scimp_progressive_enc.pv

(*

Formal analysis of the Silent Cirlce Instant Messaging Protocol (SCIMP).

Author:        Sebastian Verschoor
Email:         s.r.verschoor@student.tue.nl
Last modified: <2015-10-11 23:48:34>

This file checks the secrecy and authenticity of the initial key negotiation,
where two honest participants do not yet share a cached secret. The key
negotiation will be done with Progressive Encryption.

The description for the protocol was taken from the protocol description at:
https://github.com/SilentCircle/silent-text/tree/master/Documentation
A more informal description is given at:
https://silentcircle.com/scimp-protocol

Proverif version used: 1.90 (retrieved at 2015-07-06)

*** Short protocol description ***

Initiator Alice (A)
Responder Bob (B)
Server (S)
ECDHE-exchange using a fixed base point G

      B: skB    := random()
         pkB    := skB * G
         idPkB  := KDF(pkB, Const, nonce)
B  -> S: B, pkB, idPkB
A  -> S: B
S  -> A: B, pkB, idPkB
      A: sk0    := random()
         pk0    := sk0 * G
         Z0     := sk0 * pkB
         expand/extract/enhance: ksnd, isnd
         ct     := enc(ksnd, isnd, msg)
         skI    := random()
         pkI    := skI * G
A  -> B: pkstart = (options, idPkB, pk0, #pkI, ct)
      B: Z0     := skB * pk0
         expand/extract/enhance: krcv, ircv
         pt     := dec(krcv, ircv, ct)
         skR    := random()
         pkR    := skR * G
B  -> A: dh1     = (pkR, MAC(NULL, (#pkR, "Responder")))
      A: kdk2   := MAC(MAC(htotal, Z), (CONSTS, context, NULL))
                   where htotal  = #(commit, dh1, pkI)
                         Z       = skI * pkR
                         context = (A, B, htotal)
         extract from kdk2 and session variables:
           ksnd, krcv, maci, macr, sasi, cs1, isnd, ircv
A  -> B: dh2     = (pkI, maci)
      B: validate pkI with #pkI of commit; or abort
         kdk2   := MAC(MAC(htotal, Z), (CONSTS, context, NULL))
                   where htotal  = #(commit, dh1, pkI)
                         Z       = skR * pkI
                         context = (A, B, htotal)
         extract from kdk2 and session variables:
           krcv, ksnd, macr, maci, sasr, cs1, ircv, isnd
B  -> A: commit  = macr

A <=> B: check (sasi = sasr); or abort

*)


(*** Types ***)

type mac_key.
type secret_key.
type nonce.
type point.
type scalar.
type identity.

fun mk2bs(mac_key)    : bitstring       [data, typeConverter].
fun bs2mk(bitstring)  : mac_key         [data, typeConverter].
fun sk2bs(secret_key) : bitstring       [data, typeConverter].
fun bs2sk(bitstring)  : secret_key      [data, typeConverter].
fun pt2bs(point)      : bitstring       [data, typeConverter].
fun bs2n (bitstring)  : nonce           [data, typeConverter].
fun sk2mk(secret_key) : mac_key         [data, typeConverter].
fun mk2sk(mac_key)    : secret_key      [data, typeConverter].
fun pt2mk(point)      : mac_key         [data, typeConverter].
fun id2bs(identity)   : bitstring       [data, typeConverter].

(*** Functions ***)

fun increment(bitstring) : bitstring [data].

fun splitFst(bitstring) : bitstring.
fun splitSnd(bitstring) : bitstring.
reduc forall x:bitstring;
      unsplit(splitFst(x), splitSnd(x)) = x.

(* Cryptographic functions *)

fun hash(bitstring) : bitstring.

(* Message authentication code (MAC) *)
fun mac(mac_key, bitstring) : bitstring.

(* Key derivation function (KDF) *)
reduc forall key:mac_key, context:bitstring, label:bitstring;
      kdf(key, label, context) = mac(key, (label, context)).

(* Symmetric encryption/decryption *)
fun sym_enc(secret_key, nonce, bitstring) : bitstring.
fun sym_dec(secret_key, nonce, bitstring) : bitstring.
equation forall k:secret_key, n:nonce, m:bitstring;
         sym_dec(k, n, sym_enc(k, n, m)) = m.
equation forall k:secret_key, n:nonce, m:bitstring;
         sym_enc(k, n, sym_dec(k, n, m)) = m.

