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

Observation	Likely Cipher	First Action
All uppercase letters, uneven frequency	Monoalphabetic substitution	Frequency analysis
All uppercase, flat frequency distribution	Polyalphabetic (Vigenere)	IC + Kasiski
Only A-Z shifted uniformly	Caesar/ROT	Brute force 25 shifts
Base64 alphabet (A-Za-z0-9+/=)	Base64 encoded (decode first)	Base64 decode
Hex string (0-9a-f)	Hex encoded (decode first)	Hex decode
Binary (0s and 1s)	Binary encoded	Convert to ASCII
Dots and dashes	Morse code	Morse decode
Raised/normal text pattern	Bacon cipher	Map to A/B, decode
2-digit number pairs (11-55)	Polybius square	Grid lookup
Text appears scrambled (right letters, wrong order)	Transposition	Anagram analysis
Non-printable bytes XOR-like	XOR cipher	Single/repeating key XOR analysis

---

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')

# ROT47 (ASCII 33-126)
def rot47(text):
    return ''.join(
        chr(33 + (ord(c) - 33 + 47) % 94) if 33 <= ord(c) <= 126 else c
        for c in text
    )

---

4. VIGENERE CIPHER

4.1 Full Attack Workflow

Step 1: Confirm polyalphabetic (IC ≈ 0.04-0.05)
Step 2: Find key length (Kasiski + IC per period)
Step 3: For each key position, solve as single Caesar cipher
Step 4: Assemble key → decrypt

4.2 IC-Based Key Length Detection

def find_vigenere_key_length(ciphertext, max_key=20):
    """Use IC to find Vigenere key length."""
    text = [c for c in ciphertext.upper() if c.isalpha()]
    results = []

    for kl in range(1, max_key + 1):
        # Split text into kl columns
        columns = [[] for _ in range(kl)]
        for i, c in enumerate(text):
            columns[i % kl].append(c)

        # Average IC across columns
        avg_ic = sum(
            index_of_coincidence(''.join(col)) for col in columns
        ) / kl

        results.append((kl, avg_ic))
        print(f"  Key length {kl:2d}: IC = {avg_ic:.4f}")

    # Key length with IC closest to 0.065
    best = max(results, key=lambda x: x[1])
    return best[0]

4.3 Per-Position Frequency Attack

def crack_vigenere(ciphertext, key_length):
    """Crack Vigenere given known key length."""
    text = [c for c in ciphertext.upper() if c.isalpha()]
    key = ""

    for pos in range(key_length):
        column = ''.join(text[i] for i in range(pos, len(text), key_length))
        # Solve as Caesar cipher
        shift, score, _ = caesar_bruteforce(column)
        key += chr(shift + ord('A'))

    # Decrypt
    plaintext = ""
    ki = 0
    for c in ciphertext:
        if c.isalpha():
            shift = ord(key[ki % key_length]) - ord('A')
            base = ord('A') if c.isupper() else ord('a')
            plaintext += chr((ord(c) - base - shift) % 26 + base)
            ki += 1
        else:
            plaintext += c

    return key, plaintext

---

5. AFFINE CIPHER

5.1 Definition

E(x) = (a·x + b) mod 26 where gcd(a, 26) = 1.

Valid a values: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25 (12 values).

5.2 Brute Force (312 combinations)

def crack_affine(ciphertext):
    """Brute force affine cipher: 12 × 26 = 312 combinations."""
    valid_a = [a for a in range(1, 26) if gcd(a, 26) == 1]

    for a in valid_a:
        a_inv = pow(a, -1, 26)
        for b in range(26):
            plaintext = ""
            for c in ciphertext.upper():
                if c.isalpha():
                    y = ord(c) - ord('A')
                    x = (a_inv * (y - b)) % 26
                    plaintext += chr(x + ord('A'))
                else:
                    plaintext += c

            score = chi_squared_score(plaintext)
            if score < 50:  # reasonable English
                print(f"a={a}, b={b}: {plaintext[:50]}...")

5.3 Known Plaintext

def affine_from_known(plain1, cipher1, plain2, cipher2):
    """Recover (a, b) from two known plaintext-ciphertext pairs."""
    p1, c1 = ord(plain1) - ord('A'), ord(cipher1) - ord('A')
    p2, c2 = ord(plain2) - ord('A'), ord(cipher2) - ord('A')

    # c1 = a*p1 + b, c2 = a*p2 + b
    # c1 - c2 = a*(p1 - p2) mod 26
    diff_p = (p1 - p2) % 26
    diff_c = (c1 - c2) % 26

    if gcd(diff_p, 26) != 1:
        return None

    a = (diff_c * pow(diff_p, -1, 26)) % 26
    b = (c1 - a * p1) % 26
    return a, b

---

6. HILL CIPHER

Matrix-based cipher: C = K · P mod 26 where K is an n×n key matrix.

