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Vigenère cipher

A repeating keyword supplies a sequence of Caesar shifts.

Also found as Vigenere · repeating-key Vigenère · le chiffre indéchiffrable

How it works

Turn each keyword letter into a value from 0 to 25, repeat the keyword, and add the next Key value to each plaintext letter. In Decipher, only ASCII letters advance the Key. Case is kept, and other characters pass through unchanged.ACA VigenèreMilitary Cryptanalysis, Part IIHandbook of Applied Cryptography, chapter 7

For Key period m
C[i] = (P[i] + K[i mod m]) mod 26P[i] = (C[i] − K[i mod m]) mod 26

Worked example

Keyword LEMON
Plaintext
ATTACKATDAWN
Keystream
LEMONLEMONLE
Ciphertext
LXFOPVEFRNHR

What to look for

A short repeating Key divides the text into phases. Repeated sequences and their gaps can suggest a period, as can selected coincidence measurements. Once you have a candidate, separate the text by Key position; each part may then look like a Caesar cipher. A plausible period is a lead to test, not proof.Military Cryptanalysis, Part IIGaines, Cryptanalysis

Name and variants

The name Vigenère is convenient, but the history is messier. Vigenère’s 1586 treatise describes several systems, including an autokey idea. The repeating-key cipher taught under his name today is one part of that history. Beaufort and Variant Beaufort keep the repeating Key and change the arithmetic.Vigenère, Traicté des chiffresFriedman, Codes and Ciphers

Sources

  1. American Cryptogram Association, Vigenère instructions
  2. William F. Friedman, Military Cryptanalysis, Part II
  3. Menezes, van Oorschot, and Vanstone, Handbook of Applied Cryptography, chapter 7
  4. Helen Fouché Gaines, Cryptanalysis
  5. Blaise de Vigenère, Traicté des chiffres, 1586
  6. William F. Friedman, Codes and Ciphers (Cryptology)