(* Authenticated Encryption with Additional Data *)
letfun aead_enc(k:secret_key, n:nonce, header:bitstring, plaintext:bitstring) =
       let tag = mac(sk2mk(k), (n, header, plaintext)) in
       sym_enc(k, n, (plaintext, tag)).
letfun aead_dec(k:secret_key, n:nonce, header:bitstring, ciphertext:bitstring) =
       let (plaintext:bitstring, tag:bitstring) = sym_dec(k, n, ciphertext) in
       let (=tag) = mac(sk2mk(k), (n, header, plaintext)) in
       plaintext.


(* Diffie-Hellman-Merkle key exchange
 * Proverif does not care about the underlying group, so there is no need to
 * encode ECDH any different.
 *)
const Base : point [data].
fun mult(scalar, point) : point.

equation forall x:scalar, y:scalar;
         mult(x, mult(y, Base)) = mult(y, mult(x, Base)).


(*** Communication channels ***)

(* Public channel over which the protocol is executed. Usually the internet. *)
free ch:channel.

(*** Constants ***)

const Null            : bitstring [data]. (* NULL *)
const OK              : bitstring [data]. (* Confirmation of SAS *)

(* String constants *)
const InitStr         : bitstring [data]. (* "Initiator" *)
const RespStr         : bitstring [data]. (* "Responder" *)
const MasterStr       : bitstring [data]. (* "MasterSecret" *)
const AlgId           : bitstring [data]. (* "SCimp-ENHANCE" *)

(* Labels for key derivation *)
const InitMasterLabel : bitstring [data]. (* "InitiatorMasterKey" *)
const RespMasterLabel : bitstring [data]. (* "ResponderMasterKey" *)
const InitMACLabel    : bitstring [data]. (* "InitiatorMACkey" *)
const RespMACLabel    : bitstring [data]. (* "ResponderMACkey" *)
const SasLabel        : bitstring [data]. (* "SAS" *)
const CsLabel         : bitstring [data]. (* "RetainedSecret" *)
const InitIndexLabel  : bitstring [data]. (* "InitiatorInitialIndex" *)
const RespIndexLabel  : bitstring [data]. (* "ResponderInitialIndex" *)
const MsgKeyLabel     : bitstring [data]. (* "MessageKey" *)
const LocatorLabel    : bitstring [data]. (* "SCKey_ECC_Key" *)

const Compromised : identity [data].

(* Key table *)
table keys(identity, point, bitstring).

(*** Queries ***)

(* Prover hints *)
not attacker(new ski).  not attacker(new skiC).
not attacker(new ski0). not attacker(new ski0C).
not attacker(new skr).  not attacker(new skrC).
not attacker(new skr0). not attacker(new skr0C).

(* Queries for confidentiality *)
free ksndInitFlag, krcvInitFlag, isndInitFlag, ircvInitFlag,
     ksndRespFlag, krcvRespFlag, isndRespFlag, ircvRespFlag,
     ksnd0InitFlag, krcv0InitFlag, isnd0InitFlag, ircv0InitFlag,
     ksnd0RespFlag, krcv0RespFlag, isnd0RespFlag, ircv0RespFlag,
     cs1InitFlag, cs1RespFlag, msg0InitFlag, msg0RespFlag : bitstring [private].

query attacker(ksndInitFlag);  attacker(krcvInitFlag);
      attacker(isndInitFlag);  attacker(ircvInitFlag);
      attacker(ksndRespFlag);  attacker(krcvRespFlag);
      attacker(isndRespFlag);  attacker(ircvRespFlag);
      attacker(ksnd0InitFlag); attacker(krcv0InitFlag);
      attacker(isnd0InitFlag); attacker(ircv0InitFlag);
      attacker(ksnd0RespFlag); attacker(krcv0RespFlag);
      attacker(isnd0RespFlag); attacker(ircv0RespFlag);
      attacker(cs1InitFlag);   attacker(cs1RespFlag);
      attacker(msg0InitFlag);  attacker(msg0RespFlag).

query attacker(new msg0).
query attacker(new msg0C).

