Classical Cipher Analysis

SKILL: Classical Cipher Analysis — Expert Cryptanalysis Playbook

AI LOAD INSTRUCTION: Expert classical cipher identification and breaking techniques for CTF. Covers cipher identification methodology (frequency analysis, IC, Kasiski), monoalphabetic substitution, Caesar/ROT, Vigenere, Enigma, affine, Hill, transposition ciphers, Bacon/Polybius/Playfair, and XOR ciphers. Base models often skip the identification step and jump to the wrong cipher type, or fail to recognize encoded (base64/hex) ciphertext that needs decoding before analysis.

0. RELATED ROUTING

• symmetric-cipher-attacks when dealing with modern symmetric ciphers (AES/DES) rather than classical
• hash-attack-techniques when the challenge involves hash-based constructions
• lattice-crypto-attacks when knapsack-based ciphers are encountered

Quick identification guide

1. CIPHER IDENTIFICATION METHODOLOGY

1.1 Step 1: Character Set Analysis

def analyze_charset(ciphertext):
    """Identify encoding/cipher by character set."""
    chars = set(ciphertext.strip())

    if chars <= set('01 \n'):
        return "Binary encoding"
    if chars <= set('.-/ \n'):
        return "Morse code"
    if chars <= set('0123456789abcdef \n'):
        return "Hex encoding"
    if chars <= set('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=\n'):
        if '=' in ciphertext or len(ciphertext) % 4 == 0:
            return "Base64 encoding"
    if chars <= set('ABCDEFGHIJKLMNOPQRSTUVWXYZ \n'):
        return "Uppercase only — classical cipher"
    if all(c in '12345' for c in ciphertext.replace(' ', '').replace('\n', '')):
        return "Polybius square (digits 1-5)"

    return "Mixed charset — needs further analysis"

1.2 Step 2: Frequency Analysis

from collections import Counter

def frequency_analysis(text):
    """Compute letter frequency distribution."""
    text = text.upper()
    letters = [c for c in text if c.isalpha()]
    total = len(letters)
    freq = Counter(letters)

    print("Letter frequencies:")
    for letter, count in freq.most_common():
        pct = count / total * 100
        bar = '#' * int(pct)
        print(f"  {letter}: {pct:5.1f}% {bar}")

    return freq

# English letter frequency (for comparison):
# E T A O I N S H R D L C U M W F G Y P B V K J X Q Z
# 12.7 9.1 8.2 7.5 7.0 6.7 6.3 6.1 6.0 4.3 4.0 2.8 ...

1.3 Step 3: Index of Coincidence (IC)

def index_of_coincidence(text):
    """
    IC ≈ 0.065 → English / monoalphabetic substitution
    IC ≈ 0.038 → random / polyalphabetic cipher
    """
    text = [c for c in text.upper() if c.isalpha()]
    N = len(text)
    freq = Counter(text)

    ic = sum(f * (f - 1) for f in freq.values()) / (N * (N - 1))
    return ic

# Interpretation:
# IC > 0.060 → monoalphabetic (Caesar, simple substitution, Playfair)
# IC ≈ 0.045-0.055 → polyalphabetic with short key (Vigenere key < 10)
# IC ≈ 0.038-0.042 → polyalphabetic with long key or random

1.4 Step 4: Kasiski Examination (for Polyalphabetic)

from math import gcd
from functools import reduce

def kasiski(ciphertext, min_len=3):
    """Find repeated sequences and their distances → key length."""
    text = ''.join(c for c in ciphertext.upper() if c.isalpha())
    distances = []

    for length in range(min_len, min(20, len(text) // 3)):
        for i in range(len(text) - length):
            seq = text[i:i+length]
            j = text.find(seq, i + 1)
            while j != -1:
                distances.append(j - i)
                j = text.find(seq, j + 1)

    if not distances:
        return None

    # Key length is likely GCD of common distances
    common_gcds = Counter()
    for d in distances:
        for factor in range(2, min(d + 1, 30)):
            if d % factor == 0:
                common_gcds[factor] += 1

    print("Likely key lengths (by frequency):")
    for length, count in common_gcds.most_common(5):
        print(f"  Key length {length}: {count} occurrences")

    return common_gcds.most_common(1)[0][0]

2. MONOALPHABETIC SUBSTITUTION

2.1 Frequency Analysis Attack

def solve_substitution(ciphertext, interactive=False):
    """Solve monoalphabetic substitution via frequency analysis."""
    freq = frequency_analysis(ciphertext)

    # English frequency order
    eng_order = "ETAOINSRHLDCUMWFGYPBVKJXQZ"
    cipher_order = ''.join(c for c, _ in freq.most_common())

    # Initial mapping (frequency-based guess)
    mapping = {}
    for i, c in enumerate(cipher_order):
        if i < len(eng_order):
            mapping[c] = eng_order[i]

    # Apply mapping
    result = ""
    for c in ciphertext.upper():
        result += mapping.get(c, c)

    return result, mapping

# Better approach: use automated solvers
# quipqiup.com — online substitution solver
# dcode.fr/monoalphabetic-substitution — with word pattern matching

2.2 Known Plaintext (Crib Dragging)

If part of the plaintext is known (e.g., "flag{" prefix):

def crib_drag_substitution(ciphertext, known_plain, known_cipher):
    """Build partial mapping from known plaintext-ciphertext pair."""
    mapping = {}
    for p, c in zip(known_plain.upper(), known_cipher.upper()):
        mapping[c] = p

    # Apply partial mapping
    result = ""
    for c in ciphertext.upper():
        result += mapping.get(c, '?')

    return result, mapping

3. CAESAR / ROT CIPHERS

3.1 Brute Force

def caesar_bruteforce(ciphertext):
    """Try all 25 shifts, score by English frequency."""
    results = []
    for shift in range(26):
        decrypted = ""
        for c in ciphertext:
            if c.isalpha():
                base = ord('A') if c.isupper() else ord('a')
                decrypted += chr((ord(c) - base - shift) % 26 + base)
            else:
                decrypted += c

        # Chi-squared scoring against English frequency
        score = chi_squared_score(decrypted)
        results.append((shift, score, decrypted))

    results.sort(key=lambda x: x[1])
    return results[0]  # best match

def chi_squared_score(text):
    """Lower score = closer to English."""
    expected = {
        'E': 12.7, 'T': 9.1, 'A': 8.2, 'O': 7.5, 'I': 7.0,
        'N': 6.7, 'S': 6.3, 'H': 6.1, 'R': 6.0, 'D': 4.3,
        'L': 4.0, 'C': 2.8, 'U': 2.8, 'M': 2.4, 'W': 2.4,
        'F': 2.2, 'G': 2.0, 'Y': 2.0, 'P': 1.9, 'B': 1.5,
        'V': 1.0, 'K': 0.8, 'J': 0.2, 'X': 0.2, 'Q': 0.1, 'Z': 0.1,
    }
    text = text.upper()
    letters = [c for c in text if c.isalpha()]
    total = len(letters)
    if total == 0:
        return float('inf')

    freq = Counter(letters)
    score = sum(
        (freq.get(c, 0) / total * 100 - expected.get(c, 0)) ** 2 / max(expected.get(c, 0.1), 0.1)
        for c in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    )
    return score

3.2 ROT13 and ROT47

import codecs

# ROT13 (letters only)
rot13 = codecs.decode(ciphertext, 'rot_13')