NahamCon Winter CTF 2025: Crypto Challenge Writeups

Welcome to my writeups for the cryptography challenges from NahamCon Winter CTF 2025! This winter-themed CTF brought some interesting crypto puzzles that tested our understanding of classical ciphers and mathematical transformations.

Challenge: Linear Lines

Category: Cryptography
Difficulty: Easy-Medium
Description: A function, not a shift, guards the text. Can you unlock it and give it to me wrapped in flag{}?

Ciphertext: ODEXRKFAKVHAVKXFROLRBFOXRT

Analysis

The challenge description gives us a crucial hint: “A function, not a shift” - this immediately points us away from simple Caesar ciphers toward more complex mathematical transformations. The word “linear” in the challenge name further suggests we’re dealing with a linear mathematical function.

This combination of clues strongly indicates an affine cipher, which uses a linear mathematical function for encryption and decryption.

Understanding Affine Ciphers

The affine cipher is a type of monoalphabetic substitution cipher that uses mathematical functions:

Encryption Formula: E(x) = (ax + b) mod 26
Decryption Formula: D(x) = a^(-1)(x - b) mod 26

Where:

• a and b are the key components
• a must be coprime to 26 (valid values: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25)
• b can be any value from 0-25
• a^(-1) is the modular multiplicative inverse of a modulo 26

Solution Approach

I used two methods to solve this challenge:

Method 1: Automated Tool (Quick Solution)

For a quick solution, I used the excellent ciphey tool:

pip install ciphey
echo "ODEXRKFAKVHAVKXFROLRBFOXRT" | ciphey

This tool automatically detects and decrypts various cipher types, making it perfect for CTF scenarios.

Method 2: Manual Analysis (Educational)

For a deeper understanding, I wrote a script to brute force all possible affine cipher keys:

def affine_decrypt(ciphertext, a, b):
    # Calculate modular multiplicative inverse of a
    def mod_inverse(a, m):
        for i in range(1, m):
            if (a * i) % m == 1:
                return i
        return None

    a_inv = mod_inverse(a, 26)
    if a_inv is None:
        return None

    result = ""
    for char in ciphertext:
        if char.isalpha():
            # Convert to 0-25 range
            x = ord(char.upper()) - ord('A')
            # Apply decryption formula
            decrypted = (a_inv * (x - b)) % 26
            result += chr(decrypted + ord('A'))
        else:
            result += char

    return result

# Valid values of 'a' (must be coprime to 26)
valid_a = [1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25]
ciphertext = "ODEXRKFAKVHAVKXFROLRBFOXRT"

for a in valid_a:
    for b in range(26):
        decrypted = affine_decrypt(ciphertext, a, b)
        if decrypted and "LINEAR" in decrypted:
            print(f"a={a}, b={b}: {decrypted}")

The Solution

After testing all possible key combinations, I found the correct parameters:

• a = 21, b = 17
• Decrypted text: LINEARSTRUCTURESALWAYSLEAK

This makes perfect sense! The plaintext “LINEAR STRUCTURES ALWAYS LEAK” is a clever reference to the mathematical nature of the affine cipher and a common principle in cryptanalysis.

Key Insights

1. Challenge Design: The hint “function, not a shift” was crucial for identifying the cipher type
2. Mathematical Foundation: Understanding that affine ciphers are linear transformations helped narrow down the approach
3. Cryptanalysis Principle: The decrypted message itself teaches us that linear cryptographic structures often have weaknesses that can be exploited

Flag

Wrapping the solution in the required format: flag{LINEARSTRUCTURESALWAYSLEAK}

Lessons Learned

This challenge beautifully demonstrates several important concepts:

1. Cipher Identification: Learning to recognize cipher types from contextual clues
2. Mathematical Cryptography: Understanding how mathematical functions can be used for encryption
3. Brute Force Techniques: When the key space is small enough, exhaustive search becomes viable
4. Tool Usage: Knowing when to use automated tools vs. manual analysis for learning

The affine cipher, while more complex than Caesar ciphers, still falls into the category of classical ciphers that are vulnerable to frequency analysis and brute force attacks due to their limited key space.

This writeup is part of my NahamCon Winter CTF 2025 series. Check out my other writeups for more challenges from this excellent CTF!