(* Queries for authenticity *)
event beginInit(identity, identity,
                bitstring, bitstring, bitstring, bitstring, bitstring,
                bitstring, bitstring, bitstring, bitstring, bitstring).
event acceptInit(identity, identity,
                 bitstring, bitstring, bitstring, bitstring, bitstring,
                 bitstring, bitstring, bitstring, bitstring, bitstring).
event beginResp(identity, identity,
                bitstring, bitstring, bitstring, bitstring, bitstring,
                bitstring, bitstring, bitstring, bitstring, bitstring).
event acceptResp(identity, identity,
                 bitstring, bitstring, bitstring, bitstring, bitstring,
                 bitstring, bitstring, bitstring, bitstring, bitstring).

query x:identity, y:identity,
      ki:bitstring, kr:bitstring, ii:bitstring, ir:bitstring, cs:bitstring,
      ki0:bitstring, kr0:bitstring, ii0:bitstring, ir0:bitstring, msg:bitstring;
      inj-event(acceptInit(x, y, ki, kr, ii, ir, cs, ki0, kr0, ii0, ir0, msg))
        ==> inj-event(beginInit(x, y, ki, kr, ii, ir, cs, ki0, kr0, ii0, ir0, msg)).
query x:identity, y:identity,
      ki:bitstring, kr:bitstring, ii:bitstring, ir:bitstring, cs:bitstring,
      ki0:bitstring, kr0:bitstring, ii0:bitstring, ir0:bitstring, msg:bitstring;
      inj-event(acceptResp(x, y, ki, kr, ii, ir, cs, ki0, kr0, ii0, ir0, msg))
        ==> inj-event(beginResp(x, y, ki, kr, ii, ir, cs, ki0, kr0, ii0, ir0, msg)).

(* Query reachability: check for typos. This should result in
   not attacker(....HasTypo[]) is false. *)
free initHasTypo, initCompHasTypo, respHasTypo, respCompHasTypo : bitstring [private].
query attacker(initHasTypo); attacker(initCompHasTypo);
      attacker(respHasTypo); attacker(respCompHasTypo).


(*** Processes ***)

(* Role of the server (handing out keys) *)
let processGetKey =
  in(ch, resp:identity);
  get keys(=resp, pkResp, locResp) in
  out(ch, (pkResp, locResp)).

(* Role of the server (key registration) *)
let processKeyRegistration =
  in(ch, (id:identity, pubkey:point, locator:bitstring));
  insert keys(id, pubkey, locator).

(* Role of the initiator *)
let processInitiator(init:identity, resp:identity, phone:channel) =
  (* Get responder public key *)
  out(ch, resp);
  in(ch, (pkResp:point, locResp:bitstring));

  (* PKStart *)
  new msg0 : bitstring;
  new ski0 : scalar;
  let pki0     = mult(ski0, Base) in
  let z0       = mult(ski0, pkResp) in
  let kdk0     = bs2mk(mac(bs2mk(Null), pt2bs(z0))) in
  let context0 = (init, resp) in
  let sessId0  = hash(context0) in
  let kdk20    = bs2mk(mac(kdk0, (MasterStr, AlgId, context0, Null))) in
  let ksnd0    = kdf(kdk20, InitMasterLabel, context0) in
  let krcv0    = kdf(kdk20, RespMasterLabel, sessId0) in
  let isnd0    = kdf(kdk20, InitIndexLabel,  sessId0) in
  let ircv0    = kdf(kdk20, RespIndexLabel,  sessId0) in
  let k0       = bs2sk(splitFst(ksnd0)) in
  let n0       = bs2n(splitSnd(ksnd0)) in
  let ct0      = aead_enc(k0, n0, isnd0, msg0) in

  new ski : scalar;
  let pki     = mult(ski, Base) in
  let hpki    = hash(pt2bs(pki)) in
  let pkstart = (locResp, pki0, hpki, ct0) in
  out(ch, pkstart);

  (* DH1 *)
  in(ch, dh1:bitstring);
  let (pkr:point, hcsr:bitstring) = dh1 in

  (* DH2 *)
  let z       = mult(ski, pkr) in
  let htotal  = hash((pkstart, dh1, pki)) in
  let kdk     = bs2mk(mac(bs2mk(htotal), pt2bs(z))) in
  let context = (init, resp, htotal) in
  let sessId  = hash((init, resp)) in
  let kdk2    = bs2mk(mac(kdk, (MasterStr, AlgId, context, Null))) in
  let maci    = kdf(kdk2, InitMACLabel,    context) in
  out(ch, (pki, maci));

  (* Confirm *)
  in(ch, macr:bitstring);
  let ksnd    = kdf(kdk2, InitMasterLabel, context) in
  let krcv    = kdf(kdk2, RespMasterLabel, sessId) in
  let sas     = kdf(kdk2, SasLabel,        context) in
  let cs1     = kdf(kdk2, CsLabel,         context) in
  let (=macr) = kdf(kdk2, RespMACLabel,    context) in
  let isnd    = kdf(kdk2, InitIndexLabel,  sessId) in
  let ircv    = kdf(kdk2, RespIndexLabel,  sessId) in
  
