def generate_prime(seed):
random.seed(seed)
while True:
p = random.getrandbits(512) | (1 << 511)
if p % E == 1: continue
if not is_prime(p): continue
return p
def __init__(self, modulus, root_order=2):
"""
"""
modulus = modulus
root_order = root_order
if modulus <= 2 or not is_prime(modulus):
err = "Provided modulus is not an odd prime"
raise AlgebraError(err)
if root_order <= 0 or root_order >= modulus:
err = "Provided order of unit root is not in the allowed range"
raise AlgebraError(err)
order, s = divmod(modulus - 1, root_order)
if s != 0:
err = "Provided order of unit root does not divide the group\'s order"
raise AlgebraError(err)
self.__modulus = modulus
self.__order = order
self.__Element = ModPrimeElement
self.__unit = mpz(1)
def _validate_system(cls, modulus, order, generator, root_order,
prime_order, min_mod_size, min_gen_size, allow_weakness):
"""
"""
if root_order==2 and modulus % 4 != 3:
#
# ~ Algebraic fact: the condition p = 3 mod 4 guarantees direct
# ~ solvability of the congruence x ^ 2 = a (mod p), a E Z*_p,
# ~ allowing for efficient verification of quadratic residues
#
err = "Provided modulus is not 3 mod 4"
raise WrongCryptoError(err)
if prime_order and not is_prime(order):
err = "Order of the requested group is not prime"
raise WrongCryptoError(err)
if not allow_weakness:
MIN_MOD_SIZE = min_mod_size or cls.MIN_MOD_SIZE
if modulus.bit_length() < MIN_MOD_SIZE:
err = f"Provided modulus is < {MIN_MOD_SIZE} bits long"
raise WeakCryptoError(err)
MIN_GEN_SIZE = min_gen_size or cls.MIN_GEN_SIZE
if generator.bit_length < MIN_GEN_SIZE:
err = f"Generator is < {MIN_GEN_SIZE} bits long"
raise WeakCryptoError(err)
def __init__(self):
self.d = precompute_d()
self.primes = [is_prime(p) for p in range(2000)]
self.cache = {}