def CRT(b_arr, m_arr):
if (b_arr.__len__() != m_arr.__len__()) or (b_arr.__len__() == 0):
return -1
M = reduce(lambda x, y: x * y, m_arr)
M_arr = [M // m for m in m_arr]
''' MR means M_inverse '''
MR_arr = [Inverse(Mi % mi, mi) for Mi, mi in zip(M_arr, m_arr)]
return sum([b * Mi * MiR for b, Mi, MiR in zip(b_arr, M_arr, MR_arr)]) % M
def decrypt(self, cipher):
print(cipher)
x0y0 = self.E.multi(
self._point_decompress(cipher[0][0], cipher[0][1]),
self.m
)
return Mul(
cipher[1],
Inverse(x0y0[0], self.E.p),
self.E.p
)
def CongEq(a, b, n):
d = GCD(a, n)
if d != 1 and not DIVVerify(d, b):
return [-1]
elif d != 1:
res = CongEq(a // d, b // d, n // d)
k = 1
while k * n // d < n:
res.append(res[0] + k * n // d)
k += 1
return res
else:
return [Mul(b, Inverse(a, n), n)]
def PohligHellman(n, alpha, beta, q, c):
j = 0
arr = []
beta_j = beta
while j <= c - 1:
delta = pow(beta_j, (n // pow(q, j + 1)), n)
i = 0
while delta != pow(alpha, ((i * n // q) % n), n):
i = i + 1
arr.append(i)
''' beta_{j+1} = beta_{j}*alpha^{-a_j*q^j} (mod n) '''
beta_j = Mul(
beta_j,
pow(Inverse(alpha, n), Mul(arr[arr.__len__() - 1], pow(q, j), n),
n), n)
j = j + 1
return arr
def __init__(self, bit, opt='--null', p=None, q=None, a=None):
if opt == '-pq' or opt == '-pqa':
self.p = p
self.q = q
else:
self.p = randprime(2**(bit - 1), 2**bit)
self.q = randprime(2**(bit - 1), 2**bit)
self.phi = (self.p - 1) * (self.q - 1)
self.n = self.p * self.q
if opt == '-pqa':
self.a = a
else:
flag = True
while flag:
a_gen = randint(2**(2 * bit - 1), 2**(2 * bit))
if GCD(a_gen, self.phi) == 1:
flag = False
self.a = a_gen
self.b = Inverse(self.a, self.phi)
def Shanks(n, alpha, beta):
m = ceil(sqrt(n))
j_alpha = [{"j": j, "alpha^jm": pow(alpha, j * m, n)} for j in range(0, m)]
j_alpha.sort(key=lambda item: item["alpha^jm"])
i_ba_inv = [{
"i": i,
"beta*alpha^-i": Mul(beta, Inverse(pow(alpha, i, n), n), n)
} for i in range(0, m)]
i_ba_inv.sort(key=lambda item: item["beta*alpha^-i"])
'''
move index and jndex
to find which i, j st. alpha^jm = beta*alpha^-i
'''
index, jndex = 0, 0
while index != m and jndex != m:
if j_alpha[jndex]["alpha^jm"] > i_ba_inv[index]["beta*alpha^-i"]:
index += 1
elif j_alpha[jndex]["alpha^jm"] < i_ba_inv[index]["beta*alpha^-i"]:
jndex += 1
else:
return Add(m * j_alpha[jndex]["j"], i_ba_inv[index]["i"], n)
return -1
def decrypt(self, y_1, y_2):
return Mul(y_2, Inverse(pow(y_1, self.a, self.n), self.n), self.n)