Hackvent_2018/Day 11/decode.py

#!/usr/bin/python

import math

def linear_diophantine_equation(a, b):
    if b > a:
        return linear_diophantine_equation(b, a)

    if b == 0:
        return a, 1, 0

    d, x, y = linear_diophantine_equation(b, a % b)
    return (d, y, x - (a // b) * y)

# c = (a * b) % p
c = 0x7E65D68F84862CEA3FCC15B966767CCAED530B87FC4061517A1497A03D2
p = 0xDD8E05FF296C792D2855DB6B5331AF9D112876B41D43F73CEF3AC7425F9
b = 0x7BBE3A50F28B2BA511A860A0A32AD71D4B5B93A8AE295E83350E68B57E5

def test_solution(a):
    return (a * b) % p == c

d, x, y =  linear_diophantine_equation(b, p)

a = y * c
a += abs(a // p) * p
solution = hex(a).replace("-", "")[2:]

while True:
    a += p
    solution = hex(a).replace("-", "")[2:]
    if not test_solution(a):
        print("Not a valid solution")
        exit()

    ascii = ''.join([chr(int(solution[i:i+2],16)) for i in range(0, len(solution), 2)])
    if ascii[0:4] == "HV18":
        print(hex(a))
        print(ascii)
        break