6.1 Known-Plaintext Attack

import numpy as np

def crack_hill(known_plain, known_cipher, n=2):
    """Recover Hill cipher key from known plaintext-ciphertext (mod 26)."""
    # Convert to numbers
    P = [ord(c) - ord('A') for c in known_plain.upper()]
    C = [ord(c) - ord('A') for c in known_cipher.upper()]

    # Build matrices (need at least n pairs of n-grams)
    P_matrix = np.array(P[:n*n]).reshape(n, n).T
    C_matrix = np.array(C[:n*n]).reshape(n, n).T

    # K = C · P⁻¹ mod 26
    # Need modular matrix inverse
    from sympy import Matrix
    P_mat = Matrix(P_matrix.tolist())
    C_mat = Matrix(C_matrix.tolist())

    P_inv = P_mat.inv_mod(26)
    K = (C_mat * P_inv) % 26

    return K

---

7. TRANSPOSITION CIPHERS

7.1 Rail Fence

def rail_fence_decrypt(ciphertext, rails):
    """Decrypt rail fence cipher."""
    n = len(ciphertext)
    # Build the zigzag pattern
    pattern = []
    for i in range(n):
        row = 0
        cycle = 2 * (rails - 1)
        pos = i % cycle
        row = pos if pos < rails else cycle - pos
        pattern.append((row, i))

    pattern.sort()

    # Fill in characters
    result = [''] * n
    ci = 0
    for _, orig_pos in pattern:
        result[orig_pos] = ciphertext[ci]
        ci += 1

    return ''.join(result)

# Brute force all rail counts
for rails in range(2, 20):
    print(f"Rails {rails}: {rail_fence_decrypt(ct, rails)[:50]}")

7.2 Columnar Transposition

def columnar_decrypt(ciphertext, key):
    """Decrypt columnar transposition given key word."""
    n_cols = len(key)
    n_rows = -(-len(ciphertext) // n_cols)  # ceiling division

    # Determine column order from key
    order = sorted(range(n_cols), key=lambda i: key[i])

    # Calculate column lengths (some may be shorter)
    full_cols = len(ciphertext) % n_cols
    if full_cols == 0:
        full_cols = n_cols

    # Split ciphertext into columns (in key order)
    columns = [''] * n_cols
    pos = 0
    for col_idx in order:
        col_len = n_rows if col_idx < full_cols else n_rows - 1
        columns[col_idx] = ciphertext[pos:pos + col_len]
        pos += col_len

    # Read off row by row
    plaintext = ''
    for row in range(n_rows):
        for col in range(n_cols):
            if row < len(columns[col]):
                plaintext += columns[col][row]

    return plaintext

---

8. XOR CIPHER

8.1 Single-Byte XOR

See symmetric-cipher-attacks Section 4.2 for full implementation.

8.2 Multi-Byte XOR (xortool)

# Automatic key length detection and cracking
xortool ciphertext.bin -l 5        # try key length 5
xortool ciphertext.bin -b          # brute force key length
xortool ciphertext.bin -c 20       # assume most common char is space (0x20)

8.3 Known Plaintext XOR

def xor_known_plaintext(ciphertext, known_plain, offset=0):
    """Recover XOR key from known plaintext at given offset."""
    key_fragment = bytes(
        c ^ p for c, p in zip(ciphertext[offset:], known_plain)
    )
    print(f"Key fragment: {key_fragment}")

    # If repeating key, infer full key from fragment
    return key_fragment

---

9. SPECIAL CIPHERS

9.1 Bacon Cipher

Binary encoding using two typefaces (A=normal, B=bold/italic).

