Editing Atbash (section)

== 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 {{nowrap|0, 1, ... , ''m'' − 1.}} (The Hebrew alphabet has {{nowrap|1=''m'' = 22,}} and the standard Latin alphabet has {{nowrap|1=''m'' = 26).}} The Atbash cipher may then be enciphered and deciphered using the encryption function for an affine cipher by setting {{nowrap|1=''a'' = ''b'' = (''m'' − 1):}}

: <math>\mathrm{E}(x) = \mathrm{D}(x) = \big((m - 1) x + (m - 1)\big) \bmod m.</math>

This may be simplified to
:<math>
\begin{align}
 \mathrm{E}(x) &= (m - 1)(x + 1) \bmod m \\
               &= -(x + 1) \bmod m.
\end{align}
</math>

If, instead, the ''m'' letters of the alphabet are mapped to {{nowrap|1, 2, ..., ''m'',}} then the encryption and decryption function for the Atbash cipher becomes
: <math>\mathrm{E}(x) = (-x \bmod m) + 1.</math>