An autokey cipher (also known as the autoclave cipher) is a

cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode ...

that incorporates the message (the

plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...

) into the key. The key is generated from the message in some automated fashion, sometimes by selecting certain letters from the text or, more commonly, by adding a short ''primer key'' to the front of the message. There are two forms of autokey cipher: ''key-autokey'' and ''text-autokey'' ciphers. A key-autokey cipher uses previous members of the

keystream In cryptography, a keystream is a stream of random or pseudorandom characters that are combined with a plaintext message to produce an encrypted message (the ciphertext). The "characters" in the keystream can be bits, bytes, numbers or actual ch ...

to determine the next element in the keystream. A text-autokey uses the previous message text to determine the next element in the keystream. In modern cryptography, self-synchronising

stream cipher stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream ( keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystrea ...

s are autokey ciphers.

History

This cipher was invented in 1586 by

Blaise de Vigenère Blaise de Vigenère (5 April 1523 – 19 February 1596) () was a French diplomat, cryptographer, translator and alchemist. Biography Vigenère was born into a respectable family in the village of Saint-Pourçain. His mother, Jean, arrang ...

with a reciprocal table of ten alphabets. Vigenère's version used an agreed-upon letter of the alphabet as a primer, making the key by writing down that letter and then the rest of the message. More popular autokeys use a

tabula recta In cryptography, the ''tabula recta'' (from Latin '' tabula rēcta'') is a square table of alphabets, each row of which is made by shifting the previous one to the left. The term was invented by the German author and monk Johannes TrithemiusSa ...

, a square with 26 copies of the alphabet, the first line starting with 'A', the next line starting with 'B' etc. Instead of a single letter, a short agreed-upon keyword is used, and the key is generated by writing down the primer and then the rest of the message, as in Vigenère's version. To encrypt a plaintext, the row with the first letter of the message and the column with the first letter of the key are located. The letter in which the row and the column cross is the ciphertext letter.

Method

The autokey cipher, as used by members of the

American Cryptogram Association The American Cryptogram Association (ACA) is an American non-profit organization devoted to the hobby of cryptography, with an emphasis on types of codes, ciphers, and cryptograms that can be solved either with pencil and paper, or with computers, ...

, starts with a relatively-short keyword, the ''primer'', and appends the message to it. For example, if the keyword is and the message is , then the key would be . Plaintext: attackatdawn Key: QUEENLYATTACKATDAWN Ciphertext: QNXEPVYTWTWP The ciphertext message would thus be "QNXEPVYTWTWP". To decrypt the message, the recipient would start by writing down the agreed-upon keyword. QNXEPVYTWTWP QUEENLY The first letter of the key, Q, would then be taken, and that row would be found in a tabula recta. That column for the first letter of the ciphertext would be looked across, also Q in this case, and the letter to the top would be retrieved, A. Now, that letter would be added to the end of the key: QNXEPVYTWTWP QUEENLYA a Then, since the next letter in the key is U and the next letter in the ciphertext is N, the U row is looked across to find the N to retrieve T: QNXEPVYTWTWP QUEENLYAT at That continues until the entire key is reconstructed, when the primer can be removed from the start. With Vigenère's autokey cipher, a single mistake in encryption renders the rest of the message unintelligible.

Cryptanalysis

Autokey ciphers are somewhat more secure than polyalphabetic ciphers that use fixed keys since the key does not repeat within a single message. Therefore, methods like the

Kasiski examination In cryptanalysis, Kasiski examination (also referred to as Kasiski's test or Kasiski's method) is a method of attacking polyalphabetic substitution ciphers, such as the Vigenère cipher. It was first published by Friedrich Kasiski in 1863, but see ...

or index of coincidence analysis will not work on the ciphertext, unlike for similar ciphers that use a single repeated key. A crucial weakness of the system, however, is that the plaintext is part of the key. That means that the key will likely contain common words at various points. The key can be attacked by using a dictionary of common words,

bigram A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an ''n''-gram for ''n''=2. The frequency distribution of every bigram in a string is commonly used fo ...

trigram Trigrams are a special case of the ''n''-gram, where ''n'' is 3. They are often used in natural language processing for performing statistical analysis of texts and in cryptography for control and use of ciphers and codes. Frequency Context is ...

