hill_cracker.py

from string import ascii_lowercase
from time import perf_counter
from typing import Tuple, Generator, List

CHARSET_LENGTH = len(ascii_lowercase)

Pair = Tuple[int, int]
Key = Tuple[int, int, int, int]


def encode_pair(pair: Pair, key: Key) -> Pair:
    a, b, c, d = key
    l, r = pair

    return (
        (a * l + b * r) % CHARSET_LENGTH,
        (c * l + d * r) % CHARSET_LENGTH
    )


def brute_force(target: str, key: Key) -> str:
    def paired_chunks(lst: Tuple[int, ...]) -> Generator[Tuple[int, ...], None, None]:
        for i in range(0, len(lst), 2):
            yield tuple(lst[i:i + 2])

    _combinations = tuple(
        (left, right)
        for left in range(CHARSET_LENGTH)
        for right in range(CHARSET_LENGTH)
    )

    word: List[int] = []
    indexes = tuple(ascii_lowercase.index(c) for c in target)

    for pair in paired_chunks(indexes):
        for combination in _combinations:
            if pair == encode_pair(combination, key):
                word.extend(combination)

    return ''.join(ascii_lowercase[i] for i in word)


if __name__ == '__main__':
    print(
        brute_force(
            'fpdgxant',
            (11, 3, 7, 4)
        )
    )