def sign(curve, user_private_key, text):
h = md5(text.encode()).digest()
q = curve.q
e = bytes2long(h) % q
if e == 0:
e = 1
while True:
k = bytes2long(urandom(64)) % q
Cx, Cy = curve.mul(k)
r = Cx % q
if r == 0:
continue
d = user_private_key * r
k *= e
s = (d + k) % q
if s == 0:
continue
break
return long2bytes(s, 64) + long2bytes(r, 64)
def sign(curve, user_private_key, text):
h = md5(text.encode()).digest()
q = curve.q
e = bytes2long(h) % q
if e == 0:
e = 1
while True:
k = bytes2long(urandom(64)) % q
# C = kP,
Cx, Cy = curve.mul(k) # get (x, y) - point of our eliptic curve
# r = xc(mod q)
r = Cx % q
if r == 0:
continue
d = user_private_key * r
k *= e
# s = rd + ke(mod q)
s = (d + k) % q
if s == 0:
continue
break
return long2bytes(s, 64) + long2bytes(r, 64)
def check_signature(curve, pub_key_tuple, hash, signature):
s = bytes2long(signature[:64])
r = bytes2long(signature[64:])
q = curve.q
p = curve.p
if r <= 0 or r >= q or s <= 0 or s >= q:
return False
e = bytes2long(hash) % curve.q
if e == 0:
e = 1
v = modinvert(e, q)
z1 = s * v % q
z2 = q - r * v % q
p1x, p1y = curve.mul(z1)
q1x, q1y = curve.mul(z2, pub_key_tuple[0], pub_key_tuple[1])
Cx = q1x - p1x
if Cx < 0:
Cx += p
Cx = modinvert(Cx, p)
z1 = q1y - p1y
Cx = Cx * z1 % p
Cx = Cx * Cx % p
Cx = Cx - p1x - q1x
Cx = Cx % p
if Cx < 0:
Cx += p
R = Cx % q
return R == r
def check_signature(curve, pub_key_tuple, hash, signature):
s = bytes2long(signature[:64])
r = bytes2long(signature[64:])
q = curve.q
p = curve.p
if r <= 0 or r >= q or s <= 0 or s >= q:
return False
# e = z(mod q), и если e = 0, положить e = 1. Где z — целое число из 1..T
e = bytes2long(hash) % curve.q
if e == 0:
e = 1
# v = e - 1(mod q)
v = modinvert(e, q)
# Вычисление z1 = sv(mod q) и z2 = - rv(mod q)
z1 = s * v % q
z2 = q - r * v % q
p1x, p1y = curve.mul(z1)
q1x, q1y = curve.mul(z2, pub_key_tuple[0], pub_key_tuple[1])
Cx = q1x - p1x
if Cx < 0:
Cx += p
Cx = modinvert(Cx, p)
z1 = q1y - p1y
Cx = Cx * z1 % p
Cx = Cx * Cx % p
Cx = Cx - p1x - q1x
Cx = Cx % p
if Cx < 0:
Cx += p
R = Cx % q
return R == r
def to_ten_str(prv):
return bytes2long(prv[::-1])