Decryption function

• Points: 9

Description

You are provided with the following encryption function: f(x)=21x+11 [26]

First, you have to encrypt the word GOOGLE with this function.
Then, your mission is to find the decryption function g.
Finally, you have to decrypt the word GELKT.

Details

• [26] means “modulo 26”.
• The decryption function will be of the following form: g(y)=ay+b[26], with a and b natural integers lower than 26, and y=f(x).
• You will enter the answer lowercase in the form

  (crypted word)_(decryption function)_(decrypted word)
  

Solution

import string

alphabet = string.ascii_lowercase

def f(x: int) -> int:
    return (21 * x + 11) % 26

def f_inv(y: int) -> int:
    # y = 21 * x + 11
    # --> 21 * x = y - 11
    # --> 5 * 21 * x = 5 * (y - 11)
    # --> 1 * x = 5 * y - 3
    # --> x = 5 * y + 23
    return (5 * y + 23) % 26

def encrypt(str):
    return "".join(alphabet[f(alphabet.find(c))] for c in str)

def decrypt(str):
    return "".join(alphabet[f_inv(alphabet.find(c))] for c in str)

print(encrypt("google"))
print("----")
print(decrypt("gelkt"))

The flag is

W3C{httir_5y+23[26]_bravo}