  (* Start verification of initiator identity *)
  event beginInit(init, resp,
                  ksnd, krcv, isnd, ircv, cs1,
                  ksnd0, krcv0, isnd0, ircv0, msg0);

  (* Confirm the SAS *)
  out(phone, sas);
  in(phone, (=sas, ok:bitstring));

  (* Accept the responder identity and corresponding key material *)
  event acceptResp(init, resp,
                   ksnd, krcv, isnd, ircv, cs1,
                   ksnd0, krcv0, isnd0, ircv0, msg0);

  (* Publish secret values to test secrecy of generated key material *)
  out(ch, sym_enc(bs2sk(ksnd),  bs2n(Null), ksndInitFlag));
  out(ch, sym_enc(bs2sk(krcv),  bs2n(Null), krcvInitFlag));
  out(ch, sym_enc(bs2sk(isnd),  bs2n(Null), isndInitFlag));
  out(ch, sym_enc(bs2sk(ircv),  bs2n(Null), ircvInitFlag));
  out(ch, sym_enc(bs2sk(cs1),   bs2n(Null), cs1InitFlag));
  out(ch, sym_enc(bs2sk(ksnd0), bs2n(Null), ksnd0InitFlag));
  out(ch, sym_enc(bs2sk(krcv0), bs2n(Null), krcv0InitFlag));
  out(ch, sym_enc(bs2sk(isnd0), bs2n(Null), isnd0InitFlag));
  out(ch, sym_enc(bs2sk(ircv0), bs2n(Null), ircv0InitFlag));
  out(ch, sym_enc(bs2sk(msg0),  bs2n(Null), msg0InitFlag));

  (* Check for typos *)
  out(ch, initHasTypo)
  
  .

(* Role of the responder *)
let processResponder(init:identity, resp:identity, phone:channel) =
  (* Register public key *)
  new skr0 : scalar;
  let pkr0 = mult(skr0, Base) in
  let locr0 = kdf(pt2mk(pkr0), LocatorLabel, id2bs(resp)) in
  out(ch, (resp, pkr0, locr0));

  (* PKStart *)
  in(ch, pkstart:bitstring);
  let (=locr0, pki0:point, hpki:bitstring, ct:bitstring) = pkstart in
  let z0       = mult(skr0, pki0) in
  let kdk0     = bs2mk(mac(bs2mk(Null), pt2bs(z0))) in
  let context0 = (init, resp) in
  let sessId0  = hash(context0) in
  let kdk20    = bs2mk(mac(kdk0, (MasterStr, AlgId, context0, Null))) in
  let ksnd0    = kdf(kdk20, RespMasterLabel, sessId0) in
  let krcv0    = kdf(kdk20, InitMasterLabel, context0) in
  let isnd0    = kdf(kdk20, RespIndexLabel,  sessId0) in
  let ircv0    = kdf(kdk20, InitIndexLabel,  sessId0) in
  let k0       = bs2sk(splitFst(krcv0)) in
  let n0       = bs2n(splitSnd(krcv0)) in
  let pt0      = aead_dec(k0, n0, ircv0, ct) in

  (* DH1 *)
  new skr : scalar;
  let pkr  = mult(skr, Base) in
  let hpkr = hash(pt2bs(pkr)) in
  let hcsr = mac(bs2mk(Null), (hpkr, RespStr)) in
  let dh1  = (pkr, hcsr) in
  out(ch, dh1);

  (* DH2 *)
  in(ch, (pki:point, maci:bitstring));
  let (=hpki) = hash(pt2bs(pki)) in

  (* Confirm *)
  let z       = mult(skr, pki) in
  let htotal  = hash((pkstart, dh1, pki)) in
  let kdk     = bs2mk(mac(bs2mk(htotal), pt2bs(z))) in
  let context = (init, resp, htotal) in
  let sessId  = hash((init, resp)) in
  let kdk2    = bs2mk(mac(kdk, (MasterStr, AlgId, context, Null))) in
  let ksnd    = kdf(kdk2, RespMasterLabel, sessId) in
  let krcv    = kdf(kdk2, InitMasterLabel, context) in
  let sas     = kdf(kdk2, SasLabel,        context) in
  let cs1     = kdf(kdk2, CsLabel,         context) in
  let (=maci) = kdf(kdk2, InitMACLabel,    context) in
  let macr    = kdf(kdk2, RespMACLabel,    context) in
  let isnd    = kdf(kdk2, RespIndexLabel,  sessId) in
  let ircv    = kdf(kdk2, InitIndexLabel,  sessId) in
  out(ch, macr);

