# Atbash

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Atbash is a simple substitution cipher for the Hebrew alphabet. It consists in substituting aleph (the first letter) for tav (the last), beth (the second) for shin (one before last), and so on, reversing the alphabet. Hence the name, Aleph-Tav-Beth-Shin (אתבש). In the Book of Jeremiah, לב קמי Lev Kamai (51:1) is Atbash for כשדים Kasdim (Chaldeans), and ששך Sheshakh (25:26; 51:41) is Atbash for בבל Bavel (Babylon). It has been associated with the esoteric methodologies of Jewish mysticism's interpretations of Hebrew religious texts as in the Kabbalah.

The Atbash cipher for the modern Hebrew alphabet would be:

 Plain:  אבגדהוזחטיכלמנסעפצקרשת
Cipher: תשרקצפעסנמלכיטחזוהדגבא


An Atbash cipher for the Latin alphabet would be as follows:

 Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: ZYXWVUTSRQPONMLKJIHGFEDCBA


An easier, simpler and faster way of doing this is:

 First 13 letters: A|B|C|D|E|F|G|H|I|J|K|L|M
Last 13 Letters:  Z|Y|X|W|V|U|T|S|R|Q|P|O|N


Atbash can also be used to mean the same thing in any other alphabet as well. This is a very simple substitution cipher.

For example, in Atbash, the letters "nlmvb" indicate the word "money" Worked Example.

A few English words 'Atbash' into other English words. For example, "hob"="sly", "hold"="slow", "holy"="slob", "horn"="slim", "zoo"="all", "irk"="rip", "low"="old", "glow"="told", and "grog"="tilt." Some other English words Atbash into their own reverses, e.g., "wizard" = "draziw."

It is a very weak cipher because it only has one possible key, and it is a simple monoalphabetic substitution cipher. However, this may not have been an issue in the cipher's time.

## Relationship to the affine cipher

The Atbash cipher can be seen as a special case of the affine cipher.

Under the standard affine convention, an alphabet of m letters is mapped to the numbers $0, 1, .., m-1$. (The Hebrew alphabet has m=22, and the standard Latin alphabet has m=26). The Atbash cipher may then be enciphered and deciphered using the encryption function for an affine cipher, by setting $a=b=(m-1)$

$\mbox{E}(x)=\mbox{D}(x)=((m-1)x+(m-1))\mod{m}$

This may be simplified to:

\begin{align} \mbox{E}(x) & = (m-1)(x+1)\mod{m} \\ & = -(x+1)\mod{m} \\ \end{align}

If, instead, the m letters of the alphabet are mapped to $1, 2, .., m$, then the encryption and decryption function for the Atbash cipher becomes:

$\mbox{E}(x) = (-x\mod{m})+1$