Atbash

Atbash (Hebrew: אתבש‎‎; also transliterated Atbaš) is a mono-alphabetic substitution cipher originally used to encode the Hebrew alphabet. It can be modified for use with any known alphabet.

History

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

The Atbash cipher for the modern Hebrew alphabet would be:

Plain	אבגדהוזחטיכלמנסעפצקרשת
Cipher	תשרקצפעסנמלכיטחזוהדגבא

In the Bible

Several Biblical verses are described by commentators as being examples of Atbash:

Jeremiah 25:26 - "The king of Sheshach shall drink after them" - Sheshach meaning Babylon in Atbash (ששך=בבל)
Jeremiah 51:1 - "Behold, I will raise up against Babylon, and against the inhabitants of Lev-kamai, a destroying wind." - Lev-kamai meaning Chaldeans (לבקמי=כשדים)
Jeremiah 51:41 - "How has Sheshach been captured! and the praise of the whole earth taken! How has Babylon become a curse among the nations!" - Sheshach meaning Babylon (ששך=בבל)

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)){\bmod {m}}

This may be simplified to:

{\begin{aligned}{\mbox{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:

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

References

Paul Y. Hoskisson. "Jeremiah's Game". Insights. Retrieved 30 March 2013.

Classical cryptography

Ciphers
by family

Caesar	Affine (Atbash) ROT13

Null	Null cipher (Null encryption)

One time pad	Book One-time pad

Polybius square	ADFGVX Bifid Tap code 3D (Trifid: Nihilist and VIC cipher)

Square	Two-square Four-square

Substitution cipher	Autokey Chaocipher Great Hill Keyword Running key

Transposition cipher	Rail fence cipher

Other	Alberti BATCO (Slidex) Beaufort Dvorak Enigma Kama Sutra Navajo code Pigpen Playfair Polyalphabetic Rasterschlüssel 44 Reihenschieber Reservehandverfahren Scytale Smithy code Solitaire Straddling checkerboard Tabula recta Transposition Trithemius Vigenère

Cryptanalysis

Frequency analysis
Index of coincidence (Units: Ban and Nat)
Information leakage
Kasiski examination

Miscellaneous

Cryptography

History of cryptography Cryptanalysis Outline of cryptography

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

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