s etc. and by attempting the decryption of the message by moving that word through the key until potentially-readable text appears. Consider an example message meet at the fountain encrypted with the primer keyword KILT: To start, the autokey would be constructed by placing the primer at the front of the message: plaintext: meetatthefountain primer: KILT autokey: KILTMEETATTHEFOUN The message is then encrypted by using the key and the substitution alphabets, here a tabula recta: plaintext: meetatthefountain key: KILTMEETATTHEFOUN ciphertext: WMPMMXXAEYHBRYOCA The attacker receives only the ciphertext and can attack the text by selecting a word that is likely to appear in the plaintext. In this example, the attacker selects the word the as a potential part of the original message and then attempts to decode it by placing THE at every possible location in the key: ciphertext: WMP MMX XAE YHB RYO CA key: THE THE THE THE THE .. plaintext: dfl tft eta fax yrk .. ciphertext: W MPM MXX AEY HBR YOC A key: . THE THE THE THE THE . plaintext: . tii tqt hxu oun fhy . ciphertext: WM PMM XXA EYH BRY OCA key: .. THE THE THE THE THE plaintext: .. wfi eqw lrd iku vvw In each case, the resulting plaintext appears almost random because the key is not aligned for most of the ciphertext. However, examining the results can suggest locations of the key being properly aligned. In those cases, the resulting decrypted text is potentially part of a word. In this example, it is highly unlikely that dfl is the start of the original plaintext and so it is highly unlikely either that the first three letters of the key are THE. Examining the results, a number of fragments that are possibly words can be seen and others can be eliminated. Then, the plaintext fragments can be sorted in their order of likelihood: unlikely ←——————————————————→ promising eqw dfl tqt ... ... ... ... eta oun fax A correct plaintext fragment is also going to appear in the key, shifted right by the length of the keyword. Similarly, the guessed key fragment (THE) also appears in the plaintext shifted left. Thus, by guessing keyword lengths (probably between 3 and 12), more plaintext and key can be revealed. Trying that with oun, possibly after wasting some time with the others, results in the following: shift by 4: ciphertext: WMPMMXXAEYHBRYOCA key: ......ETA.THE.OUN plaintext: ......the.oun.ain shift by 5: ciphertext: WMPMMXXAEYHBRYOCA key: .....EQW..THE..OU plaintext: .....the..oun..og shift by 6: ciphertext: WMPMMXXAEYHBRYOCA key: ....TQT...THE...O plaintext: ....the...oun...m A shift of 4 can be seen to look good (both of the others have unlikely Qs) and so the revealed ETA can be shifted back by 4 into the plaintext: ciphertext: WMPMMXXAEYHBRYOCA key: ..LTM.ETA.THE.OUN plaintext: ..eta.the.oun.ain A lot can be worked with now. The keyword is probably 4 characters long (..LT), and some of the message is visible: m.eta.the.oun.ain Because the plaintext guesses have an effect on the key 4 characters to the left, feedback on correct and incorrect guesses is given. The gaps can quickly be filled in: meetatthefountain The ease of cryptanalysis is caused by the feedback from the relationship between plaintext and key. A three-character guess reveals six more characters (three on each side), which then reveal further characters, creating a cascade effect. That allows incorrect guesses to be ruled out quickly.

Notes

References

*Bellaso, Giovan Battista, ''Il vero modo di scrivere in cifra con facilità, prestezza, et securezza di Misser Giovan Battista Bellaso, gentil’huomo bresciano'', Iacobo Britannico, Bressa 1564. *Vigenère, Blaise de, ''Traicté des chiffres ou secrètes manières d’escrire'', Abel l’Angelier, Paris 1586. ff. 46r-49v. *LABRONICUS (Buonafalce, A), ''Early Forms of the Porta Table'', “The Cryptogram”, vol. LX n. 2, Wilbraham 1994. *Buonafalce, Augusto, ''Bellaso’s Reciprocal Ciphers'', “Cryptologia” 30 (1):39-51, 2006. *LABRONICUS (Buonafalce, A), ''Vigenère and Autokey. An Update'', “The Cryptogram”, vol. LXXIV n. 3, Plano 2008.

External links