BACON = {
    'AAAAA': 'A', 'AAAAB': 'B', 'AAABA': 'C', 'AAABB': 'D',
    'AABAA': 'E', 'AABAB': 'F', 'AABBA': 'G', 'AABBB': 'H',
    'ABAAA': 'I', 'ABAAB': 'J', 'ABABA': 'K', 'ABABB': 'L',
    'ABBAA': 'M', 'ABBAB': 'N', 'ABBBA': 'O', 'ABBBB': 'P',
    'BAAAA': 'Q', 'BAAAB': 'R', 'BAABA': 'S', 'BAABB': 'T',
    'BABAA': 'U', 'BABAB': 'V', 'BABBA': 'W', 'BABBB': 'X',
    'BAAAA': 'Y', 'BAAAB': 'Z',
}

def decode_bacon(text):
    """Decode Bacon cipher: uppercase=B, lowercase=A (or similar mapping)."""
    binary = ''.join('B' if c.isupper() else 'A' for c in text if c.isalpha())
    result = ''
    for i in range(0, len(binary) - 4, 5):
        chunk = binary[i:i+5]
        result += BACON.get(chunk, '?')
    return result

9.2 Polybius Square

    1 2 3 4 5
  ┌──────────
1 │ A B C D E
2 │ F G H I/J K
3 │ L M N O P
4 │ Q R S T U
5 │ V W X Y Z

"HELLO" = "23 15 31 31 34"

9.3 Playfair

5×5 grid cipher encrypting digraphs.

Key: "MONARCHY" → grid:
  M O N A R
  C H Y B D
  E F G I/J K
  L P Q S T
  U V W X Z

Rules:
  Same row → shift right: HE → FE → "GF"
  Same col → shift down
  Rectangle → swap columns

---

10. DECISION TREE

Unknown ciphertext — how to identify and break?
│
├─ Step 1: Check encoding
│  ├─ Base64 alphabet with padding? → Decode first, then re-analyze
│  ├─ Hex string? → Convert to bytes, re-analyze
│  ├─ Binary (01)? → Convert to ASCII
│  ├─ Morse (.-/)? → Decode Morse
│  └─ Printable text? → Continue to Step 2
│
├─ Step 2: Character set
│  ├─ Only letters (A-Z)?
│  │  ├─ Compute IC
│  │  │  ├─ IC ≈ 0.065 → Monoalphabetic
│  │  │  │  ├─ Uniform shift in freq? → Caesar → brute force 25
│  │  │  │  ├─ Random-looking mapping? → Simple substitution → frequency analysis
│  │  │  │  └─ Digraph patterns? → Playfair → digraph analysis
│  │  │  │
│  │  │  ├─ IC ≈ 0.04-0.05 → Polyalphabetic
│  │  │  │  ├─ Kasiski → find key length
│  │  │  │  └─ Per-position frequency → crack Vigenere
│  │  │  │
│  │  │  └─ IC ≈ 0.038 → Very long key or one-time pad
│  │  │     └─ Look for key reuse or weak key generation
│  │  │
│  │  └─ Letters appear scrambled (right freq, wrong order)?
│  │     └─ Transposition
│  │        ├─ Rail fence → brute force rail count
│  │        └─ Columnar → try common key lengths
│  │
│  ├─ Numbers (digit pairs)?
│  │  ├─ Pairs in range 11-55 → Polybius square
│  │  └─ Numbers mod 26 → numeric substitution
│  │
│  ├─ Mixed case with pattern?
│  │  └─ Upper/lower encodes binary → Bacon cipher
│  │
│  └─ Non-printable bytes?
│     └─ XOR cipher
│        ├─ Single-byte key → brute force 256
│        ├─ Repeating key → xortool / Hamming distance
│        └─ Known plaintext → direct key recovery
│
└─ Step 3: Apply specific attack
   ├─ Substitution → quipqiup.com / frequency analysis
   ├─ Caesar → dcode.fr / brute force
   ├─ Vigenere → Kasiski + per-column Caesar
   ├─ Affine → brute force 312 combinations
   ├─ Hill → known-plaintext matrix attack
   ├─ Transposition → pattern analysis + brute force
   └─ XOR → xortool / crib dragging

---

11. TOOLS

Tool	Purpose	URL/Usage
CyberChef	Universal encoding/cipher Swiss army knife	gchq.github.io/CyberChef
dcode.fr	200+ cipher solvers online	dcode.fr
quipqiup	Automated substitution cipher solver	quipqiup.com
xortool	XOR cipher analysis and cracking	pip install xortool
RsaCtfTool	RSA + some classical cipher support	GitHub
Ciphey	Automated cipher detection and decryption	pip install ciphey
hashID	Identify hash types	pip install hashid
Python	Custom frequency analysis and scripting	All attacks above

CyberChef Recipes (Common)

ROT13:               ROT13
Caesar brute force:   ROT13 (with offset slider)
Base64 decode:        From Base64
Hex decode:           From Hex
XOR:                  XOR (key as hex/utf8)
Vigenere:             Vigenère Decode
Morse:                From Morse Code