Atbash (Hebrew: אתבש; also transliterated Atbaš) is a monoalphabetic substitution cipher originally used to encrypt the Hebrew alphabet. It can be modified for use with any known writing system with a standard collating order.

This article relies largely or entirely on a single source. (August 2015)

The Atbash cipher is a particular type of monoalphabetic cipher formed by taking the alphabet (or abjad, syllabary, etc.) and mapping it to its reverse, so that the first letter becomes the last letter, the second letter becomes the second to last letter, and so on. For example, the Latin alphabet would work like this:

Due to the fact that there is only one way to perform this, the Atbash cipher provides no communications security, as it lacks any sort of key. If multiple collating orders are available, which one was used in encryption can be used as a key, but this does not provide significantly more security, considering that only a few letters can give away which one was used.

The name derives from the first, last, second, and second to last Hebrew letters (Aleph–Taw–Bet–Shin).

The Atbash cipher for the modern Hebrew alphabet would be:

By shifting the correlation one space to the left or the right, one may derive a variant Batgash (named for Bet–Taw–Gimel–Shin) or Ashbar (for Aleph–Shin–Bet–Reish). Either alternative mapping leaves one letter unsubstituted; respectively Aleph and Taw.

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):

${\displaystyle \mathrm {E} (x)=\mathrm {D} (x)={\big (}(m-1)x+(m-1){\big )}{\bmod {m}}.}$

This may be simplified to

${\displaystyle {\begin{aligned}\mathrm {E} (x)&=(m-1)(x+1){\bmod {m}}\\&=-(x+1){\bmod {m}}.\end{aligned}}}$

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

${\displaystyle \mathrm {E} (x)=(-x{\bmod {m}})+1.}$

• Temurah (Kabbalah)
• Gematria
• Hebrew language
• ROT13