diff --git a/ext/openssl/ossl_x509cert.c b/ext/openssl/ossl_x509cert.c
index aa6b9bb7c..9bee734fb 100644
--- a/ext/openssl/ossl_x509cert.c
+++ b/ext/openssl/ossl_x509cert.c
@@ -539,7 +539,11 @@ ossl_x509_sign(VALUE self, VALUE key, VALUE digest)
     const EVP_MD *md;
 
     pkey = GetPrivPKeyPtr(key); /* NO NEED TO DUP */
-    md = ossl_evp_get_digestbyname(digest);
+    if (NIL_P(digest)) {
+      md = NULL; /* needed for some key types, e.g. Ed25519 */
+    } else {
+      md = ossl_evp_get_digestbyname(digest);
+    }
     GetX509(self, x509);
     if (!X509_sign(x509, pkey, md)) {
 	ossl_raise(eX509CertError, NULL);
diff --git a/test/openssl/fixtures/pkey/ed25519.pem b/test/openssl/fixtures/pkey/ed25519.pem
new file mode 100644
index 000000000..fd24a8482
--- /dev/null
+++ b/test/openssl/fixtures/pkey/ed25519.pem
@@ -0,0 +1,3 @@
+-----BEGIN PRIVATE KEY-----
+MC4CAQAwBQYDK2VwBCIEIFfR9+7eHflbSCNLLWz50cKZG9J/dzNTyYCggFG1MKG9
+-----END PRIVATE KEY-----
diff --git a/test/openssl/test_x509cert.rb b/test/openssl/test_x509cert.rb
index 64805504d..925557597 100644
--- a/test/openssl/test_x509cert.rb
+++ b/test/openssl/test_x509cert.rb
@@ -222,6 +222,26 @@ def test_sign_and_verify_dsa_md5
     }
   end
 
+  def test_sign_and_verify_ed25519
+    # See test_ed25519 in test_pkey.rb
+
+    # Ed25519 is not FIPS-approved.
+    omit_on_fips
+
+    begin
+      ed25519  = Fixtures.pkey("ed25519")
+    rescue OpenSSL::PKey::PKeyError => e
+      # OpenSSL < 1.1.1
+      #
+      pend "Ed25519 is not implemented" unless openssl?(1, 1, 1)
+
+      raise e
+    end
+
+    cert = issue_cert(@ca, ed25519, 1, [], nil, nil, digest: nil)
+    assert_equal(true, cert.verify(ed25519))
+  end
+
   def test_dsa_with_sha2
     cert = issue_cert(@ca, @dsa256, 1, [], nil, nil, digest: "sha256")
     assert_equal("dsa_with_SHA256", cert.signature_algorithm)