def div(a, b, mod):
inv_b, gcd = extended_gcd(b, mod)
if gcd == 1:
raise ValueError()
return mul(a, inv_b, mod)
def chinese_remainder_theorem(ais, nis):
"""Construct a solution to the chinese remainder theorem
Given a list of a[i]'s and n[i]'s constructs an x such that
x = a[i] (mod n[i]) for all i
"""
N = reduce(lambda x, y: x*y, nis, 1)
ei = [extended_gcd(ni, N/ni)[1] * (N/ni) for ni in nis]
return sum([x[0]*x[1] for x in zip(ais, ei)]) % N
def decrypt(cipher, key_a, key_b):
inverse, am_gcd = extended_gcd(key_a, 26)
assert(am_gcd == 1)
message = ""
for c in cipher:
if c.isalpha():
x = ord(c.upper()) - ord("A")
y = ((x - key_b) * inverse) % 26
message += chr(y + ord("A"))
else:
message += c
return message
