commit 59c1d03f018026ac301c4e74facfc64da8ae4708
parent 1a8e8bc047bc6cd124b338e9c69c3bbb561db54a
Author: SomberNight <somber.night@protonmail.com>
Date: Sat, 16 Jun 2018 06:34:03 +0200
ecc.py: properly handle point at infinity
Diffstat:
2 files changed, 53 insertions(+), 6 deletions(-)
diff --git a/lib/ecc.py b/lib/ecc.py
@@ -49,6 +49,10 @@ def generator():
return ECPubkey.from_point(generator_secp256k1)
+def point_at_infinity():
+ return ECPubkey(None)
+
+
def sig_string_from_der_sig(der_sig, order=CURVE_ORDER):
r, s = ecdsa.util.sigdecode_der(der_sig, order)
return ecdsa.util.sigencode_string(r, s, order)
@@ -83,6 +87,8 @@ def point_to_ser(P, compressed=True) -> bytes:
x, y = P
else:
x, y = P.x(), P.y()
+ if x is None or y is None: # infinity
+ return None
if compressed:
return bfh(('%02x' % (2+(y&1))) + ('%064x' % x))
return bfh('04'+('%064x' % x)+('%064x' % y))
@@ -115,7 +121,10 @@ def ser_to_point(ser: bytes) -> (int, int):
def _ser_to_python_ecdsa_point(ser: bytes) -> ecdsa.ellipticcurve.Point:
x, y = ser_to_point(ser)
- return Point(curve_secp256k1, x, y, CURVE_ORDER)
+ try:
+ return Point(curve_secp256k1, x, y, CURVE_ORDER)
+ except:
+ raise InvalidECPointException()
class InvalidECPointException(Exception):
@@ -166,12 +175,19 @@ class _MySigningKey(ecdsa.SigningKey):
return r, s
+class _PubkeyForPointAtInfinity:
+ point = ecdsa.ellipticcurve.INFINITY
+
+
class ECPubkey(object):
def __init__(self, b: bytes):
- assert_bytes(b)
- point = _ser_to_python_ecdsa_point(b)
- self._pubkey = ecdsa.ecdsa.Public_key(generator_secp256k1, point)
+ if b is not None:
+ assert_bytes(b)
+ point = _ser_to_python_ecdsa_point(b)
+ self._pubkey = ecdsa.ecdsa.Public_key(generator_secp256k1, point)
+ else:
+ self._pubkey = _PubkeyForPointAtInfinity()
@classmethod
def from_sig_string(cls, sig_string: bytes, recid: int, msg_hash: bytes):
@@ -205,6 +221,7 @@ class ECPubkey(object):
return ECPubkey(_bytes)
def get_public_key_bytes(self, compressed=True):
+ if self.is_at_infinity(): raise Exception('point is at infinity')
return point_to_ser(self.point(), compressed)
def get_public_key_hex(self, compressed=True):
@@ -229,7 +246,8 @@ class ECPubkey(object):
return self.from_point(ecdsa_point)
def __eq__(self, other):
- return self.get_public_key_bytes() == other.get_public_key_bytes()
+ return self._pubkey.point.x() == other._pubkey.point.x() \
+ and self._pubkey.point.y() == other._pubkey.point.y()
def __ne__(self, other):
return not (self == other)
@@ -275,6 +293,9 @@ class ECPubkey(object):
def order(cls):
return CURVE_ORDER
+ def is_at_infinity(self):
+ return self == point_at_infinity()
+
def msg_magic(message: bytes) -> bytes:
from .bitcoin import var_int
@@ -318,7 +339,7 @@ class ECPrivkey(ECPubkey):
raise Exception('unexpected size for secret. should be 32 bytes, not {}'.format(len(privkey_bytes)))
secret = string_to_number(privkey_bytes)
if not is_secret_within_curve_range(secret):
- raise Exception('Invalid secret scalar (not within curve order)')
+ raise InvalidECPointException('Invalid secret scalar (not within curve order)')
self.secret_scalar = secret
point = generator_secp256k1 * secret
diff --git a/lib/tests/test_bitcoin.py b/lib/tests/test_bitcoin.py
@@ -126,6 +126,32 @@ class Test_bitcoin(SequentialTestCase):
eck.verify_message_for_address(signature, message)
@needs_test_with_all_ecc_implementations
+ def test_ecc_sanity(self):
+ G = ecc.generator()
+ n = G.order()
+ self.assertEqual(ecc.CURVE_ORDER, n)
+ inf = n * G
+ self.assertEqual(ecc.point_at_infinity(), inf)
+ self.assertTrue(inf.is_at_infinity())
+ self.assertFalse(G.is_at_infinity())
+ self.assertEqual(11 * G, 7 * G + 4 * G)
+ self.assertEqual((n + 2) * G, 2 * G)
+ self.assertEqual((n - 2) * G, -2 * G)
+ A = (n - 2) * G
+ B = (n - 1) * G
+ C = n * G
+ D = (n + 1) * G
+ self.assertFalse(A.is_at_infinity())
+ self.assertFalse(B.is_at_infinity())
+ self.assertTrue(C.is_at_infinity())
+ self.assertTrue((C * 5).is_at_infinity())
+ self.assertFalse(D.is_at_infinity())
+ self.assertEqual(inf, C)
+ self.assertEqual(inf, A + 2 * G)
+ self.assertEqual(inf, D + (-1) * G)
+ self.assertNotEqual(A, B)
+
+ @needs_test_with_all_ecc_implementations
def test_msg_signing(self):
msg1 = b'Chancellor on brink of second bailout for banks'
msg2 = b'Electrum'