  (* Start verification of the responder *)
  event beginResp(init, resp,
                  krcv, ksnd, ircv, isnd, cs1,
                  krcv0, ksnd0, ircv0, isnd0, pt0);

  (* Confirm the SAS *)
  in(phone, =sas);
  out(phone, (sas, OK));

  (* Accept the initiator identity and corresponding key material *)
  event acceptInit(init, resp,
                   krcv, ksnd, ircv, isnd, cs1,
                   krcv0, ksnd0, ircv0, isnd0, pt0);

  (* Publish secret values to test secrecy of generated key material *)
  out(ch, sym_enc(bs2sk(ksnd),  bs2n(Null), ksndRespFlag));
  out(ch, sym_enc(bs2sk(krcv),  bs2n(Null), krcvRespFlag));
  out(ch, sym_enc(bs2sk(isnd),  bs2n(Null), isndRespFlag));
  out(ch, sym_enc(bs2sk(ircv),  bs2n(Null), ircvRespFlag));
  out(ch, sym_enc(bs2sk(cs1),   bs2n(Null), cs1RespFlag));
  out(ch, sym_enc(bs2sk(ksnd0), bs2n(Null), ksnd0RespFlag));
  out(ch, sym_enc(bs2sk(krcv0), bs2n(Null), krcv0RespFlag));
  out(ch, sym_enc(bs2sk(isnd0), bs2n(Null), isnd0RespFlag));
  out(ch, sym_enc(bs2sk(ircv0), bs2n(Null), ircv0RespFlag));
  out(ch, sym_enc(bs2sk(pt0),   bs2n(Null), msg0RespFlag));

  (* Check for typos *)
  out(ch, respHasTypo)

  .


(* Role of the initiator *)
let processInitiatorComp(init:identity, resp:identity, phone:channel) =
  (* Get responder public key *)
  out(ch, resp);
  in(ch, (pkResp:point, locResp:bitstring));

  (* PKStart *)
  new msg0C : bitstring;
  new ski0C : scalar;
  let pki0     = mult(ski0C, Base) in
  let z0       = mult(ski0C, pkResp) in
  let kdk0     = bs2mk(mac(bs2mk(Null), pt2bs(z0))) in
  let context0 = (init, resp) in
  let sessId0  = hash(context0) in
  let kdk20    = bs2mk(mac(kdk0, (MasterStr, AlgId, context0, Null))) in
  let ksnd0    = kdf(kdk20, InitMasterLabel, context0) in
  let krcv0    = kdf(kdk20, RespMasterLabel, sessId0) in
  let isnd0    = kdf(kdk20, InitIndexLabel,  sessId0) in
  let ircv0    = kdf(kdk20, RespIndexLabel,  sessId0) in
  let k0       = bs2sk(splitFst(ksnd0)) in
  let n0       = bs2n(splitSnd(ksnd0)) in
  let ct0      = aead_enc(k0, n0, isnd0, msg0C) in

  new skiC : scalar;
  let pki     = mult(skiC, Base) in
  let hpki    = hash(pt2bs(pki)) in
  let pkstart = (locResp, pki0, hpki, ct0) in
  out(ch, pkstart);

  (* DH1 *)
  in(ch, dh1:bitstring);
  let (pkr:point, hcsr:bitstring) = dh1 in

  (* DH2 *)
  let z       = mult(skiC, pkr) in
  let htotal  = hash((pkstart, dh1, pki)) in
  let kdk     = bs2mk(mac(bs2mk(htotal), pt2bs(z))) in
  let context = (init, resp, htotal) in
  let sessId  = hash((init, resp)) in
  let kdk2    = bs2mk(mac(kdk, (MasterStr, AlgId, context, Null))) in
  let maci    = kdf(kdk2, InitMACLabel,    context) in
  out(ch, (pki, maci));

  (* Confirm *)
  in(ch, macr:bitstring);
  let ksnd    = kdf(kdk2, InitMasterLabel, context) in
  let krcv    = kdf(kdk2, RespMasterLabel, sessId) in
  let sas     = kdf(kdk2, SasLabel,        context) in
  let cs1     = kdf(kdk2, CsLabel,         context) in
  let (=macr) = kdf(kdk2, RespMACLabel,    context) in
  let isnd    = kdf(kdk2, InitIndexLabel,  sessId) in
  let ircv    = kdf(kdk2, RespIndexLabel,  sessId) in
  
  (* Start verification of initiator identity *)
  event beginInit(init, resp,
                  ksnd, krcv, isnd, ircv, cs1,
                  ksnd0, krcv0, isnd0, ircv0, msg0C);

  (* Confirm the SAS *)
  out(phone, sas);
  in(phone, (=sas, ok:bitstring));

  (* Check for typos *)
  out(ch, initCompHasTypo)
  
  .

