := uint64(BlockSize - d.offset) + + c := d.c + if c[0] < remaining { + c[1]-- + } + c[0] -= remaining + + h := d.h + hashBlocks(&h, &c, 0xFFFFFFFFFFFFFFFF, block[:]) + + for i, v := range h { + binary.LittleEndian.PutUint64(hash[8*i:], v) + } +} + +func appendUint64(b []byte, x uint64) []byte { + var a [8]byte + binary.BigEndian.PutUint64(a[:], x) + return append(b, a[:]...) +} + +func appendUint32(b []byte, x uint32) []byte { + var a [4]byte + binary.BigEndian.PutUint32(a[:], x) + return append(b, a[:]...) +} + +func consumeUint64(b []byte) ([]byte, uint64) { + x := binary.BigEndian.Uint64(b) + return b[8:], x +} + +func consumeUint32(b []byte) ([]byte, uint32) { + x := binary.BigEndian.Uint32(b) + return b[4:], x +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.go b/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.go new file mode 100644 index 00000000..56bfaaa1 --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.go @@ -0,0 +1,38 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build go1.7 && amd64 && gc && !purego +// +build go1.7,amd64,gc,!purego + +package blake2b + +import "golang.org/x/sys/cpu" + +func init() { + useAVX2 = cpu.X86.HasAVX2 + useAVX = cpu.X86.HasAVX + useSSE4 = cpu.X86.HasSSE41 +} + +//go:noescape +func hashBlocksAVX2(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) + +//go:noescape +func hashBlocksAVX(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) + +//go:noescape +func hashBlocksSSE4(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) + +func hashBlocks(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) { + switch { + case useAVX2: + hashBlocksAVX2(h, c, flag, blocks) + case useAVX: + hashBlocksAVX(h, c, flag, blocks) + case useSSE4: + hashBlocksSSE4(h, c, flag, blocks) + default: + hashBlocksGeneric(h, c, flag, blocks) + } +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.s b/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.s new file mode 100644 index 00000000..4b9daa18 --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2bAVX2_amd64.s @@ -0,0 +1,745 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build go1.7 && amd64 && gc && !purego +// +build go1.7,amd64,gc,!purego + +#include "textflag.h" + +DATA ·AVX2_iv0<>+0x00(SB)/8, $0x6a09e667f3bcc908 +DATA ·AVX2_iv0<>+0x08(SB)/8, $0xbb67ae8584caa73b +DATA ·AVX2_iv0<>+0x10(SB)/8, $0x3c6ef372fe94f82b +DATA ·AVX2_iv0<>+0x18(SB)/8, $0xa54ff53a5f1d36f1 +GLOBL ·AVX2_iv0<>(SB), (NOPTR+RODATA), $32 + +DATA ·AVX2_iv1<>+0x00(SB)/8, $0x510e527fade682d1 +DATA ·AVX2_iv1<>+0x08(SB)/8, $0x9b05688c2b3e6c1f +DATA ·AVX2_iv1<>+0x10(SB)/8, $0x1f83d9abfb41bd6b +DATA ·AVX2_iv1<>+0x18(SB)/8, $0x5be0cd19137e2179 +GLOBL ·AVX2_iv1<>(SB), (NOPTR+RODATA), $32 + +DATA ·AVX2_c40<>+0x00(SB)/8, $0x0201000706050403 +DATA ·AVX2_c40<>+0x08(SB)/8, $0x0a09080f0e0d0c0b +DATA ·AVX2_c40<>+0x10(SB)/8, $0x0201000706050403 +DATA ·AVX2_c40<>+0x18(SB)/8, $0x0a09080f0e0d0c0b +GLOBL ·AVX2_c40<>(SB), (NOPTR+RODATA), $32 + +DATA ·AVX2_c48<>+0x00(SB)/8, $0x0100070605040302 +DATA ·AVX2_c48<>+0x08(SB)/8, $0x09080f0e0d0c0b0a +DATA ·AVX2_c48<>+0x10(SB)/8, $0x0100070605040302 +DATA ·AVX2_c48<>+0x18(SB)/8, $0x09080f0e0d0c0b0a +GLOBL ·AVX2_c48<>(SB), (NOPTR+RODATA), $32 + +DATA ·AVX_iv0<>+0x00(SB)/8, $0x6a09e667f3bcc908 +DATA ·AVX_iv0<>+0x08(SB)/8, $0xbb67ae8584caa73b +GLOBL ·AVX_iv0<>(SB), (NOPTR+RODATA), $16 + +DATA ·AVX_iv1<>+0x00(SB)/8, $0x3c6ef372fe94f82b +DATA ·AVX_iv1<>+0x08(SB)/8, $0xa54ff53a5f1d36f1 +GLOBL ·AVX_iv1<>(SB), (NOPTR+RODATA), $16 + +DATA ·AVX_iv2<>+0x00(SB)/8, $0x510e527fade682d1 +DATA ·AVX_iv2<>+0x08(SB)/8, $0x9b05688c2b3e6c1f +GLOBL ·AVX_iv2<>(SB), (NOPTR+RODATA), $16 + +DATA ·AVX_iv3<>+0x00(SB)/8, $0x1f83d9abfb41bd6b +DATA ·AVX_iv3<>+0x08(SB)/8, $0x5be0cd19137e2179 +GLOBL ·AVX_iv3<>(SB), (NOPTR+RODATA), $16 + +DATA ·AVX_c40<>+0x00(SB)/8, $0x0201000706050403 +DATA ·AVX_c40<>+0x08(SB)/8, $0x0a09080f0e0d0c0b +GLOBL ·AVX_c40<>(SB), (NOPTR+RODATA), $16 + +DATA ·AVX_c48<>+0x00(SB)/8, $0x0100070605040302 +DATA ·AVX_c48<>+0x08(SB)/8, $0x09080f0e0d0c0b0a +GLOBL ·AVX_c48<>(SB), (NOPTR+RODATA), $16 + +#define VPERMQ_0x39_Y1_Y1 BYTE $0xc4; BYTE $0xe3; BYTE $0xfd; BYTE $0x00; BYTE $0xc9; BYTE $0x39 +#define VPERMQ_0x93_Y1_Y1 BYTE $0xc4; BYTE $0xe3; BYTE $0xfd; BYTE $0x00; BYTE $0xc9; BYTE $0x93 +#define VPERMQ_0x4E_Y2_Y2 BYTE $0xc4; BYTE $0xe3; BYTE $0xfd; BYTE $0x00; BYTE $0xd2; BYTE $0x4e +#define VPERMQ_0x93_Y3_Y3 BYTE $0xc4; BYTE $0xe3; BYTE $0xfd; BYTE $0x00; BYTE $0xdb; BYTE $0x93 +#define VPERMQ_0x39_Y3_Y3 BYTE $0xc4; BYTE $0xe3; BYTE $0xfd; BYTE $0x00; BYTE $0xdb; BYTE $0x39 + +#define ROUND_AVX2(m0, m1, m2, m3, t, c40, c48) \ + VPADDQ m0, Y0, Y0; \ + VPADDQ Y1, Y0, Y0; \ + VPXOR Y0, Y3, Y3; \ + VPSHUFD $-79, Y3, Y3; \ + VPADDQ Y3, Y2, Y2; \ + VPXOR Y2, Y1, Y1; \ + VPSHUFB c40, Y1, Y1; \ + VPADDQ m1, Y0, Y0; \ + VPADDQ Y1, Y0, Y0; \ + VPXOR Y0, Y3, Y3; \ + VPSHUFB c48, Y3, Y3; \ + VPADDQ Y3, Y2, Y2; \ + VPXOR Y2, Y1, Y1; \ + VPADDQ Y1, Y1, t; \ + VPSRLQ $63, Y1, Y1; \ + VPXOR t, Y1, Y1; \ + VPERMQ_0x39_Y1_Y1; \ + VPERMQ_0x4E_Y2_Y2; \ + VPERMQ_0x93_Y3_Y3; \ + VPADDQ m2, Y0, Y0; \ + VPADDQ Y1, Y0, Y0; \ + VPXOR Y0, Y3, Y3; \ + VPSHUFD $-79, Y3, Y3; \ + VPADDQ Y3, Y2, Y2; \ + VPXOR Y2, Y1, Y1; \ + VPSHUFB c40, Y1, Y1; \ + VPADDQ m3, Y0, Y0; \ + VPADDQ Y1, Y0, Y0; \ + VPXOR Y0, Y3, Y3; \ + VPSHUFB c48, Y3, Y3; \ + VPADDQ Y3, Y2, Y2; \ + VPXOR Y2, Y1, Y1; \ + VPADDQ Y1, Y1, t; \ + VPSRLQ $63, Y1, Y1; \ + VPXOR t, Y1, Y1; \ + VPERMQ_0x39_Y3_Y3; \ + VPERMQ_0x4E_Y2_Y2; \ + VPERMQ_0x93_Y1_Y1 + +#define VMOVQ_SI_X11_0 BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x1E +#define VMOVQ_SI_X12_0 BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x26 +#define VMOVQ_SI_X13_0 BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x2E +#define VMOVQ_SI_X14_0 BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x36 +#define VMOVQ_SI_X15_0 BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x3E + +#define VMOVQ_SI_X11(n) BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x5E; BYTE $n +#define VMOVQ_SI_X12(n) BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x66; BYTE $n +#define VMOVQ_SI_X13(n) BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x6E; BYTE $n +#define VMOVQ_SI_X14(n) BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x76; BYTE $n +#define VMOVQ_SI_X15(n) BYTE $0xC5; BYTE $0x7A; BYTE $0x7E; BYTE $0x7E; BYTE $n + +#define VPINSRQ_1_SI_X11_0 BYTE $0xC4; BYTE $0x63; BYTE $0xA1; BYTE $0x22; BYTE $0x1E; BYTE $0x01 +#define VPINSRQ_1_SI_X12_0 BYTE $0xC4; BYTE $0x63; BYTE $0x99; BYTE $0x22; BYTE $0x26; BYTE $0x01 +#define VPINSRQ_1_SI_X13_0 BYTE $0xC4; BYTE $0x63; BYTE $0x91; BYTE $0x22; BYTE $0x2E; BYTE $0x01 +#define VPINSRQ_1_SI_X14_0 BYTE $0xC4; BYTE $0x63; BYTE $0x89; BYTE $0x22; BYTE $0x36; BYTE $0x01 +#define VPINSRQ_1_SI_X15_0 BYTE $0xC4; BYTE $0x63; BYTE $0x81; BYTE $0x22; BYTE $0x3E; BYTE $0x01 + +#define VPINSRQ_1_SI_X11(n) BYTE $0xC4; BYTE $0x63; BYTE $0xA1; BYTE $0x22; BYTE $0x5E; BYTE $n; BYTE $0x01 +#define VPINSRQ_1_SI_X12(n) BYTE $0xC4; BYTE $0x63; BYTE $0x99; BYTE $0x22; BYTE $0x66; BYTE $n; BYTE $0x01 +#define VPINSRQ_1_SI_X13(n) BYTE $0xC4; BYTE $0x63; BYTE $0x91; BYTE $0x22; BYTE $0x6E; BYTE $n; BYTE $0x01 +#define VPINSRQ_1_SI_X14(n) BYTE $0xC4; BYTE $0x63; BYTE $0x89; BYTE $0x22; BYTE $0x76; BYTE $n; BYTE $0x01 +#define VPINSRQ_1_SI_X15(n) BYTE $0xC4; BYTE $0x63; BYTE $0x81; BYTE $0x22; BYTE $0x7E; BYTE $n; BYTE $0x01 + +#define VMOVQ_R8_X15 BYTE $0xC4; BYTE $0x41; BYTE $0xF9; BYTE $0x6E; BYTE $0xF8 +#define VPINSRQ_1_R9_X15 BYTE $0xC4; BYTE $0x43; BYTE $0x81; BYTE $0x22; BYTE $0xF9; BYTE $0x01 + +// load msg: Y12 = (i0, i1, i2, i3) +// i0, i1, i2, i3 must not be 0 +#define LOAD_MSG_AVX2_Y12(i0, i1, i2, i3) \ + VMOVQ_SI_X12(i0*8); \ + VMOVQ_SI_X11(i2*8); \ + VPINSRQ_1_SI_X12(i1*8); \ + VPINSRQ_1_SI_X11(i3*8); \ + VINSERTI128 $1, X11, Y12, Y12 + +// load msg: Y13 = (i0, i1, i2, i3) +// i0, i1, i2, i3 must not be 0 +#define LOAD_MSG_AVX2_Y13(i0, i1, i2, i3) \ + VMOVQ_SI_X13(i0*8); \ + VMOVQ_SI_X11(i2*8); \ + VPINSRQ_1_SI_X13(i1*8); \ + VPINSRQ_1_SI_X11(i3*8); \ + VINSERTI128 $1, X11, Y13, Y13 + +// load msg: Y14 = (i0, i1, i2, i3) +// i0, i1, i2, i3 must not be 0 +#define LOAD_MSG_AVX2_Y14(i0, i1, i2, i3) \ + VMOVQ_SI_X14(i0*8); \ + VMOVQ_SI_X11(i2*8); \ + VPINSRQ_1_SI_X14(i1*8); \ + VPINSRQ_1_SI_X11(i3*8); \ + VINSERTI128 $1, X11, Y14, Y14 + +// load msg: Y15 = (i0, i1, i2, i3) +// i0, i1, i2, i3 must not be 0 +#define LOAD_MSG_AVX2_Y15(i0, i1, i2, i3) \ + VMOVQ_SI_X15(i0*8); \ + VMOVQ_SI_X11(i2*8); \ + VPINSRQ_1_SI_X15(i1*8); \ + VPINSRQ_1_SI_X11(i3*8); \ + VINSERTI128 $1, X11, Y15, Y15 + +#define LOAD_MSG_AVX2_0_2_4_6_1_3_5_7_8_10_12_14_9_11_13_15() \ + VMOVQ_SI_X12_0; \ + VMOVQ_SI_X11(4*8); \ + VPINSRQ_1_SI_X12(2*8); \ + VPINSRQ_1_SI_X11(6*8); \ + VINSERTI128 $1, X11, Y12, Y12; \ + LOAD_MSG_AVX2_Y13(1, 3, 5, 7); \ + LOAD_MSG_AVX2_Y14(8, 10, 12, 14); \ + LOAD_MSG_AVX2_Y15(9, 11, 13, 15) + +#define LOAD_MSG_AVX2_14_4_9_13_10_8_15_6_1_0_11_5_12_2_7_3() \ + LOAD_MSG_AVX2_Y12(14, 4, 9, 13); \ + LOAD_MSG_AVX2_Y13(10, 8, 15, 6); \ + VMOVQ_SI_X11(11*8); \ + VPSHUFD $0x4E, 0*8(SI), X14; \ + VPINSRQ_1_SI_X11(5*8); \ + VINSERTI128 $1, X11, Y14, Y14; \ + LOAD_MSG_AVX2_Y15(12, 2, 7, 3) + +#define LOAD_MSG_AVX2_11_12_5_15_8_0_2_13_10_3_7_9_14_6_1_4() \ + VMOVQ_SI_X11(5*8); \ + VMOVDQU 11*8(SI), X12; \ + VPINSRQ_1_SI_X11(15*8); \ + VINSERTI128 $1, X11, Y12, Y12; \ + VMOVQ_SI_X13(8*8); \ + VMOVQ_SI_X11(2*8); \ + VPINSRQ_1_SI_X13_0; \ + VPINSRQ_1_SI_X11(13*8); \ + VINSERTI128 $1, X11, Y13, Y13; \ + LOAD_MSG_AVX2_Y14(10, 3, 7, 9); \ + LOAD_MSG_AVX2_Y15(14, 6, 1, 4) + +#define LOAD_MSG_AVX2_7_3_13_11_9_1_12_14_2_5_4_15_6_10_0_8() \ + LOAD_MSG_AVX2_Y12(7, 3, 13, 11); \ + LOAD_MSG_AVX2_Y13(9, 1, 12, 14); \ + LOAD_MSG_AVX2_Y14(2, 5, 4, 15); \ + VMOVQ_SI_X15(6*8); \ + VMOVQ_SI_X11_0; \ + VPINSRQ_1_SI_X15(10*8); \ + VPINSRQ_1_SI_X11(8*8); \ + VINSERTI128 $1, X11, Y15, Y15 + +#define LOAD_MSG_AVX2_9_5_2_10_0_7_4_15_14_11_6_3_1_12_8_13() \ + LOAD_MSG_AVX2_Y12(9, 5, 2, 10); \ + VMOVQ_SI_X13_0; \ + VMOVQ_SI_X11(4*8); \ + VPINSRQ_1_SI_X13(7*8); \ + VPINSRQ_1_SI_X11(15*8); \ + VINSERTI128 $1, X11, Y13, Y13; \ + LOAD_MSG_AVX2_Y14(14, 11, 6, 3); \ + LOAD_MSG_AVX2_Y15(1, 12, 8, 13) + +#define LOAD_MSG_AVX2_2_6_0_8_12_10_11_3_4_7_15_1_13_5_14_9() \ + VMOVQ_SI_X12(2*8); \ + VMOVQ_SI_X11_0; \ + VPINSRQ_1_SI_X12(6*8); \ + VPINSRQ_1_SI_X11(8*8); \ + VINSERTI128 $1, X11, Y12, Y12; \ + LOAD_MSG_AVX2_Y13(12, 10, 11, 3); \ + LOAD_MSG_AVX2_Y14(4, 7, 15, 1); \ + LOAD_MSG_AVX2_Y15(13, 5, 14, 9) + +#define LOAD_MSG_AVX2_12_1_14_4_5_15_13_10_0_6_9_8_7_3_2_11() \ + LOAD_MSG_AVX2_Y12(12, 1, 14, 4); \ + LOAD_MSG_AVX2_Y13(5, 15, 13, 10); \ + VMOVQ_SI_X14_0; \ + VPSHUFD $0x4E, 8*8(SI), X11; \ + VPINSRQ_1_SI_X14(6*8); \ + VINSERTI128 $1, X11, Y14, Y14; \ + LOAD_MSG_AVX2_Y15(7, 3, 2, 11) + +#define LOAD_MSG_AVX2_13_7_12_3_11_14_1_9_5_15_8_2_0_4_6_10() \ + LOAD_MSG_AVX2_Y12(13, 7, 12, 3); \ + LOAD_MSG_AVX2_Y13(11, 14, 1, 9); \ + LOAD_MSG_AVX2_Y14(5, 15, 8, 2); \ + VMOVQ_SI_X15_0; \ + VMOVQ_SI_X11(6*8); \ + VPINSRQ_1_SI_X15(4*8); \ + VPINSRQ_1_SI_X11(10*8); \ + VINSERTI128 $1, X11, Y15, Y15 + +#define LOAD_MSG_AVX2_6_14_11_0_15_9_3_8_12_13_1_10_2_7_4_5() \ + VMOVQ_SI_X12(6*8); \ + VMOVQ_SI_X11(11*8); \ + VPINSRQ_1_SI_X12(14*8); \ + VPINSRQ_1_SI_X11_0; \ + VINSERTI128 $1, X11, Y12, Y12; \ + LOAD_MSG_AVX2_Y13(15, 9, 3, 8); \ + VMOVQ_SI_X11(1*8); \ + VMOVDQU 12*8(SI), X14; \ + VPINSRQ_1_SI_X11(10*8); \ + VINSERTI128 $1, X11, Y14, Y14; \ + VMOVQ_SI_X15(2*8); \ + VMOVDQU 4*8(SI), X11; \ + VPINSRQ_1_SI_X15(7*8); \ + VINSERTI128 $1, X11, Y15, Y15 + +#define LOAD_MSG_AVX2_10_8_7_1_2_4_6_5_15_9_3_13_11_14_12_0() \ + LOAD_MSG_AVX2_Y12(10, 8, 7, 1); \ + VMOVQ_SI_X13(2*8); \ + VPSHUFD $0x4E, 5*8(SI), X11; \ + VPINSRQ_1_SI_X13(4*8); \ + VINSERTI128 $1, X11, Y13, Y13; \ + LOAD_MSG_AVX2_Y14(15, 9, 3, 13); \ + VMOVQ_SI_X15(11*8); \ + VMOVQ_SI_X11(12*8); \ + VPINSRQ_1_SI_X15(14*8); \ + VPINSRQ_1_SI_X11_0; \ + VINSERTI128 $1, X11, Y15, Y15 + +// func hashBlocksAVX2(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) +TEXT ·hashBlocksAVX2(SB), 4, $320-48 // frame size = 288 + 32 byte alignment + MOVQ h+0(FP), AX + MOVQ c+8(FP), BX + MOVQ flag+16(FP), CX + MOVQ blocks_base+24(FP), SI + MOVQ blocks_len+32(FP), DI + + MOVQ SP, DX + ADDQ $31, DX + ANDQ $~31, DX + + MOVQ CX, 16(DX) + XORQ CX, CX + MOVQ CX, 24(DX) + + VMOVDQU ·AVX2_c40<>(SB), Y4 + VMOVDQU ·AVX2_c48<>(SB), Y5 + + VMOVDQU 0(AX), Y8 + VMOVDQU 32(AX), Y9 + VMOVDQU ·AVX2_iv0<>(SB), Y6 + VMOVDQU ·AVX2_iv1<>(SB), Y7 + + MOVQ 0(BX), R8 + MOVQ 8(BX), R9 + MOVQ R9, 8(DX) + +loop: + ADDQ $128, R8 + MOVQ R8, 0(DX) + CMPQ R8, $128 + JGE noinc + INCQ R9 + MOVQ R9, 8(DX) + +noinc: + VMOVDQA Y8, Y0 + VMOVDQA Y9, Y1 + VMOVDQA Y6, Y2 + VPXOR 0(DX), Y7, Y3 + + LOAD_MSG_AVX2_0_2_4_6_1_3_5_7_8_10_12_14_9_11_13_15() + VMOVDQA Y12, 32(DX) + VMOVDQA Y13, 64(DX) + VMOVDQA Y14, 96(DX) + VMOVDQA Y15, 128(DX) + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_14_4_9_13_10_8_15_6_1_0_11_5_12_2_7_3() + VMOVDQA Y12, 160(DX) + VMOVDQA Y13, 192(DX) + VMOVDQA Y14, 224(DX) + VMOVDQA Y15, 256(DX) + + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_11_12_5_15_8_0_2_13_10_3_7_9_14_6_1_4() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_7_3_13_11_9_1_12_14_2_5_4_15_6_10_0_8() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_9_5_2_10_0_7_4_15_14_11_6_3_1_12_8_13() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_2_6_0_8_12_10_11_3_4_7_15_1_13_5_14_9() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_12_1_14_4_5_15_13_10_0_6_9_8_7_3_2_11() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_13_7_12_3_11_14_1_9_5_15_8_2_0_4_6_10() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_6_14_11_0_15_9_3_8_12_13_1_10_2_7_4_5() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + LOAD_MSG_AVX2_10_8_7_1_2_4_6_5_15_9_3_13_11_14_12_0() + ROUND_AVX2(Y12, Y13, Y14, Y15, Y10, Y4, Y5) + + ROUND_AVX2(32(DX), 64(DX), 96(DX), 128(DX), Y10, Y4, Y5) + ROUND_AVX2(160(DX), 192(DX), 224(DX), 256(DX), Y10, Y4, Y5) + + VPXOR Y0, Y8, Y8 + VPXOR Y1, Y9, Y9 + VPXOR Y2, Y8, Y8 + VPXOR Y3, Y9, Y9 + + LEAQ 128(SI), SI + SUBQ $128, DI + JNE loop + + MOVQ R8, 0(BX) + MOVQ R9, 8(BX) + + VMOVDQU Y8, 0(AX) + VMOVDQU Y9, 32(AX) + VZEROUPPER + + RET + +#define VPUNPCKLQDQ_X2_X2_X15 BYTE $0xC5; BYTE $0x69; BYTE $0x6C; BYTE $0xFA +#define VPUNPCKLQDQ_X3_X3_X15 BYTE $0xC5; BYTE $0x61; BYTE $0x6C; BYTE $0xFB +#define VPUNPCKLQDQ_X7_X7_X15 BYTE $0xC5; BYTE $0x41; BYTE $0x6C; BYTE $0xFF +#define VPUNPCKLQDQ_X13_X13_X15 BYTE $0xC4; BYTE $0x41; BYTE $0x11; BYTE $0x6C; BYTE $0xFD +#define VPUNPCKLQDQ_X14_X14_X15 BYTE $0xC4; BYTE $0x41; BYTE $0x09; BYTE $0x6C; BYTE $0xFE + +#define VPUNPCKHQDQ_X15_X2_X2 BYTE $0xC4; BYTE $0xC1; BYTE $0x69; BYTE $0x6D; BYTE $0xD7 +#define VPUNPCKHQDQ_X15_X3_X3 BYTE $0xC4; BYTE $0xC1; BYTE $0x61; BYTE $0x6D; BYTE $0xDF +#define VPUNPCKHQDQ_X15_X6_X6 BYTE $0xC4; BYTE $0xC1; BYTE $0x49; BYTE $0x6D; BYTE $0xF7 +#define VPUNPCKHQDQ_X15_X7_X7 BYTE $0xC4; BYTE $0xC1; BYTE $0x41; BYTE $0x6D; BYTE $0xFF +#define VPUNPCKHQDQ_X15_X3_X2 BYTE $0xC4; BYTE $0xC1; BYTE $0x61; BYTE $0x6D; BYTE $0xD7 +#define VPUNPCKHQDQ_X15_X7_X6 BYTE $0xC4; BYTE $0xC1; BYTE $0x41; BYTE $0x6D; BYTE $0xF7 +#define VPUNPCKHQDQ_X15_X13_X3 BYTE $0xC4; BYTE $0xC1; BYTE $0x11; BYTE $0x6D; BYTE $0xDF +#define VPUNPCKHQDQ_X15_X13_X7 BYTE $0xC4; BYTE $0xC1; BYTE $0x11; BYTE $0x6D; BYTE $0xFF + +#define SHUFFLE_AVX() \ + VMOVDQA X6, X13; \ + VMOVDQA X2, X14; \ + VMOVDQA X4, X6; \ + VPUNPCKLQDQ_X13_X13_X15; \ + VMOVDQA X5, X4; \ + VMOVDQA X6, X5; \ + VPUNPCKHQDQ_X15_X7_X6; \ + VPUNPCKLQDQ_X7_X7_X15; \ + VPUNPCKHQDQ_X15_X13_X7; \ + VPUNPCKLQDQ_X3_X3_X15; \ + VPUNPCKHQDQ_X15_X2_X2; \ + VPUNPCKLQDQ_X14_X14_X15; \ + VPUNPCKHQDQ_X15_X3_X3; \ + +#define SHUFFLE_AVX_INV() \ + VMOVDQA X2, X13; \ + VMOVDQA X4, X14; \ + VPUNPCKLQDQ_X2_X2_X15; \ + VMOVDQA X5, X4; \ + VPUNPCKHQDQ_X15_X3_X2; \ + VMOVDQA X14, X5; \ + VPUNPCKLQDQ_X3_X3_X15; \ + VMOVDQA X6, X14; \ + VPUNPCKHQDQ_X15_X13_X3; \ + VPUNPCKLQDQ_X7_X7_X15; \ + VPUNPCKHQDQ_X15_X6_X6; \ + VPUNPCKLQDQ_X14_X14_X15; \ + VPUNPCKHQDQ_X15_X7_X7; \ + +#define HALF_ROUND_AVX(v0, v1, v2, v3, v4, v5, v6, v7, m0, m1, m2, m3, t0, c40, c48) \ + VPADDQ m0, v0, v0; \ + VPADDQ v2, v0, v0; \ + VPADDQ m1, v1, v1; \ + VPADDQ v3, v1, v1; \ + VPXOR v0, v6, v6; \ + VPXOR v1, v7, v7; \ + VPSHUFD $-79, v6, v6; \ + VPSHUFD $-79, v7, v7; \ + VPADDQ v6, v4, v4; \ + VPADDQ v7, v5, v5; \ + VPXOR v4, v2, v2; \ + VPXOR v5, v3, v3; \ + VPSHUFB c40, v2, v2; \ + VPSHUFB c40, v3, v3; \ + VPADDQ m2, v0, v0; \ + VPADDQ v2, v0, v0; \ + VPADDQ m3, v1, v1; \ + VPADDQ v3, v1, v1; \ + VPXOR v0, v6, v6; \ + VPXOR v1, v7, v7; \ + VPSHUFB c48, v6, v6; \ + VPSHUFB c48, v7, v7; \ + VPADDQ v6, v4, v4; \ + VPADDQ v7, v5, v5; \ + VPXOR v4, v2, v2; \ + VPXOR v5, v3, v3; \ + VPADDQ v2, v2, t0; \ + VPSRLQ $63, v2, v2; \ + VPXOR t0, v2, v2; \ + VPADDQ v3, v3, t0; \ + VPSRLQ $63, v3, v3; \ + VPXOR t0, v3, v3 + +// load msg: X12 = (i0, i1), X13 = (i2, i3), X14 = (i4, i5), X15 = (i6, i7) +// i0, i1, i2, i3, i4, i5, i6, i7 must not be 0 +#define LOAD_MSG_AVX(i0, i1, i2, i3, i4, i5, i6, i7) \ + VMOVQ_SI_X12(i0*8); \ + VMOVQ_SI_X13(i2*8); \ + VMOVQ_SI_X14(i4*8); \ + VMOVQ_SI_X15(i6*8); \ + VPINSRQ_1_SI_X12(i1*8); \ + VPINSRQ_1_SI_X13(i3*8); \ + VPINSRQ_1_SI_X14(i5*8); \ + VPINSRQ_1_SI_X15(i7*8) + +// load msg: X12 = (0, 2), X13 = (4, 6), X14 = (1, 3), X15 = (5, 7) +#define LOAD_MSG_AVX_0_2_4_6_1_3_5_7() \ + VMOVQ_SI_X12_0; \ + VMOVQ_SI_X13(4*8); \ + VMOVQ_SI_X14(1*8); \ + VMOVQ_SI_X15(5*8); \ + VPINSRQ_1_SI_X12(2*8); \ + VPINSRQ_1_SI_X13(6*8); \ + VPINSRQ_1_SI_X14(3*8); \ + VPINSRQ_1_SI_X15(7*8) + +// load msg: X12 = (1, 0), X13 = (11, 5), X14 = (12, 2), X15 = (7, 3) +#define LOAD_MSG_AVX_1_0_11_5_12_2_7_3() \ + VPSHUFD $0x4E, 0*8(SI), X12; \ + VMOVQ_SI_X13(11*8); \ + VMOVQ_SI_X14(12*8); \ + VMOVQ_SI_X15(7*8); \ + VPINSRQ_1_SI_X13(5*8); \ + VPINSRQ_1_SI_X14(2*8); \ + VPINSRQ_1_SI_X15(3*8) + +// load msg: X12 = (11, 12), X13 = (5, 15), X14 = (8, 0), X15 = (2, 13) +#define LOAD_MSG_AVX_11_12_5_15_8_0_2_13() \ + VMOVDQU 11*8(SI), X12; \ + VMOVQ_SI_X13(5*8); \ + VMOVQ_SI_X14(8*8); \ + VMOVQ_SI_X15(2*8); \ + VPINSRQ_1_SI_X13(15*8); \ + VPINSRQ_1_SI_X14_0; \ + VPINSRQ_1_SI_X15(13*8) + +// load msg: X12 = (2, 5), X13 = (4, 15), X14 = (6, 10), X15 = (0, 8) +#define LOAD_MSG_AVX_2_5_4_15_6_10_0_8() \ + VMOVQ_SI_X12(2*8); \ + VMOVQ_SI_X13(4*8); \ + VMOVQ_SI_X14(6*8); \ + VMOVQ_SI_X15_0; \ + VPINSRQ_1_SI_X12(5*8); \ + VPINSRQ_1_SI_X13(15*8); \ + VPINSRQ_1_SI_X14(10*8); \ + VPINSRQ_1_SI_X15(8*8) + +// load msg: X12 = (9, 5), X13 = (2, 10), X14 = (0, 7), X15 = (4, 15) +#define LOAD_MSG_AVX_9_5_2_10_0_7_4_15() \ + VMOVQ_SI_X12(9*8); \ + VMOVQ_SI_X13(2*8); \ + VMOVQ_SI_X14_0; \ + VMOVQ_SI_X15(4*8); \ + VPINSRQ_1_SI_X12(5*8); \ + VPINSRQ_1_SI_X13(10*8); \ + VPINSRQ_1_SI_X14(7*8); \ + VPINSRQ_1_SI_X15(15*8) + +// load msg: X12 = (2, 6), X13 = (0, 8), X14 = (12, 10), X15 = (11, 3) +#define LOAD_MSG_AVX_2_6_0_8_12_10_11_3() \ + VMOVQ_SI_X12(2*8); \ + VMOVQ_SI_X13_0; \ + VMOVQ_SI_X14(12*8); \ + VMOVQ_SI_X15(11*8); \ + VPINSRQ_1_SI_X12(6*8); \ + VPINSRQ_1_SI_X13(8*8); \ + VPINSRQ_1_SI_X14(10*8); \ + VPINSRQ_1_SI_X15(3*8) + +// load msg: X12 = (0, 6), X13 = (9, 8), X14 = (7, 3), X15 = (2, 11) +#define LOAD_MSG_AVX_0_6_9_8_7_3_2_11() \ + MOVQ 0*8(SI), X12; \ + VPSHUFD $0x4E, 8*8(SI), X13; \ + MOVQ 7*8(SI), X14; \ + MOVQ 2*8(SI), X15; \ + VPINSRQ_1_SI_X12(6*8); \ + VPINSRQ_1_SI_X14(3*8); \ + VPINSRQ_1_SI_X15(11*8) + +// load msg: X12 = (6, 14), X13 = (11, 0), X14 = (15, 9), X15 = (3, 8) +#define LOAD_MSG_AVX_6_14_11_0_15_9_3_8() \ + MOVQ 6*8(SI), X12; \ + MOVQ 11*8(SI), X13; \ + MOVQ 15*8(SI), X14; \ + MOVQ 3*8(SI), X15; \ + VPINSRQ_1_SI_X12(14*8); \ + VPINSRQ_1_SI_X13_0; \ + VPINSRQ_1_SI_X14(9*8); \ + VPINSRQ_1_SI_X15(8*8) + +// load msg: X12 = (5, 15), X13 = (8, 2), X14 = (0, 4), X15 = (6, 10) +#define LOAD_MSG_AVX_5_15_8_2_0_4_6_10() \ + MOVQ 5*8(SI), X12; \ + MOVQ 8*8(SI), X13; \ + MOVQ 0*8(SI), X14; \ + MOVQ 6*8(SI), X15; \ + VPINSRQ_1_SI_X12(15*8); \ + VPINSRQ_1_SI_X13(2*8); \ + VPINSRQ_1_SI_X14(4*8); \ + VPINSRQ_1_SI_X15(10*8) + +// load msg: X12 = (12, 13), X13 = (1, 10), X14 = (2, 7), X15 = (4, 5) +#define LOAD_MSG_AVX_12_13_1_10_2_7_4_5() \ + VMOVDQU 12*8(SI), X12; \ + MOVQ 1*8(SI), X13; \ + MOVQ 2*8(SI), X14; \ + VPINSRQ_1_SI_X13(10*8); \ + VPINSRQ_1_SI_X14(7*8); \ + VMOVDQU 4*8(SI), X15 + +// load msg: X12 = (15, 9), X13 = (3, 13), X14 = (11, 14), X15 = (12, 0) +#define LOAD_MSG_AVX_15_9_3_13_11_14_12_0() \ + MOVQ 15*8(SI), X12; \ + MOVQ 3*8(SI), X13; \ + MOVQ 11*8(SI), X14; \ + MOVQ 12*8(SI), X15; \ + VPINSRQ_1_SI_X12(9*8); \ + VPINSRQ_1_SI_X13(13*8); \ + VPINSRQ_1_SI_X14(14*8); \ + VPINSRQ_1_SI_X15_0 + +// func hashBlocksAVX(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) +TEXT ·hashBlocksAVX(SB), 4, $288-48 // frame size = 272 + 16 byte alignment + MOVQ h+0(FP), AX + MOVQ c+8(FP), BX + MOVQ flag+16(FP), CX + MOVQ blocks_base+24(FP), SI + MOVQ blocks_len+32(FP), DI + + MOVQ SP, R10 + ADDQ $15, R10 + ANDQ $~15, R10 + + VMOVDQU ·AVX_c40<>(SB), X0 + VMOVDQU ·AVX_c48<>(SB), X1 + VMOVDQA X0, X8 + VMOVDQA X1, X9 + + VMOVDQU ·AVX_iv3<>(SB), X0 + VMOVDQA X0, 0(R10) + XORQ CX, 0(R10) // 0(R10) = ·AVX_iv3 ^ (CX || 0) + + VMOVDQU 0(AX), X10 + VMOVDQU 16(AX), X11 + VMOVDQU 32(AX), X2 + VMOVDQU 48(AX), X3 + + MOVQ 0(BX), R8 + MOVQ 8(BX), R9 + +loop: + ADDQ $128, R8 + CMPQ R8, $128 + JGE noinc + INCQ R9 + +noinc: + VMOVQ_R8_X15 + VPINSRQ_1_R9_X15 + + VMOVDQA X10, X0 + VMOVDQA X11, X1 + VMOVDQU ·AVX_iv0<>(SB), X4 + VMOVDQU ·AVX_iv1<>(SB), X5 + VMOVDQU ·AVX_iv2<>(SB), X6 + + VPXOR X15, X6, X6 + VMOVDQA 0(R10), X7 + + LOAD_MSG_AVX_0_2_4_6_1_3_5_7() + VMOVDQA X12, 16(R10) + VMOVDQA X13, 32(R10) + VMOVDQA X14, 48(R10) + VMOVDQA X15, 64(R10) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX(8, 10, 12, 14, 9, 11, 13, 15) + VMOVDQA X12, 80(R10) + VMOVDQA X13, 96(R10) + VMOVDQA X14, 112(R10) + VMOVDQA X15, 128(R10) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX(14, 4, 9, 13, 10, 8, 15, 6) + VMOVDQA X12, 144(R10) + VMOVDQA X13, 160(R10) + VMOVDQA X14, 176(R10) + VMOVDQA X15, 192(R10) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_1_0_11_5_12_2_7_3() + VMOVDQA X12, 208(R10) + VMOVDQA X13, 224(R10) + VMOVDQA X14, 240(R10) + VMOVDQA X15, 256(R10) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX_11_12_5_15_8_0_2_13() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX(10, 3, 7, 9, 14, 6, 1, 4) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX(7, 3, 13, 11, 9, 1, 12, 14) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_2_5_4_15_6_10_0_8() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX_9_5_2_10_0_7_4_15() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX(14, 11, 6, 3, 1, 12, 8, 13) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX_2_6_0_8_12_10_11_3() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX(4, 7, 15, 1, 13, 5, 14, 9) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX(12, 1, 14, 4, 5, 15, 13, 10) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_0_6_9_8_7_3_2_11() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX(13, 