def point_addition(self, point1, point2):
# If we try to add the same point
if point1.x == point2.x and point1.y == point2.y:
return self.__point_doubling(point1)
# if we are adding different points
else:
if point1.x == point2.x and point1.y == (self.p -
point2.y) % self.p:
return Point(0, 0)
if point1.x == 0 and point1.y == 0:
return Point(point2.x, point2.y)
if point2.x == 0 and point2.y == 0:
return Point(point1.x, point1.y)
neg_flag = 1
if point2.x - point1.x < 0:
neg_flag = -1
inv = euclideans_algorithm.eea(abs(point2.x - point1.x),
self.p)
else:
inv = euclideans_algorithm.eea(point2.x - point1.x, self.p)
s = ((point2.y - point1.y) * (inv * neg_flag)) % self.p
x3 = (s * s - point1.x - point2.x) % self.p
y3 = (s * (point1.x - x3) - point1.y) % self.p
result_point = Point(x3, y3)
if self.testPoint(result_point):
return result_point
else:
raise Exception(
"Point addition does not result in a valid curve point. Aborting."
)
def verify_sig(self, r, s, pk, M, hash_value):
if 1 < r < self.n - 1 and 1 < s < self.n - 1:
#calculate hash of message
if hash_value == "sha256":
sha256 = hashlib.sha256()
sha256.update(M)
H = sha256.digest()
elif hash_value == "sha384":
sha384 = hashlib.sha384()
sha384.update(M)
H = sha384.digest()
else:
sha512 = hashlib.sha512()
sha512.update(M)
H = sha512.digest()
e = int(H.encode('hex'), 16)
w = euclideans_algorithm.eea(s, self.n)
u1 = (e * w) % self.n
u2 = (r * w) % self.n
R = self.point_addition(self.multiply(u1, self.getGPoint()),
self.multiply(u2, pk))
v = R.x % self.n
if v == r:
return "Signature Validates!"
else:
return "Signature FAIL!"
def __point_doubling(self, point1):
s = ((3 * (point1.x * point1.x) + self.a) *
(euclideans_algorithm.eea(2 * point1.y, self.p)) % self.p)
x3 = (s * s - point1.x - point1.x) % self.p
y3 = (s * (point1.x - x3) - point1.y) % self.p
result_point = Point(x3, y3)
if self.testPoint(result_point):
return result_point
else:
print "Result Point: x = %d, y = %d" % (result_point.x,
result_point.y)
raise Exception(
"Point doubling does not result in a valid curve point. Aborting."
)
def sign(self, data, skey, hash_value):
system = SystemRandom()
ephemeral = system.randrange(self.n) + 1
R = self.multiply(ephemeral, self.getGPoint())
r = R.x % self.n
inv_ephemeral = euclideans_algorithm.eea(ephemeral, self.n)
if hash_value == "sha256":
sha256 = hashlib.sha256()
sha256.update(data)
H = sha256.digest()
elif hash_value == "sha384":
sha384 = hashlib.sha384()
sha384.update(data)
H = sha384.digest()
else:
sha512 = hashlib.sha512()
sha512.update(data)
H = sha512.digest()
e = int(H.encode('hex'), 16)
return r, (inv_ephemeral * (e + (skey * r))) % self.n
test_curve = EllipticCurve(secp256_dparameters[0], secp256_dparameters[1], secp256_dparameters[2],
secp256_dparameters[3], secp256_dparameters[4], secp256_dparameters[5],
secp256_dparameters[6])
sk = 0x70a12c2db16845ed56ff68cfc21a472b3f04d7d6851bf6349f2d7d5b3452b38a
pk = test_curve.multiply(sk, test_curve.getGPoint())
print "pk x -> ", hex(pk.x)
print "pk y -> ", hex(pk.y)
if pk.x == 0x8101ece47464a6ead70cf69a6e2bd3d88691a3262d22cba4f7635eaff26680a8 and \
pk.y == 0xd8a12ba61d599235f67d9cb4d58f1783d3ca43e78f0a5abaa624079936c0c3a9:
print "PK TEST SUCCESSFUL"
else:
print "PK TEST FAIL"
k = 0x580ec00d856434334cef3f71ecaed4965b12ae37fa47055b1965c7b134ee45d0
inv_k = euclideans_algorithm.eea(k, secp256_dparameters[5])
if inv_k == 0x6a664fa115356d33f16331b54c4e7ce967965386c7dcbf2904604d0c132b4a74:
print "TEST INVERSE SUCCESSFUL"
else:
print "TEST INVERSE FAIL"
R = test_curve.gen_pkey(k)
xr = 0x7214bc9647160bbd39ff2f80533f5dc6ddd70ddf86bb815661e805d5d4e6f27c
xy = 0x8b81e3e977597110c7cf2633435b2294b72642987defd3d4007e1cfc5df84541
if R.x == xr and R.y == xy:
print "Ephemeral key gen successful"
else:
print "Ephemeral key gen fail"
r = xr % secp256_dparameters[5]