def decrypt(self,
g=None,
modulus=None,
private_key=None,
cipher_text_1=None,
cipher_text_2=None):
if private_key is not None:
self.set_private_key(private_key)
if g is not None:
self.set_g(g)
if modulus is not None:
self.set_modulus(modulus)
if cipher_text_1 is not None:
self.set_cipher_text_1(cipher_text_1)
if cipher_text_2 is not None:
self.set_cipher_text_2(cipher_text_2)
if None not in [
self.private_key, self.g, self.modulus, self.cipher_text_1,
self.cipher_text_2
]:
x = mod_inv(
fast_power(self.cipher_text_1, self.private_key, self.modulus),
self.modulus)
self.message = (x * self.cipher_text_2) % self.modulus
return self.message
else:
return None
def bsgs(
g,
h,
p,
smoothness=10000
): # Solving x given g,h,p for the equation g^x (mod p) = h, so logg(h) (mod p) = x
N = order(g, p, smoothness)
n = int(sqrt(N)) + 1
e = 1
u = mod_inv(fast_power(g, n, p), p)
uk = u
gi = g
hui = (h * uk) % p
list_one = {gi: 1}
list_two = {hui: 1}
# Create the two list
for i in range(2, n + 1):
gi = (gi * g) % p
uk = (uk * u) % p
hui = (h * uk) % p
list_one.update({gi: i})
list_two.update({hui: i})
# Now Check for a collision between the list
for huk in list_two.keys():
for gk in list_one.keys():
if huk == gk:
x = (list_one.get(gk) + (list_two.get(huk) * n)) % N
xs = []
for i in range(0, int(((p - 1) / N) + 1)):
xs.append(x + N * i)
return xs
def slope(self, P, Q): # Where P and Q are tuples
if P == Q:
inv_2y_p = mod_inv((2 * P[1]) % self.modulus, self.modulus)
if isinstance(inv_2y_p, tuple):
d = inv_2y_p[1]
return [None, None, d]
slope = ((3 * P[0] * P[0] + self.A) * inv_2y_p) % self.modulus
return slope
else:
y_diff = (P[1] - Q[1]) % self.modulus
x_diff = (P[0] - Q[0]) % self.modulus
inv_x_diff = mod_inv(x_diff, self.modulus)
if isinstance(inv_x_diff, tuple):
d = inv_x_diff[1]
return [None, None, d]
slope = (y_diff * inv_x_diff) % self.modulus
return slope
def decrypt(self, c, p = None, q = None, e = None):
if q is not None and p is not None:
self.q = q
self.p = p
self. N = self.p * self.q
if e is not None:
self.e = e
self.c = c
if None in [self.N, self.p, self.q, self.e, self.c]:
raise ValueError("c, e, p, q, or N is None")
g = eea(self.p - 1, self.q-1).get("gcd")
self.d = int(mod_inv(self.e % ((self.p-1)*(self.q-1)/g), (self.p-1)*(self.q-1)/g))
self.m = fast_power(self.c, self.d, self.N)
return self.m
def test_mod_inv_4(self):
a = 173920
m = 100207
with self.assertRaises(ValueError):
self.assertEqual(mod_inv(a, m), b)
def test_mod_inv_3(self):
a = 632
m = 999749
b = 93331
self.assertEqual(mod_inv(a, m), b)
def test_mod_inv_2(self):
a = 3
m = 7
b = 5
self.assertEqual(mod_inv(a, m), b)
def test_mod_inv_1(self):
print("\n\nRunning test for src module: mod_inv")
a = 5
m = 7
b = 3
self.assertEqual(mod_inv(a, m), b)