enigma.py

from Crypto.PublicKey import RSA

with open('public_key.pem', 'rb') as f:
	modulus = RSA.importKey(f.read()).n

with open('message.enc', 'rb') as f:
	message = int.from_bytes(f.read(), byteorder='big')

def cube_root(n):
	guess, previous = n, 0
	while abs(guess - previous) > 1:
		previous = guess
		guess = guess - (guess // 3) + (n // (3 * pow(guess, 2)))
	
	while pow(guess, 3) > n:
		guess -= 1

	return guess

def to_bytes(n):
	return n.to_bytes((n.bit_length() // 8) + 1, byteorder='big')

def try_multiple(k):
	message_guess = cube_root(message + k * modulus)
	message_bytes = to_bytes(message_guess)

	if max(message_bytes) < 128:
		print(message_bytes)
		return True
	else:
		return False

k = 0
while not try_multiple(k):
	k += 1