Atbash

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

The Cipher

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:

Plain	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Cipher	Z	Y	X	W	V	U	T	S	R	Q	P	O	N	M	L	K	J	I	H	G	F	E	D	C	B	A

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.

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	א	ב	ג	ד	ה	ו	ז	ח	ט	י	כ	ל	מ	נ	ס	ע	פ	צ	ק	ר	ש	ת
Cipher	ת	ש	ר	ק	צ	פ	ע	ס	נ	מ	ל	כ	י	ט	ח	ז	ו	ה	ד	ג	ב	א

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)

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 Elian 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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