7, 12, 3, 11, 14, 1, 9) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_5_15_8_2_0_4_6_10() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX_6_14_11_0_15_9_3_8() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_12_13_1_10_2_7_4_5() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + LOAD_MSG_AVX(10, 8, 7, 1, 2, 4, 6, 5) + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX() + LOAD_MSG_AVX_15_9_3_13_11_14_12_0() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, X12, X13, X14, X15, X15, X8, X9) + SHUFFLE_AVX_INV() + + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, 16(R10), 32(R10), 48(R10), 64(R10), X15, X8, X9) + SHUFFLE_AVX() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, 80(R10), 96(R10), 112(R10), 128(R10), X15, X8, X9) + SHUFFLE_AVX_INV() + + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, 144(R10), 160(R10), 176(R10), 192(R10), X15, X8, X9) + SHUFFLE_AVX() + HALF_ROUND_AVX(X0, X1, X2, X3, X4, X5, X6, X7, 208(R10), 224(R10), 240(R10), 256(R10), X15, X8, X9) + SHUFFLE_AVX_INV() + + VMOVDQU 32(AX), X14 + VMOVDQU 48(AX), X15 + VPXOR X0, X10, X10 + VPXOR X1, X11, X11 + VPXOR X2, X14, X14 + VPXOR X3, X15, X15 + VPXOR X4, X10, X10 + VPXOR X5, X11, X11 + VPXOR X6, X14, X2 + VPXOR X7, X15, X3 + VMOVDQU X2, 32(AX) + VMOVDQU X3, 48(AX) + + LEAQ 128(SI), SI + SUBQ $128, DI + JNE loop + + VMOVDQU X10, 0(AX) + VMOVDQU X11, 16(AX) + + MOVQ R8, 0(BX) + MOVQ R9, 8(BX) + VZEROUPPER + + RET diff --git a/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.go b/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.go new file mode 100644 index 00000000..5fa1b328 --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.go @@ -0,0 +1,25 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !go1.7 && amd64 && gc && !purego +// +build !go1.7,amd64,gc,!purego + +package blake2b + +import "golang.org/x/sys/cpu" + +func init() { + useSSE4 = cpu.X86.HasSSE41 +} + +//go:noescape +func hashBlocksSSE4(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) + +func hashBlocks(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) { + if useSSE4 { + hashBlocksSSE4(h, c, flag, blocks) + } else { + hashBlocksGeneric(h, c, flag, blocks) + } +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.s b/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.s new file mode 100644 index 00000000..ae75eb9a --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2b_amd64.s @@ -0,0 +1,279 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && gc && !purego +// +build amd64,gc,!purego + +#include "textflag.h" + +DATA ·iv0<>+0x00(SB)/8, $0x6a09e667f3bcc908 +DATA ·iv0<>+0x08(SB)/8, $0xbb67ae8584caa73b +GLOBL ·iv0<>(SB), (NOPTR+RODATA), $16 + +DATA ·iv1<>+0x00(SB)/8, $0x3c6ef372fe94f82b +DATA ·iv1<>+0x08(SB)/8, $0xa54ff53a5f1d36f1 +GLOBL ·iv1<>(SB), (NOPTR+RODATA), $16 + +DATA ·iv2<>+0x00(SB)/8, $0x510e527fade682d1 +DATA ·iv2<>+0x08(SB)/8, $0x9b05688c2b3e6c1f +GLOBL ·iv2<>(SB), (NOPTR+RODATA), $16 + +DATA ·iv3<>+0x00(SB)/8, $0x1f83d9abfb41bd6b +DATA ·iv3<>+0x08(SB)/8, $0x5be0cd19137e2179 +GLOBL ·iv3<>(SB), (NOPTR+RODATA), $16 + +DATA ·c40<>+0x00(SB)/8, $0x0201000706050403 +DATA ·c40<>+0x08(SB)/8, $0x0a09080f0e0d0c0b +GLOBL ·c40<>(SB), (NOPTR+RODATA), $16 + +DATA ·c48<>+0x00(SB)/8, $0x0100070605040302 +DATA ·c48<>+0x08(SB)/8, $0x09080f0e0d0c0b0a +GLOBL ·c48<>(SB), (NOPTR+RODATA), $16 + +#define SHUFFLE(v2, v3, v4, v5, v6, v7, t1, t2) \ + MOVO v4, t1; \ + MOVO v5, v4; \ + MOVO t1, v5; \ + MOVO v6, t1; \ + PUNPCKLQDQ v6, t2; \ + PUNPCKHQDQ v7, v6; \ + PUNPCKHQDQ t2, v6; \ + PUNPCKLQDQ v7, t2; \ + MOVO t1, v7; \ + MOVO v2, t1; \ + PUNPCKHQDQ t2, v7; \ + PUNPCKLQDQ v3, t2; \ + PUNPCKHQDQ t2, v2; \ + PUNPCKLQDQ t1, t2; \ + PUNPCKHQDQ t2, v3 + +#define SHUFFLE_INV(v2, v3, v4, v5, v6, v7, t1, t2) \ + MOVO v4, t1; \ + MOVO v5, v4; \ + MOVO t1, v5; \ + MOVO v2, t1; \ + PUNPCKLQDQ v2, t2; \ + PUNPCKHQDQ v3, v2; \ + PUNPCKHQDQ t2, v2; \ + PUNPCKLQDQ v3, t2; \ + MOVO t1, v3; \ + MOVO v6, t1; \ + PUNPCKHQDQ t2, v3; \ + PUNPCKLQDQ v7, t2; \ + PUNPCKHQDQ t2, v6; \ + PUNPCKLQDQ t1, t2; \ + PUNPCKHQDQ t2, v7 + +#define HALF_ROUND(v0, v1, v2, v3, v4, v5, v6, v7, m0, m1, m2, m3, t0, c40, c48) \ + PADDQ m0, v0; \ + PADDQ m1, v1; \ + PADDQ v2, v0; \ + PADDQ v3, v1; \ + PXOR v0, v6; \ + PXOR v1, v7; \ + PSHUFD $0xB1, v6, v6; \ + PSHUFD $0xB1, v7, v7; \ + PADDQ v6, v4; \ + PADDQ v7, v5; \ + PXOR v4, v2; \ + PXOR v5, v3; \ + PSHUFB c40, v2; \ + PSHUFB c40, v3; \ + PADDQ m2, v0; \ + PADDQ m3, v1; \ + PADDQ v2, v0; \ + PADDQ v3, v1; \ + PXOR v0, v6; \ + PXOR v1, v7; \ + PSHUFB c48, v6; \ + PSHUFB c48, v7; \ + PADDQ v6, v4; \ + PADDQ v7, v5; \ + PXOR v4, v2; \ + PXOR v5, v3; \ + MOVOU v2, t0; \ + PADDQ v2, t0; \ + PSRLQ $63, v2; \ + PXOR t0, v2; \ + MOVOU v3, t0; \ + PADDQ v3, t0; \ + PSRLQ $63, v3; \ + PXOR t0, v3 + +#define LOAD_MSG(m0, m1, m2, m3, src, i0, i1, i2, i3, i4, i5, i6, i7) \ + MOVQ i0*8(src), m0; \ + PINSRQ $1, i1*8(src), m0; \ + MOVQ i2*8(src), m1; \ + PINSRQ $1, i3*8(src), m1; \ + MOVQ i4*8(src), m2; \ + PINSRQ $1, i5*8(src), m2; \ + MOVQ i6*8(src), m3; \ + PINSRQ $1, i7*8(src), m3 + +// func hashBlocksSSE4(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) +TEXT ·hashBlocksSSE4(SB), 4, $288-48 // frame size = 272 + 16 byte alignment + MOVQ h+0(FP), AX + MOVQ c+8(FP), BX + MOVQ flag+16(FP), CX + MOVQ blocks_base+24(FP), SI + MOVQ blocks_len+32(FP), DI + + MOVQ SP, R10 + ADDQ $15, R10 + ANDQ $~15, R10 + + MOVOU ·iv3<>(SB), X0 + MOVO X0, 0(R10) + XORQ CX, 0(R10) // 0(R10) = ·iv3 ^ (CX || 0) + + MOVOU ·c40<>(SB), X13 + MOVOU ·c48<>(SB), X14 + + MOVOU 0(AX), X12 + MOVOU 16(AX), X15 + + MOVQ 0(BX), R8 + MOVQ 8(BX), R9 + +loop: + ADDQ $128, R8 + CMPQ R8, $128 + JGE noinc + INCQ R9 + +noinc: + MOVQ R8, X8 + PINSRQ $1, R9, X8 + + MOVO X12, X0 + MOVO X15, X1 + MOVOU 32(AX), X2 + MOVOU 48(AX), X3 + MOVOU ·iv0<>(SB), X4 + MOVOU ·iv1<>(SB), X5 + MOVOU ·iv2<>(SB), X6 + + PXOR X8, X6 + MOVO 0(R10), X7 + + LOAD_MSG(X8, X9, X10, X11, SI, 0, 2, 4, 6, 1, 3, 5, 7) + MOVO X8, 16(R10) + MOVO X9, 32(R10) + MOVO X10, 48(R10) + MOVO X11, 64(R10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 8, 10, 12, 14, 9, 11, 13, 15) + MOVO X8, 80(R10) + MOVO X9, 96(R10) + MOVO X10, 112(R10) + MOVO X11, 128(R10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 14, 4, 9, 13, 10, 8, 15, 6) + MOVO X8, 144(R10) + MOVO X9, 160(R10) + MOVO X10, 176(R10) + MOVO X11, 192(R10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 1, 0, 11, 5, 12, 2, 7, 3) + MOVO X8, 208(R10) + MOVO X9, 224(R10) + MOVO X10, 240(R10) + MOVO X11, 256(R10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 11, 12, 5, 15, 8, 0, 2, 13) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 10, 3, 7, 9, 14, 6, 1, 4) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 7, 3, 13, 11, 9, 1, 12, 14) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 2, 5, 4, 15, 6, 10, 0, 8) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 9, 5, 2, 10, 0, 7, 4, 15) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 14, 11, 6, 3, 1, 12, 8, 13) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 2, 6, 0, 8, 12, 10, 11, 3) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 4, 7, 15, 1, 13, 5, 14, 9) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 12, 1, 14, 4, 5, 15, 13, 10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 0, 6, 9, 8, 7, 3, 2, 11) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 13, 7, 12, 3, 11, 14, 1, 9) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 5, 15, 8, 2, 0, 4, 6, 10) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 6, 14, 11, 0, 15, 9, 3, 8) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 12, 13, 1, 10, 2, 7, 4, 5) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + LOAD_MSG(X8, X9, X10, X11, SI, 10, 8, 7, 1, 2, 4, 6, 5) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + LOAD_MSG(X8, X9, X10, X11, SI, 15, 9, 3, 13, 11, 14, 12, 0) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, 16(R10), 32(R10), 48(R10), 64(R10), X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, 80(R10), 96(R10), 112(R10), 128(R10), X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, 144(R10), 160(R10), 176(R10), 192(R10), X11, X13, X14) + SHUFFLE(X2, X3, X4, X5, X6, X7, X8, X9) + HALF_ROUND(X0, X1, X2, X3, X4, X5, X6, X7, 208(R10), 224(R10), 240(R10), 256(R10), X11, X13, X14) + SHUFFLE_INV(X2, X3, X4, X5, X6, X7, X8, X9) + + MOVOU 32(AX), X10 + MOVOU 48(AX), X11 + PXOR X0, X12 + PXOR X1, X15 + PXOR X2, X10 + PXOR X3, X11 + PXOR X4, X12 + PXOR X5, X15 + PXOR X6, X10 + PXOR X7, X11 + MOVOU X10, 32(AX) + MOVOU X11, 48(AX) + + LEAQ 128(SI), SI + SUBQ $128, DI + JNE loop + + MOVOU X12, 0(AX) + MOVOU X15, 16(AX) + + MOVQ R8, 0(BX) + MOVQ R9, 8(BX) + + RET diff --git a/vendor/golang.org/x/crypto/blake2b/blake2b_generic.go b/vendor/golang.org/x/crypto/blake2b/blake2b_generic.go new file mode 100644 index 00000000..3168a8aa --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2b_generic.go @@ -0,0 +1,182 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package blake2b + +import ( + "encoding/binary" + "math/bits" +) + +// the precomputed values for BLAKE2b +// there are 12 16-byte arrays - one for each round +// the entries are calculated from the sigma constants. +var precomputed = [12][16]byte{ + {0, 2, 4, 6, 1, 3, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15}, + {14, 4, 9, 13, 10, 8, 15, 6, 1, 0, 11, 5, 12, 2, 7, 3}, + {11, 12, 5, 15, 8, 0, 2, 13, 10, 3, 7, 9, 14, 6, 1, 4}, + {7, 3, 13, 11, 9, 1, 12, 14, 2, 5, 4, 15, 6, 10, 0, 8}, + {9, 5, 2, 10, 0, 7, 4, 15, 14, 11, 6, 3, 1, 12, 8, 13}, + {2, 6, 0, 8, 12, 10, 11, 3, 4, 7, 15, 1, 13, 5, 14, 9}, + {12, 1, 14, 4, 5, 15, 13, 10, 0, 6, 9, 8, 7, 3, 2, 11}, + {13, 7, 12, 3, 11, 14, 1, 9, 5, 15, 8, 2, 0, 4, 6, 10}, + {6, 14, 11, 0, 15, 9, 3, 8, 12, 13, 1, 10, 2, 7, 4, 5}, + {10, 8, 7, 1, 2, 4, 6, 5, 15, 9, 3, 13, 11, 14, 12, 0}, + {0, 2, 4, 6, 1, 3, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15}, // equal to the first + {14, 4, 9, 13, 10, 8, 15, 6, 1, 0, 11, 5, 12, 2, 7, 3}, // equal to the second +} + +func hashBlocksGeneric(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) { + var m [16]uint64 + c0, c1 := c[0], c[1] + + for i := 0; i < len(blocks); { + c0 += BlockSize + if c0 < BlockSize { + c1++ + } + + v0, v1, v2, v3, v4, v5, v6, v7 := h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7] + v8, v9, v10, v11, v12, v13, v14, v15 := iv[0], iv[1], iv[2], iv[3], iv[4], iv[5], iv[6], iv[7] + v12 ^= c0 + v13 ^= c1 + v14 ^= flag + + for j := range m { + m[j] = binary.LittleEndian.Uint64(blocks[i:]) + i += 8 + } + + for j := range precomputed { + s := &(precomputed[j]) + + v0 += m[s[0]] + v0 += v4 + v12 ^= v0 + v12 = bits.RotateLeft64(v12, -32) + v8 += v12 + v4 ^= v8 + v4 = bits.RotateLeft64(v4, -24) + v1 += m[s[1]] + v1 += v5 + v13 ^= v1 + v13 = bits.RotateLeft64(v13, -32) + v9 += v13 + v5 ^= v9 + v5 = bits.RotateLeft64(v5, -24) + v2 += m[s[2]] + v2 += v6 + v14 ^= v2 + v14 = bits.RotateLeft64(v14, -32) + v10 += v14 + v6 ^= v10 + v6 = bits.RotateLeft64(v6, -24) + v3 += m[s[3]] + v3 += v7 + v15 ^= v3 + v15 = bits.RotateLeft64(v15, -32) + v11 += v15 + v7 ^= v11 + v7 = bits.RotateLeft64(v7, -24) + + v0 += m[s[4]] + v0 += v4 + v12 ^= v0 + v12 = bits.RotateLeft64(v12, -16) + v8 += v12 + v4 ^= v8 + v4 = bits.RotateLeft64(v4, -63) + v1 += m[s[5]] + v1 += v5 + v13 ^= v1 + v13 = bits.RotateLeft64(v13, -16) + v9 += v13 + v5 ^= v9 + v5 = bits.RotateLeft64(v5, -63) + v2 += m[s[6]] + v2 += v6 + v14 ^= v2 + v14 = bits.RotateLeft64(v14, -16) + v10 += v14 + v6 ^= v10 + v6 = bits.RotateLeft64(v6, -63) + v3 += m[s[7]] + v3 += v7 + v15 ^= v3 + v15 = bits.RotateLeft64(v15, -16) + v11 += v15 + v7 ^= v11 + v7 = bits.RotateLeft64(v7, -63) + + v0 += m[s[8]] + v0 += v5 + v15 ^= v0 + v15 = bits.RotateLeft64(v15, -32) + v10 += v15 + v5 ^= v10 + v5 = bits.RotateLeft64(v5, -24) + v1 += m[s[9]] + v1 += v6 + v12 ^= v1 + v12 = bits.RotateLeft64(v12, -32) + v11 += v12 + v6 ^= v11 + v6 = bits.RotateLeft64(v6, -24) + v2 += m[s[10]] + v2 += v7 + v13 ^= v2 + v13 = bits.RotateLeft64(v13, -32) + v8 += v13 + v7 ^= v8 + v7 = bits.RotateLeft64(v7, -24) + v3 += m[s[11]] + v3 += v4 + v14 ^= v3 + v14 = bits.RotateLeft64(v14, -32) + v9 += v14 + v4 ^= v9 + v4 = bits.RotateLeft64(v4, -24) + + v0 += m[s[12]] + v0 += v5 + v15 ^= v0 + v15 = bits.RotateLeft64(v15, -16) + v10 += v15 + v5 ^= v10 + v5 = bits.RotateLeft64(v5, -63) + v1 += m[s[13]] + v1 += v6 + v12 ^= v1 + v12 = bits.RotateLeft64(v12, -16) + v11 += v12 + v6 ^= v11 + v6 = bits.RotateLeft64(v6, -63) + v2 += m[s[14]] + v2 += v7 + v13 ^= v2 + v13 = bits.RotateLeft64(v13, -16) + v8 += v13 + v7 ^= v8 + v7 = bits.RotateLeft64(v7, -63) + v3 += m[s[15]] + v3 += v4 + v14 ^= v3 + v14 = bits.RotateLeft64(v14, -16) + v9 += v14 + v4 ^= v9 + v4 = bits.RotateLeft64(v4, -63) + + } + + h[0] ^= v0 ^ v8 + h[1] ^= v1 ^ v9 + h[2] ^= v2 ^ v10 + h[3] ^= v3 ^ v11 + h[4] ^= v4 ^ v12 + h[5] ^= v5 ^ v13 + h[6] ^= v6 ^ v14 + h[7] ^= v7 ^ v15 + } + c[0], c[1] = c0, c1 +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2b_ref.go b/vendor/golang.org/x/crypto/blake2b/blake2b_ref.go new file mode 100644 index 00000000..b0137cdf --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2b_ref.go @@ -0,0 +1,12 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !amd64 || purego || !gc +// +build !amd64 purego !gc + +package blake2b + +func hashBlocks(h *[8]uint64, c *[2]uint64, flag uint64, blocks []byte) { + hashBlocksGeneric(h, c, flag, blocks) +} diff --git a/vendor/golang.org/x/crypto/blake2b/blake2x.go b/vendor/golang.org/x/crypto/blake2b/blake2x.go new file mode 100644 index 00000000..52c414db --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/blake2x.go @@ -0,0 +1,177 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package blake2b + +import ( + "encoding/binary" + "errors" + "io" +) + +// XOF defines the interface to hash functions that +// support arbitrary-length output. +type XOF interface { + // Write absorbs more data into the hash's state. It panics if called + // after Read. + io.Writer + + // Read reads more output from the hash. It returns io.EOF if the limit + // has been reached. + io.Reader + + // Clone returns a copy of the XOF in its current state. + Clone() XOF + + // Reset resets the XOF to its initial state. + Reset() +} + +// OutputLengthUnknown can be used as the size argument to NewXOF to indicate +// the length of the output is not known in advance. +const OutputLengthUnknown = 0 + +// magicUnknownOutputLength is a magic value for the output size that indicates +// an unknown number of output bytes. +const magicUnknownOutputLength = (1 << 32) - 1 + +// maxOutputLength is the absolute maximum number of bytes to produce when the +// number of output bytes is unknown. +const maxOutputLength = (1 << 32) * 64 + +// NewXOF creates a new variable-output-length hash. The hash either produce a +// known number of bytes (1 <= size < 2**32-1), or an unknown number of bytes +// (size == OutputLengthUnknown). In the latter case, an absolute limit of +// 256GiB applies. +// +// A non-nil key turns the hash into a MAC. The key must between +// zero and 32 bytes long. +func NewXOF(size uint32, key []byte) (XOF, error) { + if len(key) > Size { + return nil, errKeySize + } + if size == magicUnknownOutputLength { + // 2^32-1 indicates an unknown number of bytes and thus isn't a + // valid length. + return nil, errors.New("blake2b: XOF length too large") + } + if size == OutputLengthUnknown { + size = magicUnknownOutputLength + } + x := &xof{ + d: digest{ + size: Size, + keyLen: len(key), + }, + length: size, + } + copy(x.d.key[:], key) + x.Reset() + return x, nil +} + +type xof struct { + d digest + length uint32 + remaining uint64 + cfg, root, block [Size]byte + offset int + nodeOffset uint32 + readMode bool +} + +func (x *xof) Write(p []byte) (n int, err error) { + if x.readMode { + panic("blake2b: write to XOF after read") + } + return x.d.Write(p) +} + +func (x *xof) Clone() XOF { + clone := *x + return &clone +} + +func (x *xof) Reset() { + x.cfg[0] = byte(Size) + binary.LittleEndian.PutUint32(x.cfg[4:], uint32(Size)) // leaf length + binary.LittleEndian.PutUint32(x.cfg[12:], x.length) // XOF length + x.cfg[17] = byte(Size) // inner hash size + + x.d.Reset() + x.d.h[1] ^= uint64(x.length) << 32 + + x.remaining = uint64(x.length) + if x.remaining == magicUnknownOutputLength { + x.remaining = maxOutputLength + } + x.offset, x.nodeOffset = 0, 0 + x.readMode = false +} + +func (x *xof) Read(p []byte) (n int, err error) { + if !x.readMode { + x.d.finalize(&x.root) + x.readMode = true + } + + if x.remaining == 0 { + return 0, io.EOF + } + + n = len(p) + if uint64(n) > x.remaining { + n = int(x.remaining) + p = p[:n] + } + + if x.offset > 0 { + blockRemaining := Size - x.offset + if n < blockRemaining { + x.offset += copy(p, x.block[x.offset:]) + x.remaining -= uint64(n) + return + } + copy(p, x.block[x.offset:]) + p = p[blockRemaining:] + x.offset = 0 + x.remaining -= uint64(blockRemaining) + } + + for len(p) >= Size { + binary.LittleEndian.PutUint32(x.cfg[8:], x.nodeOffset) + x.nodeOffset++ + + x.d.initConfig(&x.cfg) + x.d.Write(x.root[:]) + x.d.finalize(&x.block) + + copy(p, x.block[:]) + p = p[Size:] + x.remaining -= uint64(Size) + } + + if todo := len(p); todo > 0 { + if x.remaining < uint64(Size) { + x.cfg[0] = byte(x.remaining) + } + binary.LittleEndian.PutUint32(x.cfg[8:], x.nodeOffset) + x.nodeOffset++ + + x.d.initConfig(&x.cfg) + x.d.Write(x.root[:]) + x.d.finalize(&x.block) + + x.offset = copy(p, x.block[:todo]) + x.remaining -= uint64(todo) + } + return +} + +func (d *digest) initConfig(cfg *[Size]byte) { + d.offset, d.c[0], d.c[1] = 0, 0, 0 + for i := range d.h { + d.h[i] = iv[i] ^ binary.LittleEndian.Uint64(cfg[i*8:]) + } +} diff --git a/vendor/golang.org/x/crypto/blake2b/register.go b/vendor/golang.org/x/crypto/blake2b/register.go new file mode 100644 index 00000000..9d863396 --- /dev/null +++ b/vendor/golang.org/x/crypto/blake2b/register.go @@ -0,0 +1,33 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build go1.9 +// +build go1.9 + +package blake2b + +import ( + "crypto" + "hash" +) + +func init() { + newHash256 := func() hash.Hash { + h, _ := New256(nil) + return h + } + newHash384 := func() hash.Hash { + h, _ := New384(nil) + return h + } + + newHash512 := func() hash.Hash { + h, _ := New512(nil) + return h + } + + crypto.RegisterHash(crypto.BLAKE2b_256, newHash256) + crypto.RegisterHash(crypto.BLAKE2b_384, newHash384) + crypto.RegisterHash(crypto.BLAKE2b_512, newHash512) +} diff --git a/vendor/golang.org/x/crypto/sha3/doc.go b/vendor/golang.org/x/crypto/sha3/doc.go new file mode 100644 index 00000000..decd8cf9 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/doc.go @@ -0,0 +1,62 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package sha3 implements the SHA-3 fixed-output-length hash functions and +// the SHAKE variable-output-length hash functions defined by FIPS-202. +// +// Both types of hash function use the "sponge" construction and the Keccak +// permutation. For a detailed specification see http://keccak.noekeon.org/ +// +// # Guidance +// +// If you aren't sure what function you need, use SHAKE256 with at least 64 +// bytes of output. The SHAKE instances are faster than the SHA3 instances; +// the latter have to allocate memory to conform to the hash.Hash interface. +// +// If you need a secret-key MAC (message authentication code), prepend the +// secret key to the input, hash with SHAKE256 and read at least 32 bytes of +// output. +// +// # Security strengths +// +// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security +// strength against preimage attacks of x bits. Since they only produce "x" +// bits of output, their collision-resistance is only "x/2" bits. +// +// The SHAKE-256 and -128 functions have a generic security strength of 256 and +// 128 bits against all attacks, provided that at least 2x bits of their output +// is used. Requesting more than 64 or 32 bytes of output, respectively, does +// not increase the collision-resistance of the SHAKE functions. +// +// # The sponge construction +// +// A sponge builds a pseudo-random function from a public pseudo-random +// permutation, by applying the permutation to a state of "rate + capacity" +// bytes, but hiding "capacity" of the bytes. +// +// A sponge starts out with a zero state. To hash an input using a sponge, up +// to "rate" bytes of the input are XORed into the sponge's state. The sponge +// is then "full" and the permutation is applied to "empty" it. This process is +// repeated until all the input has been "absorbed". The input is then padded. +// The digest is "squeezed" from the sponge in the same way, except that output +// is copied out instead of input being XORed in. +// +// A sponge is parameterized by its generic security strength, which is equal +// to half its capacity; capacity + rate is equal to the permutation's width. +// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means +// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. +// +// # Recommendations +// +// The SHAKE functions are recommended for most new uses. They can produce +// output of arbitrary length. SHAKE256, with an output length of at least +// 64 bytes, provides 256-bit security against all attacks. The Keccak team +// recommends it for most applications upgrading from SHA2-512. (NIST chose a +// much stronger, but much slower, sponge instance for SHA3-512.) +// +// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. +// They produce output of the same length, with the same security strengths +// against all attacks. This means, in particular, that SHA3-256 only has +// 128-bit collision resistance, because its output length is 32 bytes. +package sha3 // import "golang.org/x/crypto/sha3" diff --git a/vendor/golang.org/x/crypto/sha3/hashes.go b/vendor/golang.org/x/crypto/sha3/hashes.go new file mode 100644 index 00000000..0d8043fd --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/hashes.go @@ -0,0 +1,97 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file provides functions for creating instances of the SHA-3 +// and SHAKE hash functions, as well as utility functions for hashing +// bytes. + +import ( + "hash" +) + +// New224 creates a new SHA3-224 hash. +// Its generic security strength is 224 bits against preimage attacks, +// and 112 bits against collision attacks. +func New224() hash.Hash { + if h := new224Asm(); h != nil { + return h + } + return &state{rate: 144, outputLen: 28, dsbyte: 0x06} +} + +// New256 creates a new SHA3-256 hash. +// Its generic security strength is 256 bits against preimage attacks, +// and 128 bits against collision attacks. +func New256() hash.Hash { + if h := new256Asm(); h != nil { + return h + } + return &state{rate: 136, outputLen: 32, dsbyte: 0x06} +} + +// New384 creates a new SHA3-384 hash. +// Its generic security strength is 384 bits against preimage attacks, +// and 192 bits against collision attacks. +func New384() hash.Hash { + if h := new384Asm(); h != nil { + return h + } + return &state{rate: 104, outputLen: 48, dsbyte: 0x06} +} + +// New512 creates a new SHA3-512 hash. +// Its generic security strength is 512 bits against preimage attacks, +// and 256 bits against collision attacks. +func New512() hash.Hash { + if h := new512Asm(); h != nil { + return h + } + return &state{rate: 72, outputLen: 64, dsbyte: 0x06} +} + +// NewLegacyKeccak256 creates a new Keccak-256 hash. +// +// Only use this function if you require compatibility with an existing cryptosystem +// that uses non-standard padding. All other users should use New256 instead. +func NewLegacyKeccak256() hash.Hash { return &state{rate: 136, outputLen: 32, dsbyte: 0x01} } + +// NewLegacyKeccak512 creates a new Keccak-512 hash. +// +// Only use this function if you require compatibility with an existing cryptosystem +// that uses non-standard padding. All other users should use New512 instead. +func NewLegacyKeccak512() hash.Hash { return &state{rate: 72, outputLen: 64, dsbyte: 0x01} } + +// Sum224 returns the SHA3-224 digest of the data. +func Sum224(data []byte) (digest [28]byte) { + h := New224() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum256 returns the SHA3-256 digest of the data. +func Sum256(data []byte) (digest [32]byte) { + h := New256() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum384 returns the SHA3-384 digest of the data. +func Sum384(data []byte) (digest [48]byte) { + h := New384() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum512 returns the SHA3-512 digest of the data. +func Sum512(data []byte) (digest [64]byte) { + h := New512() + h.Write(data) + h.Sum(digest[:0]) + return +} diff --git a/vendor/golang.org/x/crypto/sha3/hashes_generic.go b/vendor/golang.org/x/crypto/sha3/hashes_generic.go new file mode 100644 index 00000000..c74fc20f --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/hashes_generic.go @@ -0,0 +1,28 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !gc || purego || !s390x +// +build !gc purego !s390x + +package sha3 + +import ( + "hash" +) + +// new224Asm returns an assembly implementation of SHA3-224 if available, +// otherwise it returns nil. +func new224Asm() hash.Hash { return nil } + +// new256Asm returns an assembly implementation of SHA3-256 if available, +// otherwise it returns nil. +func new256Asm() hash.Hash { return nil } + +// new384Asm returns an assembly implementation of SHA3-384 if available, +// otherwise it returns nil. +func new384Asm() hash.Hash { return nil } + +// new512Asm returns an assembly implementation of SHA3-512 if available, +// otherwise it returns nil. +func new512Asm() hash.Hash { return nil } diff --git a/vendor/golang.org/x/crypto/sha3/keccakf.go b/vendor/golang.org/x/crypto/sha3/keccakf.go new file mode 100644 index 00000000..e5faa375 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/keccakf.go @@ -0,0 +1,415 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !amd64 || purego || !gc +// +build !amd64 purego !gc + +package sha3 + +import "math/bits" + +// rc stores the round constants for use in the ι step. +var rc = [24]uint64{ + 0x0000000000000001, + 0x0000000000008082, + 0x800000000000808A, + 0x8000000080008000, + 0x000000000000808B, + 0x0000000080000001, + 0x8000000080008081, + 0x8000000000008009, + 0x000000000000008A, + 0x0000000000000088, + 0x0000000080008009, + 0x000000008000000A, + 0x000000008000808B, + 0x800000000000008B, + 0x8000000000008089, + 0x8000000000008003, + 0x8000000000008002, + 0x8000000000000080, + 0x000000000000800A, + 0x800000008000000A, + 0x8000000080008081, + 0x8000000000008080, + 0x0000000080000001, + 0x8000000080008008, +} + +// keccakF1600 applies the Keccak permutation to a 1600b-wide +// state represented as a slice of 25 uint64s. +func keccakF1600(a *[25]uint64) { + // Implementation translated from Keccak-inplace.c + // in the keccak reference code. + var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 + + for i := 0; i < 24; i += 4 { + // Combines the 5 steps in each round into 2 steps. + // Unrolls 4 rounds per loop and spreads some steps across rounds. + + // Round 1 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[6] ^ d1 + bc1 = bits.RotateLeft64(t, 44) + t = a[12] ^ d2 + bc2 = bits.RotateLeft64(t, 43) + t = a[18] ^ d3 + bc3 = bits.RotateLeft64(t, 21) + t = a[24] ^ d4 + bc4 = bits.RotateLeft64(t, 14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i] + a[6] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc2 = bits.RotateLeft64(t, 3) + t = a[16] ^ d1 + bc3 = bits.RotateLeft64(t, 45) + t = a[22] ^ d2 + bc4 = bits.RotateLeft64(t, 61) + t = a[3] ^ d3 + bc0 = bits.RotateLeft64(t, 28) + t = a[9] ^ d4 + bc1 = bits.RotateLeft64(t, 20) + a[10] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc4 = bits.RotateLeft64(t, 18) + t = a[1] ^ d1 + bc0 = bits.RotateLeft64(t, 1) + t = a[7] ^ d2 + bc1 = bits.RotateLeft64(t, 6) + t = a[13] ^ d3 + bc2 = bits.RotateLeft64(t, 25) + t = a[19] ^ d4 + bc3 = bits.RotateLeft64(t, 8) + a[20] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc1 = bits.RotateLeft64(t, 36) + t = a[11] ^ d1 + bc2 = bits.RotateLeft64(t, 10) + t = a[17] ^ d2 + bc3 = bits.RotateLeft64(t, 15) + t = a[23] ^ d3 + bc4 = bits.RotateLeft64(t, 56) + t = a[4] ^ d4 + bc0 = bits.RotateLeft64(t, 27) + a[5] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc3 = bits.RotateLeft64(t, 41) + t = a[21] ^ d1 + bc4 = bits.RotateLeft64(t, 2) + t = a[2] ^ d2 + bc0 = bits.RotateLeft64(t, 62) + t = a[8] ^ d3 + bc1 = bits.RotateLeft64(t, 55) + t = a[14] ^ d4 + bc2 = bits.RotateLeft64(t, 39) + a[15] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + // Round 2 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[16] ^ d1 + bc1 = bits.RotateLeft64(t, 44) + t = a[7] ^ d2 + bc2 = bits.RotateLeft64(t, 43) + t = a[23] ^ d3 + bc3 = bits.RotateLeft64(t, 21) + t = a[14] ^ d4 + bc4 = bits.RotateLeft64(t, 14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+1] + a[16] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc2 = bits.RotateLeft64(t, 3) + t = a[11] ^ d1 + bc3 = bits.RotateLeft64(t, 45) + t = a[2] ^ d2 + bc4 = bits.RotateLeft64(t, 61) + t = a[18] ^ d3 + bc0 = bits.RotateLeft64(t, 28) + t = a[9] ^ d4 + bc1 = bits.RotateLeft64(t, 20) + a[20] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc4 = bits.RotateLeft64(t, 18) + t = a[6] ^ d1 + bc0 = bits.RotateLeft64(t, 1) + t = a[22] ^ d2 + bc1 = bits.RotateLeft64(t, 6) + t = a[13] ^ d3 + bc2 = bits.RotateLeft64(t, 25) + t = a[4] ^ d4 + bc3 = bits.RotateLeft64(t, 8) + a[15] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc1 = bits.RotateLeft64(t, 36) + t = a[1] ^ d1 + bc2 = bits.RotateLeft64(t, 10) + t = a[17] ^ d2 + bc3 = bits.RotateLeft64(t, 15) + t = a[8] ^ d3 + bc4 = bits.RotateLeft64(t, 56) + t = a[24] ^ d4 + bc0 = bits.RotateLeft64(t, 27) + a[10] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc3 = bits.RotateLeft64(t, 41) + t = a[21] ^ d1 + bc4 = bits.RotateLeft64(t, 2) + t = a[12] ^ d2 + bc0 = bits.RotateLeft64(t, 62) + t = a[3] ^ d3 + bc1 = bits.RotateLeft64(t, 55) + t = a[19] ^ d4 + bc2 = bits.RotateLeft64(t, 39) + a[5] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + // Round 3 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[11] ^ d1 + bc1 = bits.RotateLeft64(t, 44) + t = a[22] ^ d2 + bc2 = bits.RotateLeft64(t, 43) + t = a[8] ^ d3 + bc3 = bits.RotateLeft64(t, 21) + t = a[19] ^ d4 + bc4 = bits.RotateLeft64(t, 14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+2] + a[11] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc2 = bits.RotateLeft64(t, 3) + t = a[1] ^ d1 + bc3 = bits.RotateLeft64(t, 45) + t = a[12] ^ d2 + bc4 = bits.RotateLeft64(t, 61) + t = a[23] ^ d3 + bc0 = bits.RotateLeft64(t, 28) + t = a[9] ^ d4 + bc1 = bits.RotateLeft64(t, 20) + a[15] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc4 = bits.RotateLeft64(t, 18) + t = a[16] ^ d1 + bc0 = bits.RotateLeft64(t, 1) + t = a[2] ^ d2 + bc1 = bits.RotateLeft64(t, 6) + t = a[13] ^ d3 + bc2 = bits.RotateLeft64(t, 25) + t = a[24] ^ d4 + bc3 = bits.RotateLeft64(t, 8) + a[5] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc1 = bits.RotateLeft64(t, 36) + t = a[6] ^ d1 + bc2 = bits.RotateLeft64(t, 10) + t = a[17] ^ d2 + bc3 = bits.RotateLeft64(t, 15) + t = a[3] ^ d3 + bc4 = bits.RotateLeft64(t, 56) + t = a[14] ^ d4 + bc0 = bits.RotateLeft64(t, 27) + a[20] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc3 = bits.RotateLeft64(t, 41) + t = a[21] ^ d1 + bc4 = bits.RotateLeft64(t, 2) + t = a[7] ^ d2 + bc0 = bits.RotateLeft64(t, 62) + t = a[18] ^ d3 + bc1 = bits.RotateLeft64(t, 55) + t = a[4] ^ d4 + bc2 = bits.RotateLeft64(t, 39) + a[10] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + // Round 4 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[1] ^ d1 + bc1 = bits.RotateLeft64(t, 44) + t = a[2] ^ d2 + bc2 = bits.RotateLeft64(t, 43) + t = a[3] ^ d3 + bc3 = bits.RotateLeft64(t, 21) + t = a[4] ^ d4 + bc4 = bits.RotateLeft64(t, 14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+3] + a[1] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc2 = bits.RotateLeft64(t, 3) + t = a[6] ^ d1 + bc3 = bits.RotateLeft64(t, 45) + t = a[7] ^ d2 + bc4 = bits.RotateLeft64(t, 61) + t = a[8] ^ d3 + bc0 = bits.RotateLeft64(t, 28) + t = a[9] ^ d4 + bc1 = bits.RotateLeft64(t, 20) + a[5] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc4 = bits.RotateLeft64(t, 18) + t = a[11] ^ d1 + bc0 = bits.RotateLeft64(t, 1) + t = a[12] ^ d2 + bc1 = bits.RotateLeft64(t, 6) + t = a[13] ^ d3 + bc2 = bits.RotateLeft64(t, 25) + t = a[14] ^ d4 + bc3 = bits.RotateLeft64(t, 8) + a[10] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc1 = bits.RotateLeft64(t, 36) + t = a[16] ^ d1 + bc2 = bits.RotateLeft64(t, 10) + t = a[17] ^ d2 + bc3 = bits.RotateLeft64(t, 15) + t = a[18] ^ d3 + bc4 = bits.RotateLeft64(t, 56) + t = a[19] ^ d4 + bc0 = bits.RotateLeft64(t, 27) + a[15] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc3 = bits.RotateLeft64(t, 41) + t = a[21] ^ d1 + bc4 = bits.RotateLeft64(t, 2) + t = a[22] ^ d2 + bc0 = bits.RotateLeft64(t, 62) + t = a[23] ^ d3 + bc1 = bits.RotateLeft64(t, 55) + t = a[24] ^ d4 + bc2 = bits.RotateLeft64(t, 39) + a[20] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + } +} diff --git a/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go b/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go new file mode 100644 index 00000000..248a3824 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go @@ -0,0 +1,14 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && !purego && gc +// +build amd64,!purego,gc + +package sha3 + +// This function is implemented in keccakf_amd64.s. + +//go:noescape + +func keccakF1600(a *[25]uint64) diff --git a/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s b/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s new file mode 100644 index 00000000..4cfa5438 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s @@ -0,0 +1,391 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && !purego && gc +// +build amd64,!purego,gc + +// This code was translated into a form compatible with 6a from the public +// domain sources at https://github.com/gvanas/KeccakCodePackage + +// Offsets in state +#define _ba (0*8) +#define _be (1*8) +#define _bi (2*8) +#define _bo (3*8) +#define _bu (4*8) +#define _ga (5*8) +#define _ge (6*8) +#define _gi (7*8) +#define _go (8*8) +#define _gu (9*8) +#define _ka (10*8) +#define _ke (11*8) +#define _ki (12*8) +#define _ko (13*8) +#define _ku (14*8) +#define _ma (15*8) +#define _me (16*8) +#define _mi (17*8) +#define _mo (18*8) +#define _mu (19*8) +#define _sa (20*8) +#define _se (21*8) +#define _si (22*8) +#define _so (23*8) +#define _su (24*8) + +// Temporary registers +#define rT1 AX + +// Round vars +#define rpState DI +#define rpStack SP + +#define rDa BX +#define rDe CX +#define rDi DX +#define rDo R8 +#define rDu R9 + +#define rBa R10 +#define rBe R11 +#define rBi R12 +#define rBo R13 +#define rBu R14 + +#define rCa SI +#define rCe BP +#define rCi rBi +#define rCo rBo +#define rCu R15 + +#define MOVQ_RBI_RCE MOVQ rBi, rCe +#define XORQ_RT1_RCA XORQ rT1, rCa +#define XORQ_RT1_RCE XORQ rT1, rCe +#define XORQ_RBA_RCU XORQ rBa, rCu +#define XORQ_RBE_RCU XORQ rBe, rCu +#define XORQ_RDU_RCU XORQ rDu, rCu +#define XORQ_RDA_RCA XORQ rDa, rCa +#define XORQ_RDE_RCE XORQ rDe, rCe + +#define mKeccakRound(iState, oState, rc, B_RBI_RCE, G_RT1_RCA, G_RT1_RCE, G_RBA_RCU, K_RT1_RCA, K_RT1_RCE, K_RBA_RCU, M_RT1_RCA, M_RT1_RCE, M_RBE_RCU, S_RDU_RCU, S_RDA_RCA, S_RDE_RCE) \ + /* Prepare round */ \ + MOVQ rCe, rDa; \ + ROLQ $1, rDa; \ + \ + MOVQ _bi(iState), rCi; \ + XORQ _gi(iState), rDi; \ + XORQ rCu, rDa; \ + XORQ _ki(iState), rCi; \ + XORQ _mi(iState), rDi; \ + XORQ rDi, rCi; \ + \ + MOVQ rCi, rDe; \ + ROLQ $1, rDe; \ + \ + MOVQ _bo(iState), rCo; \ + XORQ _go(iState), rDo; \ + XORQ rCa, rDe; \ + XORQ _ko(iState), rCo; \ + XORQ _mo(iState), rDo; \ + XORQ rDo, rCo; \ + \ + MOVQ rCo, rDi; \ + ROLQ $1, rDi; \ + \ + MOVQ rCu, rDo; \ + XORQ rCe, rDi; \ + ROLQ $1, rDo; \ + \ + MOVQ rCa, rDu; \ + XORQ rCi, rDo; \ + ROLQ $1, rDu; \ + \ + /* Result b */ \ + MOVQ _ba(iState), rBa; \ + MOVQ _ge(iState), rBe; \ + XORQ rCo, rDu; \ + MOVQ _ki(iState), rBi; \ + MOVQ _mo(iState), rBo; \ + MOVQ _su(iState), rBu; \ + XORQ rDe, rBe; \ + ROLQ $44, rBe; \ + XORQ rDi, rBi; \ + XORQ rDa, rBa; \ + ROLQ $43, rBi; \ + \ + MOVQ rBe, rCa; \ + MOVQ rc, rT1; \ + ORQ rBi, rCa; \ + XORQ rBa, rT1; \ + XORQ rT1, rCa; \ + MOVQ rCa, _ba(oState); \ + \ + XORQ rDu, rBu; \ + ROLQ $14, rBu; \ + MOVQ rBa, rCu; \ + ANDQ rBe, rCu; \ + XORQ rBu, rCu; \ + MOVQ rCu, _bu(oState); \ + \ + XORQ rDo, rBo; \ + ROLQ $21, rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _bi(oState); \ + \ + NOTQ rBi; \ + ORQ rBa, rBu; \ + ORQ rBo, rBi; \ + XORQ rBo, rBu; \ + XORQ rBe, rBi; \ + MOVQ rBu, _bo(oState); \ + MOVQ rBi, _be(oState); \ + B_RBI_RCE; \ + \ + /* Result g */ \ + MOVQ _gu(iState), rBe; \ + XORQ rDu, rBe; \ + MOVQ _ka(iState), rBi; \ + ROLQ $20, rBe; \ + XORQ rDa, rBi; \ + ROLQ $3, rBi; \ + MOVQ _bo(iState), rBa; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDo, rBa; \ + MOVQ _me(iState), rBo; \ + MOVQ _si(iState), rBu; \ + ROLQ $28, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ga(oState); \ + G_RT1_RCA; \ + \ + XORQ rDe, rBo; \ + ROLQ $45, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ge(oState); \ + G_RT1_RCE; \ + \ + XORQ rDi, rBu; \ + ROLQ $61, rBu; \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _go(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _gu(oState); \ + NOTQ rBu; \ + G_RBA_RCU; \ + \ + ORQ rBu, rBo; \ + XORQ rBi, rBo; \ + MOVQ rBo, _gi(oState); \ + \ + /* Result k */ \ + MOVQ _be(iState), rBa; \ + MOVQ _gi(iState), rBe; \ + MOVQ _ko(iState), rBi; \ + MOVQ _mu(iState), rBo; \ + MOVQ _sa(iState), rBu; \ + XORQ rDi, rBe; \ + ROLQ $6, rBe; \ + XORQ rDo, rBi; \ + ROLQ $25, rBi; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDe, rBa; \ + ROLQ $1, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ka(oState); \ + K_RT1_RCA; \ + \ + XORQ rDu, rBo; \ + ROLQ $8, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ke(oState); \ + K_RT1_RCE; \ + \ + XORQ rDa, rBu; \ + ROLQ $18, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _ki(oState); \ + \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _ko(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _ku(oState); \ + K_RBA_RCU; \ + \ + /* Result m */ \ + MOVQ _ga(iState), rBe; \ + XORQ rDa, rBe; \ + MOVQ _ke(iState), rBi; \ + ROLQ $36, rBe; \ + XORQ rDe, rBi; \ + MOVQ _bu(iState), rBa; \ + ROLQ $10, rBi; \ + MOVQ rBe, rT1; \ + MOVQ _mi(iState), rBo; \ + ANDQ rBi, rT1; \ + XORQ rDu, rBa; \ + MOVQ _so(iState), rBu; \ + ROLQ $27, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ma(oState); \ + M_RT1_RCA; \ + \ + XORQ rDi, rBo; \ + ROLQ $15, rBo; \ + MOVQ rBi, rT1; \ + ORQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _me(oState); \ + M_RT1_RCE; \ + \ + XORQ rDo, rBu; \ + ROLQ $56, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ORQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _mi(oState); \ + \ + ORQ rBa, rBe; \ + XORQ rBu, rBe; \ + MOVQ rBe, _mu(oState); \ + \ + ANDQ rBa, rBu; \ + XORQ rBo, rBu; \ + MOVQ rBu, _mo(oState); \ + M_RBE_RCU; \ + \ + /* Result s */ \ + MOVQ _bi(iState), rBa; \ + MOVQ _go(iState), rBe; \ + MOVQ _ku(iState), rBi; \ + XORQ rDi, rBa; \ + MOVQ _ma(iState), rBo; \ + ROLQ $62, rBa; \ + XORQ rDo, rBe; \ + MOVQ _se(iState), rBu; \ + ROLQ $55, rBe; \ + \ + XORQ rDu, rBi; \ + MOVQ rBa, rDu; \ + XORQ rDe, rBu; \ + ROLQ $2, rBu; \ + ANDQ rBe, rDu; \ + XORQ rBu, rDu; \ + MOVQ rDu, _su(oState); \ + \ + ROLQ $39, rBi; \ + S_RDU_RCU; \ + NOTQ rBe; \ + XORQ rDa, rBo; \ + MOVQ rBe, rDa; \ + ANDQ rBi, rDa; \ + XORQ rBa, rDa; \ + MOVQ rDa, _sa(oState); \ + S_RDA_RCA; \ + \ + ROLQ $41, rBo; \ + MOVQ rBi, rDe; \ + ORQ rBo, rDe; \ + XORQ rBe, rDe; \ + MOVQ rDe, _se(oState); \ + S_RDE_RCE; \ + \ + MOVQ rBo, rDi; \ + MOVQ rBu, rDo; \ + ANDQ rBu, rDi; \ + ORQ rBa, rDo; \ + XORQ rBi, rDi; \ + XORQ rBo, rDo; \ + MOVQ rDi, _si(oState); \ + MOVQ rDo, _so(oState) \ + +// func keccakF1600(state *[25]uint64) +TEXT ·keccakF1600(SB), 0, $200-8 + MOVQ state+0(FP), rpState + + // Convert the user state into an internal state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + // Execute the KeccakF permutation + MOVQ _ba(rpState), rCa + MOVQ _be(rpState), rCe + MOVQ _bu(rpState), rCu + + XORQ _ga(rpState), rCa + XORQ _ge(rpState), rCe + XORQ _gu(rpState), rCu + + XORQ _ka(rpState), rCa + XORQ _ke(rpState), rCe + XORQ _ku(rpState), rCu + + XORQ _ma(rpState), rCa + XORQ _me(rpState), rCe + XORQ _mu(rpState), rCu + + XORQ _sa(rpState), rCa + XORQ _se(rpState), rCe + MOVQ _si(rpState), rDi + MOVQ _so(rpState), rDo + XORQ _su(rpState), rCu + + mKeccakRound(rpState, rpStack, $0x0000000000000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000008082, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x800000000000808a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008000, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000008a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000000088, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x000000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000008000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000000000008b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008089, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008003, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008002, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000000080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000800a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008008, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP) + + // Revert the internal state to the user state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + RET diff --git a/vendor/golang.org/x/crypto/sha3/register.go b/vendor/golang.org/x/crypto/sha3/register.go new file mode 100644 index 00000000..8b4453aa --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/register.go @@ -0,0 +1,19 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build go1.4 +// +build go1.4 + +package sha3 + +import ( + "crypto" +) + +func init() { + crypto.RegisterHash(crypto.SHA3_224, New224) + crypto.RegisterHash(crypto.SHA3_256, New256) + crypto.RegisterHash(crypto.SHA3_384, New384) + crypto.RegisterHash(crypto.SHA3_512, New512) +} diff --git a/vendor/golang.org/x/crypto/sha3/sha3.go b/vendor/golang.org/x/crypto/sha3/sha3.go new file mode 100644 index 00000000..4884d172 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/sha3.go @@ -0,0 +1,197 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// spongeDirection indicates the direction bytes are flowing through the sponge. +type spongeDirection int + +const ( + // spongeAbsorbing indicates that the sponge is absorbing input. + spongeAbsorbing spongeDirection = iota + // spongeSqueezing indicates that the sponge is being squeezed. + spongeSqueezing +) + +const ( + // maxRate is the maximum size of the internal buffer. SHAKE-256 + // currently needs the largest buffer. + maxRate = 168 +) + +type state struct { + // Generic sponge components. + a [25]uint64 // main state of the hash + buf []byte // points into storage + rate int // the number of bytes of state to use + + // dsbyte contains the "domain separation" bits and the first bit of + // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the + // SHA-3 and SHAKE functions by appending bitstrings to the message. + // Using a little-endian bit-ordering convention, these are "01" for SHA-3 + // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the + // padding rule from section 5.1 is applied to pad the message to a multiple + // of the rate, which involves adding a "1" bit, zero or more "0" bits, and + // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, + // giving 00000110b (0x06) and 00011111b (0x1f). + // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf + // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and + // Extendable-Output Functions (May 2014)" + dsbyte byte + + storage storageBuf + + // Specific to SHA-3 and SHAKE. + outputLen int // the default output size in bytes + state spongeDirection // whether the sponge is absorbing or squeezing +} + +// BlockSize returns the rate of sponge underlying this hash function. +func (d *state) BlockSize() int { return d.rate } + +// Size returns the output size of the hash function in bytes. +func (d *state) Size() int { return d.outputLen } + +// Reset clears the internal state by zeroing the sponge state and +// the byte buffer, and setting Sponge.state to absorbing. +func (d *state) Reset() { + // Zero the permutation's state. + for i := range d.a { + d.a[i] = 0 + } + d.state = spongeAbsorbing + d.buf = d.storage.asBytes()[:0] +} + +func (d *state) clone() *state { + ret := *d + if ret.state == spongeAbsorbing { + ret.buf = ret.storage.asBytes()[:len(ret.buf)] + } else { + ret.buf = ret.storage.asBytes()[d.rate-cap(d.buf) : d.rate] + } + + return &ret +} + +// permute applies the KeccakF-1600 permutation. It handles +// any input-output buffering. +func (d *state) permute() { + switch d.state { + case spongeAbsorbing: + // If we're absorbing, we need to xor the input into the state + // before applying the permutation. + xorIn(d, d.buf) + d.buf = d.storage.asBytes()[:0] + keccakF1600(&d.a) + case spongeSqueezing: + // If we're squeezing, we need to apply the permutation before + // copying more output. + keccakF1600(&d.a) + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) + } +} + +// pads appends the domain separation bits in dsbyte, applies +// the multi-bitrate 10..1 padding rule, and permutes the state. +func (d *state) padAndPermute(dsbyte byte) { + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + // Pad with this instance's domain-separator bits. We know that there's + // at least one byte of space in d.buf because, if it were full, + // permute would have been called to empty it. dsbyte also