The Atbash Cipher: Examples for the Latin, Russian and Hebrew Alphabets

A simple substitution cipher used for the Hebrew alphabet, from which it also takes its name. Encryption is performed by replacing the first letter of the alphabet with the last, the second with the second-to-last, and so on. (Aleph (the first letter) is replaced by tav (the last), bet (the second) is replaced by shin (the second-to-last); the cipher took its name from these letter pairs).

Atbash is, in essence, a temurah — in Hebrew tradition this means "substitution". In this method of encryption, one set of letters is substituted for another, producing a new word that modifies the meaning of the original. In the case of Atbash, the pairs in this temurah are the first and last letters of the alphabet, the second and the second-to-last, the third from the start and the third from the end, and so on. The name Atbash itself is an abbreviation of its first two pairs: Aleph - Tav, Bet — Shin. Besides Atbash there are other variants - Albam and Aik-bekar [nine “chambers»]. In Albam the pairs are made up of letters from the first [1- 11] and second [12-22] halves of the alphabet. The name of this temurah is formed from its first two pairs, Aleph - Lamed, Bet — Mem. In the Aik-bekar temurah [nine «chambers»] the twenty-two ordinary letters of the alphabet plus the five final forms are distributed among nine chambers according to their absolute numerical values: the first chamber holds the three letters whose gematria reduces to one [Aleph - Yod - Qof], the second to two [Bet - Kaf - Resh], and so on. Gematria — this is one of the methods [alongside temurah] for analysing the meaning of words and phrases based on the numerical values of the letters they contain. The gematria of a word is the sum of the numerical values of the letters that make it up.

The Atbash cipher for the English alphabet:

Original alphabet: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Substitution alphabet: Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

The keyword (codeword) cipher

The keyword cipher is one of the simplest ciphers, both to implement and to decrypt. The idea is that a keyword is chosen and written at the front, after which the remaining letters of the alphabet are written out in their usual order. Keyword cipher using the word WORD. Original alphabet: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Substitution alphabet: W O R D A B C E F G H I J K L M N P Q S T U V X Y Z

As we can see, using a short keyword gives us a very, very simple substitution. Likewise, we cannot use a word with repeated letters as the keyword, since this leads to ambiguous decryption: two different letters of the original alphabet would end up mapping to one and the same letter of the ciphertext.

For the letters of the Russian alphabet

Atbash correspondence table for Hebrew

Tarabarskaya Gramota

The Russian analogue of Atbash can be considered the tarabarskaya gramota (simple litorea). Just as in Hebrew, where vowels were omitted in writing, in the tarabarskaya gramota only consonants were replaced. The alphabet was divided into two halves, the second half was written beneath the first in reverse order, and each consonant of the text was replaced by its paired letter.

Method of letter substitution in the tarabarskaya gramota

Atbash and the Transposition of the Tarot Major Arcana

Atbash helps explain why the Major Arcana were rearranged in the Thoth Tarot designed by Aleister Crowley, and in the Rider—Waite Tarot, designed by a prominent member of the Hermetic Order of the Golden Dawn. The cipher explains why the cards Justice and Strength were swapped. The new sequence in the Atbash cipher, likewise based on the ideas of gematria, gives us a detailed explanation for this fact.

Let us look at the letter-substitution table used in Atbash encryption

The table above can easily be simplified by removing the second half, since it is simply a repetition:

When the founders of the Golden Dawn set about decrypting a series of texts (using Masonic codes) in order to create their own rituals and structures, they were instructed to transpose L and T (Justice and Strength). The table below illustrates this.

That said, a convincing explanation for this transposition has never been given, but there are hints in the Atbash code if we look at the pairs rather than the direct use of the cipher

The bottom row shows the sum of the two letters in each column. The letter-to-number correspondence is taken from gematria. The last two columns, YM and KL, have identical numeric values. Considering this fact from the point of view of gematria, the founders of the Golden Dawn regarded such a coincidence as unacceptable. Members of the Order of the Golden Dawn, in their instructions for encrypting with Atbash, decided to swap the letter T, which was the first letter before the two «identical» pairs, with the letter L, which comes right after the letters Y and K..

This transposition removed the repetition of the numeric values assigned to the pairs. Every word in Hebrew containing the letters L N K T now had a different form when encrypted.

The Cipher in Cinema

Knowledge of the Atbash cipher comes to the aid of the characters in the film The Da Vinci Code — Robert Langdon, Sophie Neveu and Leigh Teabing — when they set out to decipher the meaning of a line of verse: «…atbash will reveal the truth, like a beam of light». According to the plot, it turns out that the word «Baphomet» was encrypted using the Atbash cipher, helping to guess the word «Sophia». This is no coincidence, since the heroine of Dan Brown's novel is named Sophie Neveu.

See Also

• Caesar Cipher
• Affine Cipher
• ROT13
• History of Cryptography