def test_inverse_mod(self):
prime = generator_secp256k1.curve().p()
order = generator_secp256k1.order()
for v in range(70):
n = int(float("1e%d" % v))
i = inverse_mod(n, prime)
assert n * i % prime == 1
i = inverse_mod(n, order)
assert n * i % order == 1
def verify_dash_signature(generator, address, message, signature):
compressed = False
G = generator
curve = G.curve()
order = G.order()
_a, _b, _p = curve.a(), curve.b(), curve.p()
sig = base64.b64decode(signature)
if len(sig) != 65:
raise Exception("vmB", "Bad signature")
hb = ord(sig[0])
r, s = map(str_to_long, [sig[1:33], sig[33:65]])
if hb < 27 or hb >= 35:
raise Exception("vmB", "Bad first byte")
if hb >= 31:
compressed = True
hb -= 4
recid = hb - 27
x = (r + (recid / 2) * order) % _p
y2 = (pow(x, 3, _p) + _a * x + _b) % _p
yomy = numbertheory.modular_sqrt(y2, _p)
if (yomy - recid) % 2 == 0:
y = yomy
else:
y = _p - yomy
R = ellipticcurve.Point(curve, x, y, order)
e = str_to_long(message)
minus_e = -e % order
inv_r = numbertheory.inverse_mod(r, order)
Q = inv_r * (R * s + G * minus_e)
key = Key(public_pair=(Q.x(), Q.y()), netcode='DASH')
return key.address(use_uncompressed=not compressed) == address
def sign(self, message, compact=True):
"""Signs the supplied message with the private key"""
if compact:
fd = io.BytesIO()
stream_bc_string(fd, bytearray('Bitcoin Signed Message:\n', 'ascii'))
stream_bc_string(fd, bytearray(message, 'utf-8'))
mhash = from_bytes_32(double_sha256(fd.getvalue()))
G = generator_secp256k1
n = G.order()
k = from_bytes_32(os.urandom(32))
p1 = k * G
r = p1.x()
if r == 0:
raise RuntimeError("amazingly unlucky random number r")
s = (numbertheory.inverse_mod(k, n) *
(mhash + (self.keypair.secret_exponent() * r) % n)) % n
if s == 0:
raise RuntimeError("amazingly unlucky random number s")
y_odd = p1.y() % 2
assert y_odd in (0, 1)
first = 27 + y_odd + (4 if not self.keypair._use_uncompressed(False) else 0)
sig = binascii.b2a_base64(bytearray([first]) + to_bytes_32(r) + to_bytes_32(s)).strip()
if not isinstance(sig, str):
# python3 b2a wrongness
sig = str(sig, 'ascii')
return sig
else:
return keys.sign_sha256(self.private_key, message)
