Холмы (Hills)

Platform: CUSTOM | Category: Crypto | Type: Challenge | Difficulty: Easy | OS: N/A | **Author: XESXOR Techniques: Hill cipher decryption with 6x6 key matrix, ASCII code interpretation for hint extraction, Modular matrix inverse calculation (mod 27)

Summary

Walkthrough of the CUSTOM Crypto Холмы (Hills). Detailed walkthrough.

Description

Данный шифр не получил широкого распространения в криптографии из-за своей недостаточной стойкости к взлому. Сможешь ли ты его сломать?

Формат флага: CODEBY{FLAG}

Analysis

Task file (task.txt.txt)

-------------------------
|76 |101|115|116|101|114|
-------------------------
|32 |83 |97 |110|100|101|
-------------------------
|114|115|32 |115|104|111|
-------------------------
|117|108|100|32 |104|101|
-------------------------
|108|112|32 |121|111|117|
-------------------------
|32 |58 |41 |41 |41 |42 |
-------------------------
‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

KLZCOUKTVOUWUKDOBGZVJIIIRGVHXCRQUCNOX_IBBL

Decoding the matrix

The numbers in the matrix are ASCII codes. Decoding:

 python read-only • copy allowed Copy
matrix = [
    [76, 101, 115, 116, 101, 114],
    [32, 83, 97, 110, 100, 101],
    [114, 115, 32, 115, 104, 111],
    [117, 108, 100, 32, 104, 101],
    [108, 112, 32, 121, 111, 117],
    [32, 58, 41, 41, 41, 42]
]

text = ''.join(chr(c) for row in matrix for c in row)
# "Lester Sanders should help you :)))*"

Lester Sanders Hill — inventor of the Hill cipher, patented in 1929. ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Cipher identification

1. Task name "Холмы" (Hills) — direct hint at Hill cipher
2. Hint in the matrix points to Lester Sanders Hill
3. Description mentions a cipher with "insufficient resistance" — Hill cipher is vulnerable to known-plaintext attacks
4. 6x6 matrix — key for a block cipher with block size 6

Hill Cipher

Hill cipher is a polygraphic substitution cipher using linear algebra:

• Encryption: C = K × P (mod m)
• Decryption: P = K⁻¹ × C (mod m)

Where:

• K — key matrix
• P — plaintext vector
• C — ciphertext vector
• m — alphabet size ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Determining the alphabet

The ciphertext contains the _ character, meaning an extended alphabet:

ABCDEFGHIJKLMNOPQRSTUVWXYZ_

Alphabet size: 27 characters (mod 27)

Solution

 python read-only • copy allowed Copy
from sympy import Matrix

# Key matrix (ASCII codes from the task)
matrix = [
    [76, 101, 115, 116, 101, 114],
    [32, 83, 97, 110, 100, 101],
    [114, 115, 32, 115, 104, 111],
    [117, 108, 100, 32, 104, 101],
    [108, 112, 32, 121, 111, 117],
    [32, 58, 41, 41, 41, 42]
]

ciphertext = "KLZCOUKTVOUWUKDOBGZVJIIIRGVHXCRQUCNOX_IBBL"
alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ_"
mod = 27
‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

# Calculate the inverse matrix modulo 27
m = Matrix(matrix)
m_inv = m.inv_mod(mod)

# Convert ciphertext to numbers
ct_nums = [alphabet.index(c) for c in ciphertext]

# Decrypt in blocks of 6 characters
pt_nums = []
for i in range(0, len(ct_nums), 6):
    block = Matrix(ct_nums[i:i+6])
    res = (m_inv * block)
    for x in res:
        pt_nums.append(int(x) % mod)

plaintext = "".join(alphabet[n] for n in pt_nums)
print(plaintext)

Result:

REDACTED

Interpretation

The decrypted message is the flag itself! It says: "By the way, there exists an interesting film about hills" — but this is not a hint to search for another answer, it is the flag itself. ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Theory: Hill Cipher

Encryption

For a plaintext block P = [p₁, p₂, ..., pₙ]ᵀ:

C = K × P (mod m)

Decryption

P = K⁻¹ × C (mod m)

Invertibility condition

Matrix K is invertible modulo m if and only if:

gcd(det(K), m) = 1

For m = 27 = 3³, the determinant must not be divisible by 3.

Vulnerabilities

• Known-plaintext attack: knowing n² pairs (plaintext, ciphertext), the key can be recovered
• Frequency analysis of n-grams
• Linear structure allows algebraic attacks ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Key Takeaways / Lessons

• Mastering Hill cipher decryption with 6x6 key matrix, ASCII code interpretation for hint extraction, Modular matrix inverse calculation (mod 27) was key to this challenge.
• Always check for common misconfigurations and verify assumptions.

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Crafted by XESXOR Research • 2025-12-25 • CUSTOM • Холмы (Hills) • Difficulty: Easy