Caesar Cipher — Substitution Encryption

The Caesar cipher is the entry point to cryptography for a reason — it is simple enough to understand completely, and broken in enough ways to illustrate every major weakness that centuries of cryptanalysis have identified. ROT13, the internet's favourite 'obfuscation', is a Caesar cipher with shift 13. The Vigenère cipher, which stumped cryptanalysts for 300 years, is just multiple Caesar ciphers stacked. And frequency analysis — the attack that breaks Caesar — is the same technique that cracked the Enigma machine.

Start with Caesar. Understand why it fails. Every modern cipher is essentially a series of answers to the questions Caesar's failure raises.

Implementation

Caesar cipher with shift k: encrypt by adding k mod 26 to each letter's position, decrypt by subtracting k. Non-letters pass through unchanged.

def caesar_encrypt(text: str, shift: int) -> str:
    result = []
    for ch in text:
        if ch.isalpha():
            base = ord('A') if ch.isupper() else ord('a')
            result.append(chr((ord(ch) - base + shift) % 26 + base))
        else:
            result.append(ch)
    return ''.join(result)

def caesar_decrypt(text: str, shift: int) -> str:
    return caesar_encrypt(text, -shift)

print(caesar_encrypt('Hello, World!', 3))   # Khoor, Zruog!
print(caesar_decrypt('Khoor, Zruog!', 3))   # Hello, World!
print(caesar_encrypt('Hello', 13))          # ROT13: Uryyb
print(caesar_encrypt('Uryyb', 13))          # ROT13 is self-inverse: Hello

Breaking Caesar — Brute Force and Frequency Analysis

Caesar has only 26 possible keys. Brute force tries all 26. But frequency analysis is more powerful: in English, 'E' appears ~13% of the time, 'T' ~9%, 'A' ~8%. The most frequent letter in the ciphertext is almost certainly 'E'. Find it, compute the shift, decrypt.

from collections import Counter

def break_caesar(ciphertext: str) -> tuple[int, str]:
    """Break Caesar cipher using frequency analysis."""
    letters = [c.upper() for c in ciphertext if c.isalpha()]
    if not letters:
        return 0, ciphertext
    # Most frequent letter in English is 'E'
    most_common = Counter(letters).most_common(1)[0][0]
    shift = (ord(most_common) - ord('E')) % 26
    return shift, caesar_decrypt(ciphertext, shift)

# Brute force — try all 26 shifts
def brute_force_caesar(ciphertext: str) -> list:
    return [(shift, caesar_decrypt(ciphertext, shift)) for shift in range(26)]

ct = caesar_encrypt('The quick brown fox jumps over the lazy dog', 7)
shift, plaintext = break_caesar(ct)
print(f'Detected shift: {shift}')
print(f'Decrypted: {plaintext}')

Why Caesar Fails — The Two Properties of Secure Ciphers

Caesar fails on both criteria that define a secure cipher:

Confusion (key relationship to ciphertext should be complex): Caesar's relationship between key and ciphertext is linear and trivially invertible. Knowing one plaintext-ciphertext pair reveals the key instantly.

Diffusion (each plaintext bit should affect many ciphertext bits): Caesar maps each letter independently. 'E' always maps to the same letter. No letter affects any other. Letter frequencies are perfectly preserved.

Modern ciphers (AES, ChaCha20) address both: complex non-linear key schedules for confusion, and mixing operations that propagate each bit throughout the entire block for diffusion. Caesar has neither.

Historical Context and the Road to Vigenère

Julius Caesar used shift 3. His nephew Augustus used shift 1. Suetonius documented this in 'The Twelve Caesars' (121 AD) — making the Caesar cipher the oldest documented encryption method.

The cipher survived in various forms for 1500 years because letter frequency analysis was not documented until Al-Kindi described it around 850 AD. Once frequency analysis was understood, the Caesar cipher was immediately broken.

The response was the Vigenère cipher (1553) — use a different shift for each letter position, determined by a keyword. This defeated frequency analysis for 300 years until Charles Babbage (1854) and Friedrich Kasiski (1863) independently discovered how to detect the keyword length. The pattern of attack-and-response continues to define cryptographic history.

Frequently Asked Questions