Pk Recovery (#102)

* Added recover_public_keys() to Signature
* Added pk recovery support in wrapper

Author: gianlucafrei

src/ecdsa/ecdsa.py

@@ -69,6 +69,34 @@ def __init__(self, r, s):
     self.r = r
     self.s = s
 
+  def recover_public_keys(self, hash, generator):
+    """Returns two public keys for which the signature is valid
+    hash is signed hash
+    generator is the used generator of the signature
+    """
+    curve = generator.curve()
+    n = generator.order()
+    r = self.r
+    s = self.s
+    e = hash
+    x = r
+
+    # Compute the curve point with x as x-coordinate
+    alpha = (pow(x, 3, curve.p()) + (curve.a() * x) + curve.b()) % curve.p()
+    beta = numbertheory.square_root_mod_prime(alpha, curve.p())
+    y = beta if beta % 2 == 0 else curve.p() - beta
+
+    # Compute the public key
+    R1 = ellipticcurve.Point(curve, x, y, n)
+    Q1 = numbertheory.inverse_mod(r, n) * (s * R1 + (-e % n) * generator)
+    Pk1 = Public_key(generator, Q1)
+
+    # And the second solution
+    R2 = ellipticcurve.Point(curve, x, -y, n)
+    Q2 = numbertheory.inverse_mod(r, n) * (s * R2 + (-e % n) * generator)
+    Pk2 = Public_key(generator, Q2)
+
+    return [Pk1, Pk2]
 
 class Public_key(object):
   """Public key for ECDSA.

src/ecdsa/keys.py

@@ -79,6 +79,30 @@ def from_der(klass, string):
         assert point_str.startswith(b("\x00\x04"))
         return klass.from_string(point_str[2:], curve)
 
+    @classmethod
+    def from_public_key_recovery(klass, signature, data, curve, hashfunc=sha1, sigdecode=sigdecode_string):
+        # Given a signature and corresponding message this function
+        # returns a list of verifying keys for this signature and message
+        
+        digest = hashfunc(data).digest()
+        return klass.from_public_key_recovery_with_digest(signature, digest, curve, hashfunc=sha1, sigdecode=sigdecode_string)
+
+    @classmethod
+    def from_public_key_recovery_with_digest(klass, signature, digest, curve, hashfunc=sha1, sigdecode=sigdecode_string):
+        # Given a signature and corresponding digest this function
+        # returns a list of verifying keys for this signature and message
+        
+        generator = curve.generator
+        r, s = sigdecode(signature, generator.order())
+        sig = ecdsa.Signature(r, s)
+
+        digest_as_number = string_to_number(digest)
+        pks = sig.recover_public_keys(digest_as_number, generator)
+
+        # Transforms the ecdsa.Public_key object into a VerifyingKey
+        verifying_keys = [klass.from_public_point(pk.point, curve, hashfunc) for pk in pks]
+        return verifying_keys
+
     def to_string(self):
         # VerifyingKey.from_string(vk.to_string()) == vk as long as the
         # curves are the same: the curve itself is not included in the

src/ecdsa/test_ecdsa.py

@@ -30,6 +30,33 @@ def test_signature_validity(Msg, Qx, Qy, R, S, expected):
       raise TestFailure("*** Signature test failed: got %s, expected %s." % \
                         (got, expected))
 
+  def test_pk_recovery(Msg, R, S, Qx, Qy):
+    
+    sign = Signature(R,S)
+    pks = sign.recover_public_keys(digest_integer(Msg), generator_192)
+
+    print_("Test pk recover")
+
+    if pks:
+
+      # Test if the signature is valid for all found public keys
+      for pk in pks:
+        q = pk.point
+        print_("Recovered q: %s" % q)
+        test_signature_validity(Msg, q.x(), q.y(), R, S, True)
+
+      # Test if the original public key is in the set of found keys
+      original_q = ellipticcurve.Point(curve_192, Qx, Qy)
+      points = [pk.point for pk in pks]
+      if original_q in points:
+        print_("Original q was found")
+      else:
+        raise TestFailure("Original q is not in the list of recovered public keys")
+
+    else:
+      raise TestFailure("*** NO valid public key returned")
+
+
   print_("NIST Curve P-192:")
 
   p192 = generator_192
@@ -165,13 +192,15 @@ def test_signature_validity(Msg, Qx, Qy, R, S, expected):
   R = 0x64dca58a20787c488d11d6dd96313f1b766f2d8efe122916
   S = 0x1ecba28141e84ab4ecad92f56720e2cc83eb3d22dec72479
   test_signature_validity(Msg, Qx, Qy, R, S, True)
+  test_pk_recovery(Msg, R, S, Qx, Qy)
 
   Msg = 0x94bb5bacd5f8ea765810024db87f4224ad71362a3c28284b2b9f39fab86db12e8beb94aae899768229be8fdb6c4f12f28912bb604703a79ccff769c1607f5a91450f30ba0460d359d9126cbd6296be6d9c4bb96c0ee74cbb44197c207f6db326ab6f5a659113a9034e54be7b041ced9dcf6458d7fb9cbfb2744d999f7dfd63f4
   Qx = 0x3e53ef8d3112af3285c0e74842090712cd324832d4277ae7
   Qy = 0xcc75f8952d30aec2cbb719fc6aa9934590b5d0ff5a83adb7
   R = 0x8285261607283ba18f335026130bab31840dcfd9c3e555af
   S = 0x356d89e1b04541afc9704a45e9c535ce4a50929e33d7e06c
   test_signature_validity(Msg, Qx, Qy, R, S, True)
+  test_pk_recovery(Msg, R, S, Qx, Qy)
 
   Msg = 0xf6227a8eeb34afed1621dcc89a91d72ea212cb2f476839d9b4243c66877911b37b4ad6f4448792a7bbba76c63bdd63414b6facab7dc71c3396a73bd7ee14cdd41a659c61c99b779cecf07bc51ab391aa3252386242b9853ea7da67fd768d303f1b9b513d401565b6f1eb722dfdb96b519fe4f9bd5de67ae131e64b40e78c42dd
   Qx = 0x16335dbe95f8e8254a4e04575d736befb258b8657f773cb7

src/ecdsa/test_pyecdsa.py

@@ -311,6 +311,33 @@ def test_hashfunc(self):
                                        curve=NIST256p)
         self.assertTrue(vk3.verify(sig, data, hashfunc=sha256))
 
+    def test_public_key_recovery(self):
+        # Create keys
+        curve = NIST256p
+
+        sk = SigningKey.generate(curve=curve)
+        vk = sk.get_verifying_key()
+
+        # Sign a message
+        data = b("blahblah")
+        signature = sk.sign(data)
+
+        # Recover verifying keys
+        recovered_vks = VerifyingKey.from_public_key_recovery(signature, data, curve)
+
+        # Test if each pk is valid
+        for recovered_vk in recovered_vks:
+            # Test if recovered vk is valid for the data
+            self.assertTrue(recovered_vk.verify(signature, data))
+
+            # Test if properties are equal
+            self.assertEqual(vk.curve, recovered_vk.curve)
+            self.assertEqual(vk.default_hashfunc, recovered_vk.default_hashfunc)
+
+        # Test if original vk is the list of recovered keys
+        self.assertTrue(
+            vk.pubkey.point in [recovered_vk.pubkey.point for recovered_vk in recovered_vks])
+        
 
 class OpenSSL(unittest.TestCase):
     # test interoperability with OpenSSL tools. Note that openssl's ECDSA