# Atbash: Map

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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. In the Book of Jeremiah, Lev Kamai (51:1) is Atbash for Kasdim (Chaldeans), and Sheshakh (25:26; 51:41) is Atbash for Bavel (Babylon). It has been associated with the esoteric methodologies of Jewish mysticism's interpretations of Hebrew religious texts as in the Kabbalah.

An Atbash cipher for the Roman 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".

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".

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.

The Atbash cipher is referenced in Google's Da Vinci Code Quest, in which participants must decode a common word from Atbash.

## The Atbash Cipher as an Affine cipher

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

If you define the first letter of the alphabet to be 0, the second letter to be 1 and so on up to the last letter of the alphabet being the number of letters in the alphabet-1; then the Atbash cipher may be enciphered & deciphered using the encryption function for an Affine cipher:

f(x)=(ax+b)\mod{m}

Where, for the Atbash cipher: a=b=(m-1) in which m is the number of letters in the alphabet (m = 26 for monocase English).

This may be simplified to:

\begin{align}f(x) & = (m-1)(x+1)\mod{m} \\
    & = -(x+1)\mod{m} \\

\end{align}

If, instead, the first letter of the alphabet is defined to be 1, the second letter to be 2 and so on, the encryption function for the Affine Cipher becomes:

f(x)=((ax+b-1)\mod{m})+1

Where, for the Atbash cipher: a=(m-1), b=1 in which m is the length of the alphabet.

This may be simplified to:

\begin{align}f(x) & = (x(m-1)\mod{m})+1 \\
    & = (-x\mod{m})+1 \\

\end{align}

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