The Polyalphabetic Revolution
"Le chiffre indéchiffrable" — The unbreakable cipher. Until it wasn't.
The solution to frequency analysis seemed elegant: use multiple substitution alphabets, switching between them according to a keyword. The same plaintext letter encrypts differently each time. Frequency peaks vanish. For 300 years — from 1553 to 1863 — cryptographers believed this made the Vigenère cipher unbreakable. Charles Babbage proved them wrong. This hall tells the story of the longest-standing myth in cryptographic history.
The key insight of polyalphabetic ciphers: Instead of one fixed substitution alphabet, use a different alphabet for each letter position — determined by a keyword. The same plaintext letter E might encrypt as L in position 1, X in position 2, F in position 3. This defeats simple frequency analysis. But if the keyword repeats, the cipher repeats — and repetition is always the enemy of secrecy.
Giovan Battista Bellaso invented it; Blaise de Vigenère got the credit. A 26×26 "tabula recta" and a repeating keyword. Called "le chiffre indéchiffrable" for 300 years. Broken by Babbage in the 1850s, published by Kasiski in 1863.
Key: LEMONLEMONLE
Cipher: LXFOPVEFRNHR
Admiral Sir Francis Beaufort's reciprocal variant of Vigenère: the same operation encrypts and decrypts. Used by the British Royal Navy. Elegant, but it shares Vigenère's fatal flaw — a repeating key creates detectable patterns.
C = (Key − Plain) mod 26
Giambattista della Porta's 13-row reciprocal tableau, where each row is selected by pairs of key letters. More complex than Vigenère in structure, equally vulnerable to key-length detection through the index of coincidence.
Reciprocal: same operation decrypts
Count Josef von Gronsfeld restricted Vigenère to digit keys (0–9). Easier to memorize — "my key is 31415" — but the reduced alphabet means only 10 possible shift values per position instead of 26. Weaker than its parent.
Shift by digit value — only 10 options per position
The logical endpoint of the polyalphabetic idea: make the key as long as the message itself, drawn from a book or speech. No repeating patterns to detect. No Kasiski test possible. Nearly as secure as a one-time pad — if the source text is never identified.
Key: FROMTHISBOOK
Vigenère's other cipher, and the better one. After the keyword is exhausted, the plaintext itself extends the key. The key never repeats — Kasiski cannot grip. It took until Friedman's 1920s index of coincidence work to find a tractable attack.
Key: KEYATTACKATDA
How the Repeating Key Betrays Itself
When the same plaintext aligns with the same key letter, it produces the same ciphertext. Search the ciphertext for repeated 3+ letter sequences. The distances between them are multiples of the key length.
Ciphertext:
LXFOPVEFRNHRLXFOPVEFRNHR
↑ ↑
pos 6 pos 18
Distance = 12 → key length divides 12
William Friedman's 1920 method works even without visible repetitions. Random text: IC ≈ 0.038. Natural English: IC ≈ 0.066. A Vigenère cipher falls between. The IC value narrows down the key length — split the ciphertext into columns matching the guessed key length, then apply frequency analysis to each column.
| Text Type | IC Value |
|---|---|
| Random | ~0.038 |
| Vigenère (key=5) | ~0.052 |
| English | ~0.066 |
Vigenère uses a repeating key stream. Modern stream ciphers like ChaCha20 generate a non-repeating, cryptographically random keystream of the same length as the message — the same XOR operation, with an unguessable key.
The running key cipher is one step from the one-time pad. The difference: a book passage is not random. If the source text has linguistic structure, that structure leaks into the ciphertext and enables statistical attacks.
The Vigenère lesson: short repeating keys are fatal. Modern cryptography uses 128–256 bit keys that never repeat within a session, and key derivation functions ensure no two sessions share key material.