def discrete_log(prime, public_key, primitive_root):
m = int(math.floor((prime - 1) ** .5))
base_exponents = {}
for j in xrange(0, m):
base_exponents[fast_exponentiation(primitive_root, j, prime)] = j
inverse_b = extended_euclidean_algorithm(primitive_root, prime) % prime
c = fast_exponentiation(inverse_b, m, prime)
x = public_key
for i in xrange(0, m):
if x in base_exponents:
return (m * i) + base_exponents[x]
else:
x = (x * c) % prime
def decrypt(message, header, l, p):
c_r = fast_exponentiation(header, l, p)
inverse = extended_euclidean_algorithm(c_r, p)
plaintext = (inverse * message) % p
return plaintext
def multiplicative_inverse(phi_n, key):
inverse_n = extended_euclidean_algorithm(phi_n, key)
inverse_n = inverse_n % phi_n
return inverse_n