def generate_keys():
'''Alice builds a dicsrete-log public-key cipher system.
'''
cyclic_group = large_random_prime()
generator = random_near_primitive_root(cyclic_group)
private_key = random.randint(1, cyclic_group - 1)
public_key = fast_exponentiation(generator, private_key, cyclic_group)
return (generator, public_key, cyclic_group), private_key
def encrypt(message, b, c, p):
r = large_random_prime()
c_r = fast_exponentiation(c, r, p)
encrypted_message = message * c_r % p
header = fast_exponentiation(b, r, p)
return encrypted_message, header
def large_random_p_and_q():
yield large_random_prime()
yield large_random_prime()