(* Role of the responder *)
let processCompResponder(init:identity, resp:identity, phone:channel) =
  (* Register public key *)
  new skr0C : scalar;
  let pkr0 = mult(skr0C, Base) in
  let locr0 = kdf(pt2mk(pkr0), LocatorLabel, id2bs(resp)) in
  out(ch, (resp, pkr0, locr0));

  (* PKStart *)
  in(ch, pkstart:bitstring);
  let (=locr0, pki0:point, hpki:bitstring, ct:bitstring) = pkstart in
  let z0       = mult(skr0C, pki0) in
  let kdk0     = bs2mk(mac(bs2mk(Null), pt2bs(z0))) in
  let context0 = (init, resp) in
  let sessId0  = hash(context0) in
  let kdk20    = bs2mk(mac(kdk0, (MasterStr, AlgId, context0, Null))) in
  let ksnd0    = kdf(kdk20, RespMasterLabel, sessId0) in
  let krcv0    = kdf(kdk20, InitMasterLabel, context0) in
  let isnd0    = kdf(kdk20, RespIndexLabel,  sessId0) in
  let ircv0    = kdf(kdk20, InitIndexLabel,  sessId0) in
  let k0       = bs2sk(splitFst(krcv0)) in
  let n0       = bs2n(splitSnd(krcv0)) in
  let pt0      = aead_dec(k0, n0, ircv0, ct) in

  (* DH1 *)
  new skrC : scalar;
  let pkr  = mult(skrC, Base) in
  let hpkr = hash(pt2bs(pkr)) in
  let hcsr = mac(bs2mk(Null), (hpkr, RespStr)) in
  let dh1  = (pkr, hcsr) in
  out(ch, dh1);

  (* DH2 *)
  in(ch, (pki:point, maci:bitstring));
  let (=hpki) = hash(pt2bs(pki)) in

  (* Confirm *)
  let z       = mult(skrC, pki) in
  let htotal  = hash((pkstart, dh1, pki)) in
  let kdk     = bs2mk(mac(bs2mk(htotal), pt2bs(z))) in
  let context = (init, resp, htotal) in
  let sessId  = hash((init, resp)) in
  let kdk2    = bs2mk(mac(kdk, (MasterStr, AlgId, context, Null))) in
  let ksnd    = kdf(kdk2, RespMasterLabel, sessId) in
  let krcv    = kdf(kdk2, InitMasterLabel, context) in
  let sas     = kdf(kdk2, SasLabel,        context) in
  let cs1     = kdf(kdk2, CsLabel,         context) in
  let (=maci) = kdf(kdk2, InitMACLabel,    context) in
  let macr    = kdf(kdk2, RespMACLabel,    context) in
  let isnd    = kdf(kdk2, RespIndexLabel,  sessId) in
  let ircv    = kdf(kdk2, InitIndexLabel,  sessId) in
  out(ch, macr);

  (* Start verification of the responder *)
  event beginResp(init, resp,
                  krcv, ksnd, ircv, isnd, cs1,
                  krcv0, ksnd0, ircv0, isnd0, pt0);

  (* Confirm the SAS *)
  in(phone, =sas);
  out(phone, (sas, OK));

  (* Check for typos *)
  out(ch, respCompHasTypo)

  .


(*** Main ***)

process
  (* Allow arbitrary many protocol runs *)
  !
  (* Let the adversary decide who will engage in key negotation *)
  in(ch, (init:identity, resp:identity));
  (* Create a new phone channel *)
  new phone : channel;
  (* Allow eavesdropping on the phone channel *)
  (! in(phone, x:bitstring); out(ch, x)) |

  (* Server processes *)
  (! processKeyRegistration) |
  (! processGetKey) |
  if init = Compromised then (
    out(ch, phone);
    processCompResponder(init, resp, phone)
  ) else if resp = Compromised then (
    out(ch, phone);
    processInitiatorComp(init, resp, phone)
  ) else (
    processInitiator(init, resp, phone) |
    processResponder(init, resp, phone)
  )