Atbash

Atbash (also transliterated Atbaš) is a simple substitution cipher originally for the Hebrew alphabet, but possible with any known alphabet.

It is considered a 'weak' or 'simple' cipher because it only has one possible key, and it is a simple monoalphabetic substitution cipher. However, this may not have been an issue at the time when the cipher was first devised.

History

The name derives from the first, last, second, and second to last Hebrew letters (Aleph-Tav-Beth-Shin). 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).

The Atbash cipher for the modern Hebrew alphabet would be:

 Plain:  אבגדהוזחטיכלמנסעפצקרשת
 Cipher: תשרקצפעסנמלכיטחזוהדגבא

Use

It works by substituting the first letter of an alphabet for the last letter, the second letter for the second to last and so on, effectively reversing the alphabet. 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

Examples

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

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:

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

See also

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