contains the + // first one bit for the padding. See the comment in the state struct. + d.buf = append(d.buf, dsbyte) + zerosStart := len(d.buf) + d.buf = d.storage.asBytes()[:d.rate] + for i := zerosStart; i < d.rate; i++ { + d.buf[i] = 0 + } + // This adds the final one bit for the padding. Because of the way that + // bits are numbered from the LSB upwards, the final bit is the MSB of + // the last byte. + d.buf[d.rate-1] ^= 0x80 + // Apply the permutation + d.permute() + d.state = spongeSqueezing + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) +} + +// Write absorbs more data into the hash's state. It panics if any +// output has already been read. +func (d *state) Write(p []byte) (written int, err error) { + if d.state != spongeAbsorbing { + panic("sha3: Write after Read") + } + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + written = len(p) + + for len(p) > 0 { + if len(d.buf) == 0 && len(p) >= d.rate { + // The fast path; absorb a full "rate" bytes of input and apply the permutation. + xorIn(d, p[:d.rate]) + p = p[d.rate:] + keccakF1600(&d.a) + } else { + // The slow path; buffer the input until we can fill the sponge, and then xor it in. + todo := d.rate - len(d.buf) + if todo > len(p) { + todo = len(p) + } + d.buf = append(d.buf, p[:todo]...) + p = p[todo:] + + // If the sponge is full, apply the permutation. + if len(d.buf) == d.rate { + d.permute() + } + } + } + + return +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (d *state) Read(out []byte) (n int, err error) { + // If we're still absorbing, pad and apply the permutation. + if d.state == spongeAbsorbing { + d.padAndPermute(d.dsbyte) + } + + n = len(out) + + // Now, do the squeezing. + for len(out) > 0 { + n := copy(out, d.buf) + d.buf = d.buf[n:] + out = out[n:] + + // Apply the permutation if we've squeezed the sponge dry. + if len(d.buf) == 0 { + d.permute() + } + } + + return +} + +// Sum applies padding to the hash state and then squeezes out the desired +// number of output bytes. It panics if any output has already been read. +func (d *state) Sum(in []byte) []byte { + if d.state != spongeAbsorbing { + panic("sha3: Sum after Read") + } + + // Make a copy of the original hash so that caller can keep writing + // and summing. + dup := d.clone() + hash := make([]byte, dup.outputLen, 64) // explicit cap to allow stack allocation + dup.Read(hash) + return append(in, hash...) +} diff --git a/vendor/golang.org/x/crypto/sha3/sha3_s390x.go b/vendor/golang.org/x/crypto/sha3/sha3_s390x.go new file mode 100644 index 00000000..ec26f147 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/sha3_s390x.go @@ -0,0 +1,289 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build gc && !purego +// +build gc,!purego + +package sha3 + +// This file contains code for using the 'compute intermediate +// message digest' (KIMD) and 'compute last message digest' (KLMD) +// instructions to compute SHA-3 and SHAKE hashes on IBM Z. + +import ( + "hash" + + "golang.org/x/sys/cpu" +) + +// codes represent 7-bit KIMD/KLMD function codes as defined in +// the Principles of Operation. +type code uint64 + +const ( + // function codes for KIMD/KLMD + sha3_224 code = 32 + sha3_256 = 33 + sha3_384 = 34 + sha3_512 = 35 + shake_128 = 36 + shake_256 = 37 + nopad = 0x100 +) + +// kimd is a wrapper for the 'compute intermediate message digest' instruction. +// src must be a multiple of the rate for the given function code. +// +//go:noescape +func kimd(function code, chain *[200]byte, src []byte) + +// klmd is a wrapper for the 'compute last message digest' instruction. +// src padding is handled by the instruction. +// +//go:noescape +func klmd(function code, chain *[200]byte, dst, src []byte) + +type asmState struct { + a [200]byte // 1600 bit state + buf []byte // care must be taken to ensure cap(buf) is a multiple of rate + rate int // equivalent to block size + storage [3072]byte // underlying storage for buf + outputLen int // output length for full security + function code // KIMD/KLMD function code + state spongeDirection // whether the sponge is absorbing or squeezing +} + +func newAsmState(function code) *asmState { + var s asmState + s.function = function + switch function { + case sha3_224: + s.rate = 144 + s.outputLen = 28 + case sha3_256: + s.rate = 136 + s.outputLen = 32 + case sha3_384: + s.rate = 104 + s.outputLen = 48 + case sha3_512: + s.rate = 72 + s.outputLen = 64 + case shake_128: + s.rate = 168 + s.outputLen = 32 + case shake_256: + s.rate = 136 + s.outputLen = 64 + default: + panic("sha3: unrecognized function code") + } + + // limit s.buf size to a multiple of s.rate + s.resetBuf() + return &s +} + +func (s *asmState) clone() *asmState { + c := *s + c.buf = c.storage[:len(s.buf):cap(s.buf)] + return &c +} + +// copyIntoBuf copies b into buf. It will panic if there is not enough space to +// store all of b. +func (s *asmState) copyIntoBuf(b []byte) { + bufLen := len(s.buf) + s.buf = s.buf[:len(s.buf)+len(b)] + copy(s.buf[bufLen:], b) +} + +// resetBuf points buf at storage, sets the length to 0 and sets cap to be a +// multiple of the rate. +func (s *asmState) resetBuf() { + max := (cap(s.storage) / s.rate) * s.rate + s.buf = s.storage[:0:max] +} + +// Write (via the embedded io.Writer interface) adds more data to the running hash. +// It never returns an error. +func (s *asmState) Write(b []byte) (int, error) { + if s.state != spongeAbsorbing { + panic("sha3: Write after Read") + } + length := len(b) + for len(b) > 0 { + if len(s.buf) == 0 && len(b) >= cap(s.buf) { + // Hash the data directly and push any remaining bytes + // into the buffer. + remainder := len(b) % s.rate + kimd(s.function, &s.a, b[:len(b)-remainder]) + if remainder != 0 { + s.copyIntoBuf(b[len(b)-remainder:]) + } + return length, nil + } + + if len(s.buf) == cap(s.buf) { + // flush the buffer + kimd(s.function, &s.a, s.buf) + s.buf = s.buf[:0] + } + + // copy as much as we can into the buffer + n := len(b) + if len(b) > cap(s.buf)-len(s.buf) { + n = cap(s.buf) - len(s.buf) + } + s.copyIntoBuf(b[:n]) + b = b[n:] + } + return length, nil +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (s *asmState) Read(out []byte) (n int, err error) { + n = len(out) + + // need to pad if we were absorbing + if s.state == spongeAbsorbing { + s.state = spongeSqueezing + + // write hash directly into out if possible + if len(out)%s.rate == 0 { + klmd(s.function, &s.a, out, s.buf) // len(out) may be 0 + s.buf = s.buf[:0] + return + } + + // write hash into buffer + max := cap(s.buf) + if max > len(out) { + max = (len(out)/s.rate)*s.rate + s.rate + } + klmd(s.function, &s.a, s.buf[:max], s.buf) + s.buf = s.buf[:max] + } + + for len(out) > 0 { + // flush the buffer + if len(s.buf) != 0 { + c := copy(out, s.buf) + out = out[c:] + s.buf = s.buf[c:] + continue + } + + // write hash directly into out if possible + if len(out)%s.rate == 0 { + klmd(s.function|nopad, &s.a, out, nil) + return + } + + // write hash into buffer + s.resetBuf() + if cap(s.buf) > len(out) { + s.buf = s.buf[:(len(out)/s.rate)*s.rate+s.rate] + } + klmd(s.function|nopad, &s.a, s.buf, nil) + } + return +} + +// Sum appends the current hash to b and returns the resulting slice. +// It does not change the underlying hash state. +func (s *asmState) Sum(b []byte) []byte { + if s.state != spongeAbsorbing { + panic("sha3: Sum after Read") + } + + // Copy the state to preserve the original. + a := s.a + + // Hash the buffer. Note that we don't clear it because we + // aren't updating the state. + klmd(s.function, &a, nil, s.buf) + return append(b, a[:s.outputLen]...) +} + +// Reset resets the Hash to its initial state. +func (s *asmState) Reset() { + for i := range s.a { + s.a[i] = 0 + } + s.resetBuf() + s.state = spongeAbsorbing +} + +// Size returns the number of bytes Sum will return. +func (s *asmState) Size() int { + return s.outputLen +} + +// BlockSize returns the hash's underlying block size. +// The Write method must be able to accept any amount +// of data, but it may operate more efficiently if all writes +// are a multiple of the block size. +func (s *asmState) BlockSize() int { + return s.rate +} + +// Clone returns a copy of the ShakeHash in its current state. +func (s *asmState) Clone() ShakeHash { + return s.clone() +} + +// new224Asm returns an assembly implementation of SHA3-224 if available, +// otherwise it returns nil. +func new224Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_224) + } + return nil +} + +// new256Asm returns an assembly implementation of SHA3-256 if available, +// otherwise it returns nil. +func new256Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_256) + } + return nil +} + +// new384Asm returns an assembly implementation of SHA3-384 if available, +// otherwise it returns nil. +func new384Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_384) + } + return nil +} + +// new512Asm returns an assembly implementation of SHA3-512 if available, +// otherwise it returns nil. +func new512Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_512) + } + return nil +} + +// newShake128Asm returns an assembly implementation of SHAKE-128 if available, +// otherwise it returns nil. +func newShake128Asm() ShakeHash { + if cpu.S390X.HasSHA3 { + return newAsmState(shake_128) + } + return nil +} + +// newShake256Asm returns an assembly implementation of SHAKE-256 if available, +// otherwise it returns nil. +func newShake256Asm() ShakeHash { + if cpu.S390X.HasSHA3 { + return newAsmState(shake_256) + } + return nil +} diff --git a/vendor/golang.org/x/crypto/sha3/sha3_s390x.s b/vendor/golang.org/x/crypto/sha3/sha3_s390x.s new file mode 100644 index 00000000..a0e051b0 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/sha3_s390x.s @@ -0,0 +1,34 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build gc && !purego +// +build gc,!purego + +#include "textflag.h" + +// func kimd(function code, chain *[200]byte, src []byte) +TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG src+16(FP), R2, R3 // R2=base, R3=len + +continue: + WORD $0xB93E0002 // KIMD --, R2 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET + +// func klmd(function code, chain *[200]byte, dst, src []byte) +TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 + // TODO: SHAKE support + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG dst+16(FP), R2, R3 // R2=base, R3=len + LMG src+40(FP), R4, R5 // R4=base, R5=len + +continue: + WORD $0xB93F0024 // KLMD R2, R4 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET diff --git a/vendor/golang.org/x/crypto/sha3/shake.go b/vendor/golang.org/x/crypto/sha3/shake.go new file mode 100644 index 00000000..bb699840 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/shake.go @@ -0,0 +1,172 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file defines the ShakeHash interface, and provides +// functions for creating SHAKE and cSHAKE instances, as well as utility +// functions for hashing bytes to arbitrary-length output. +// +// +// SHAKE implementation is based on FIPS PUB 202 [1] +// cSHAKE implementations is based on NIST SP 800-185 [2] +// +// [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf +// [2] https://doi.org/10.6028/NIST.SP.800-185 + +import ( + "encoding/binary" + "hash" + "io" +) + +// ShakeHash defines the interface to hash functions that support +// arbitrary-length output. When used as a plain [hash.Hash], it +// produces minimum-length outputs that provide full-strength generic +// security. +type ShakeHash