def test_order_functional_1(self):
print("\n\nRunning test for cryptanalysis module: order")
generator = 9704
modulus = 17389
expected_order = 1242
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)
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 pohlig_hellman(
g, h, p
): #Solving x given g,h,p for the equation g^x (mod p) = h, so logg(h) (mod p) = x
n = p - 1
congruences_and_mods = []
prime_factors = naive_factor(n, 10000).get("prime_factors_dict")
for factor in prime_factors.keys():
modulo = factor**prime_factors.get(factor)
gi = fast_power(g, n / modulo, p)
hi = fast_power(h, n / modulo, p)
ax = bsgs(
gi, hi,
p)[0] # retuns a list of solutions, we just want the first one
congruences_and_mods.append((ax, modulo))
x = crt(congruences_and_mods)
N = order(g, p, 10000)
xs = []
for i in range(1, int(((p - 1) / N) + 1)):
xs.append(int((x + N * i) % n))
return xs
def test_order_functional_6(self):
generator = 1
modulus = 2
expected_order = 1
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)
def test_order_functional_5(self):
generator = 37
modulus = 839
expected_order = 419
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)
def test_order_functional_4(self):
generator = 3
modulus = 7
expected_order = 6
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)
def test_order_functional_3(self):
generator = 23378
modulus = 2860486313
expected_order = 2860486312
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)
def test_order_functional_2(self):
generator = 2
modulus = 3267000013
expected_order = 1089000004
output_order = order(generator, modulus)
self.assertEqual(output_order, expected_order)