classical-cipher-analysis

$27

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