interface { + hash.Hash + + // Read reads more output from the hash; reading affects the hash's + // state. (ShakeHash.Read is thus very different from Hash.Sum) + // It never returns an error, but subsequent calls to Write or Sum + // will panic. + io.Reader + + // Clone returns a copy of the ShakeHash in its current state. + Clone() ShakeHash +} + +// cSHAKE specific context +type cshakeState struct { + *state // SHA-3 state context and Read/Write operations + + // initBlock is the cSHAKE specific initialization set of bytes. It is initialized + // by newCShake function and stores concatenation of N followed by S, encoded + // by the method specified in 3.3 of [1]. + // It is stored here in order for Reset() to be able to put context into + // initial state. + initBlock []byte +} + +// Consts for configuring initial SHA-3 state +const ( + dsbyteShake = 0x1f + dsbyteCShake = 0x04 + rate128 = 168 + rate256 = 136 +) + +func bytepad(input []byte, w int) []byte { + // leftEncode always returns max 9 bytes + buf := make([]byte, 0, 9+len(input)+w) + buf = append(buf, leftEncode(uint64(w))...) + buf = append(buf, input...) + padlen := w - (len(buf) % w) + return append(buf, make([]byte, padlen)...) +} + +func leftEncode(value uint64) []byte { + var b [9]byte + binary.BigEndian.PutUint64(b[1:], value) + // Trim all but last leading zero bytes + i := byte(1) + for i < 8 && b[i] == 0 { + i++ + } + // Prepend number of encoded bytes + b[i-1] = 9 - i + return b[i-1:] +} + +func newCShake(N, S []byte, rate, outputLen int, dsbyte byte) ShakeHash { + c := cshakeState{state: &state{rate: rate, outputLen: outputLen, dsbyte: dsbyte}} + + // leftEncode returns max 9 bytes + c.initBlock = make([]byte, 0, 9*2+len(N)+len(S)) + c.initBlock = append(c.initBlock, leftEncode(uint64(len(N)*8))...) + c.initBlock = append(c.initBlock, N...) + c.initBlock = append(c.initBlock, leftEncode(uint64(len(S)*8))...) + c.initBlock = append(c.initBlock, S...) + c.Write(bytepad(c.initBlock, c.rate)) + return &c +} + +// Reset resets the hash to initial state. +func (c *cshakeState) Reset() { + c.state.Reset() + c.Write(bytepad(c.initBlock, c.rate)) +} + +// Clone returns copy of a cSHAKE context within its current state. +func (c *cshakeState) Clone() ShakeHash { + b := make([]byte, len(c.initBlock)) + copy(b, c.initBlock) + return &cshakeState{state: c.clone(), initBlock: b} +} + +// Clone returns copy of SHAKE context within its current state. +func (c *state) Clone() ShakeHash { + return c.clone() +} + +// NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. +// Its generic security strength is 128 bits against all attacks if at +// least 32 bytes of its output are used. +func NewShake128() ShakeHash { + if h := newShake128Asm(); h != nil { + return h + } + return &state{rate: rate128, outputLen: 32, dsbyte: dsbyteShake} +} + +// NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. +// Its generic security strength is 256 bits against all attacks if +// at least 64 bytes of its output are used. +func NewShake256() ShakeHash { + if h := newShake256Asm(); h != nil { + return h + } + return &state{rate: rate256, outputLen: 64, dsbyte: dsbyteShake} +} + +// NewCShake128 creates a new instance of cSHAKE128 variable-output-length ShakeHash, +// a customizable variant of SHAKE128. +// N is used to define functions based on cSHAKE, it can be empty when plain cSHAKE is +// desired. S is a customization byte string used for domain separation - two cSHAKE +// computations on same input with different S yield unrelated outputs. +// When N and S are both empty, this is equivalent to NewShake128. +func NewCShake128(N, S []byte) ShakeHash { + if len(N) == 0 && len(S) == 0 { + return NewShake128() + } + return newCShake(N, S, rate128, 32, dsbyteCShake) +} + +// NewCShake256 creates a new instance of cSHAKE256 variable-output-length ShakeHash, +// a customizable variant of SHAKE256. +// N is used to define functions based on cSHAKE, it can be empty when plain cSHAKE is +// desired. S is a customization byte string used for domain separation - two cSHAKE +// computations on same input with different S yield unrelated outputs. +// When N and S are both empty, this is equivalent to NewShake256. +func NewCShake256(N, S []byte) ShakeHash { + if len(N) == 0 && len(S) == 0 { + return NewShake256() + } + return newCShake(N, S, rate256, 64, dsbyteCShake) +} + +// ShakeSum128 writes an arbitrary-length digest of data into hash. +func ShakeSum128(hash, data []byte) { + h := NewShake128() + h.Write(data) + h.Read(hash) +} + +// ShakeSum256 writes an arbitrary-length digest of data into hash. +func ShakeSum256(hash, data []byte) { + h := NewShake256() + h.Write(data) + h.Read(hash) +} diff --git a/vendor/golang.org/x/crypto/sha3/shake_generic.go b/vendor/golang.org/x/crypto/sha3/shake_generic.go new file mode 100644 index 00000000..5c0710ef --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/shake_generic.go @@ -0,0 +1,20 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !gc || purego || !s390x +// +build !gc purego !s390x + +package sha3 + +// newShake128Asm returns an assembly implementation of SHAKE-128 if available, +// otherwise it returns nil. +func newShake128Asm() ShakeHash { + return nil +} + +// newShake256Asm returns an assembly implementation of SHAKE-256 if available, +// otherwise it returns nil. +func newShake256Asm() ShakeHash { + return nil +} diff --git a/vendor/golang.org/x/crypto/sha3/xor.go b/vendor/golang.org/x/crypto/sha3/xor.go new file mode 100644 index 00000000..59c8eb94 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/xor.go @@ -0,0 +1,24 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (!amd64 && !386 && !ppc64le) || purego +// +build !amd64,!386,!ppc64le purego + +package sha3 + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate]byte + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(b) +} + +var ( + xorIn = xorInGeneric + copyOut = copyOutGeneric + xorInUnaligned = xorInGeneric + copyOutUnaligned = copyOutGeneric +) + +const xorImplementationUnaligned = "generic" diff --git a/vendor/golang.org/x/crypto/sha3/xor_generic.go b/vendor/golang.org/x/crypto/sha3/xor_generic.go new file mode 100644 index 00000000..8d947711 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/xor_generic.go @@ -0,0 +1,28 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +import "encoding/binary" + +// xorInGeneric xors the bytes in buf into the state; it +// makes no non-portable assumptions about memory layout +// or alignment. +func xorInGeneric(d *state, buf []byte) { + n := len(buf) / 8 + + for i := 0; i < n; i++ { + a := binary.LittleEndian.Uint64(buf) + d.a[i] ^= a + buf = buf[8:] + } +} + +// copyOutGeneric copies uint64s to a byte buffer. +func copyOutGeneric(d *state, b []byte) { + for i := 0; len(b) >= 8; i++ { + binary.LittleEndian.PutUint64(b, d.a[i]) + b = b[8:] + } +} diff --git a/vendor/golang.org/x/crypto/sha3/xor_unaligned.go b/vendor/golang.org/x/crypto/sha3/xor_unaligned.go new file mode 100644 index 00000000..1ce60624 --- /dev/null +++ b/vendor/golang.org/x/crypto/sha3/xor_unaligned.go @@ -0,0 +1,68 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (amd64 || 386 || ppc64le) && !purego +// +build amd64 386 ppc64le +// +build !purego + +package sha3 + +import "unsafe" + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate / 8]uint64 + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(unsafe.Pointer(b)) +} + +// xorInUnaligned uses unaligned reads and writes to update d.a to contain d.a +// XOR buf. +func xorInUnaligned(d *state, buf []byte) { + n := len(buf) + bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] + if n >= 72 { + d.a[0] ^= bw[0] + d.a[1] ^= bw[1] + d.a[2] ^= bw[2] + d.a[3] ^= bw[3] + d.a[4] ^= bw[4] + d.a[5] ^= bw[5] + d.a[6] ^= bw[6] + d.a[7] ^= bw[7] + d.a[8] ^= bw[8] + } + if n >= 104 { + d.a[9] ^= bw[9] + d.a[10] ^= bw[10] + d.a[11] ^= bw[11] + d.a[12] ^= bw[12] + } + if n >= 136 { + d.a[13] ^= bw[13] + d.a[14] ^= bw[14] + d.a[15] ^= bw[15] + d.a[16] ^= bw[16] + } + if n >= 144 { + d.a[17] ^= bw[17] + } + if n >= 168 { + d.a[18] ^= bw[18] + d.a[19] ^= bw[19] + d.a[20] ^= bw[20] + } +} + +func copyOutUnaligned(d *state, buf []byte) { + ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) + copy(buf, ab[:]) +} + +var ( + xorIn = xorInUnaligned + copyOut = copyOutUnaligned +) + +const xorImplementationUnaligned = "unaligned" diff --git a/vendor/modules.txt b/vendor/modules.txt index dcf294e6..79846c46 100644 --- a/vendor/modules.txt +++ b/vendor/modules.txt @@ -29,6 +29,26 @@ github.com/Masterminds/semver/v3 # github.com/Masterminds/sprig/v3 v3.2.3 ## explicit; go 1.13 github.com/Masterminds/sprig/v3 +# github.com/ProtonMail/go-crypto v0.0.0-20230626094100-7e9e0395ebec +## explicit; go 1.13 +github.com/ProtonMail/go-crypto/bitcurves +github.com/ProtonMail/go-crypto/brainpool +github.com/ProtonMail/go-crypto/eax +github.com/ProtonMail/go-crypto/internal/byteutil +github.com/ProtonMail/go-crypto/ocb +github.com/ProtonMail/go-crypto/openpgp +github.com/ProtonMail/go-crypto/openpgp/aes/keywrap +github.com/ProtonMail/go-crypto/openpgp/armor +github.com/ProtonMail/go-crypto/openpgp/ecdh +github.com/ProtonMail/go-crypto/openpgp/ecdsa +github.com/ProtonMail/go-crypto/openpgp/eddsa +github.com/ProtonMail/go-crypto/openpgp/elgamal +github.com/ProtonMail/go-crypto/openpgp/errors +github.com/ProtonMail/go-crypto/openpgp/internal/algorithm +github.com/ProtonMail/go-crypto/openpgp/internal/ecc +github.com/ProtonMail/go-crypto/openpgp/internal/encoding +github.com/ProtonMail/go-crypto/openpgp/packet +github.com/ProtonMail/go-crypto/openpgp/s2k # github.com/agext/levenshtein v1.2.3 ## explicit github.com/agext/levenshtein @@ -122,6 +142,20 @@ github.com/bgentry/go-netrc/netrc # github.com/bgentry/speakeasy v0.1.0 ## explicit github.com/bgentry/speakeasy +# github.com/cloudflare/circl v1.3.3 +## explicit; go 1.19 +github.com/cloudflare/circl/dh/x25519 +github.com/cloudflare/circl/dh/x448 +github.com/cloudflare/circl/ecc/goldilocks +github.com/cloudflare/circl/internal/conv +github.com/cloudflare/circl/internal/sha3 +github.com/cloudflare/circl/math +github.com/cloudflare/circl/math/fp25519 +github.com/cloudflare/circl/math/fp448 +github.com/cloudflare/circl/math/mlsbset +github.com/cloudflare/circl/sign +github.com/cloudflare/circl/sign/ed25519 +github.com/cloudflare/circl/sign/ed448 # github.com/davecgh/go-spew v1.1.2-0.20180830191138-d8f796af33cc ## explicit github.com/davecgh/go-spew/spew @@ -321,8 +355,8 @@ github.com/hashicorp/terraform-plugin-test/v2 github.com/hashicorp/terraform-svchost github.com/hashicorp/terraform-svchost/auth github.com/hashicorp/terraform-svchost/disco -# github.com/hashicorp/vault v1.7.10 -## explicit; go 1.15 +# github.com/hashicorp/vault v1.13.10 +## explicit; go 1.19 github.com/hashicorp/vault/helper/pgpkeys # github.com/hashicorp/vault/sdk v0.10.2 ## explicit; go 1.19 @@ -470,7 +504,9 @@ go.opencensus.io/trace/propagation go.opencensus.io/trace/tracestate # golang.org/x/crypto v0.14.0 ## explicit; go 1.17 +golang.org/x/crypto/argon2 golang.org/x/crypto/bcrypt +golang.org/x/crypto/blake2b golang.org/x/crypto/blowfish golang.org/x/crypto/cast5 golang.org/x/crypto/chacha20 @@ -490,6 +526,7 @@ golang.org/x/crypto/openpgp/packet golang.org/x/crypto/openpgp/s2k golang.org/x/crypto/pbkdf2 golang.org/x/crypto/scrypt +golang.org/x/crypto/sha3 golang.org/x/crypto/ssh golang.org/x/crypto/ssh/internal/bcrypt_pbkdf # golang.org/x/net v0.17.0