Atbash

The Hebrew Alpha bet, run through Atbash.

Atbash(Hebrew:אתבש;also transliteratedAtbaš) is a mono Alpha beticsubstitution cipheroriginally used toencrypttheHebrew Alpha bet.It can be modified for use with any knownwriting systemwith a standardcollating order.

Encryption

The Atbash cipher is a particular type ofmono Alpha betic cipherformed by taking theAlpha bet(orabjad,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, theLatin Alpha betwould 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 nocommunications security,as it lacks any sort ofkey.If multiplecollating ordersare 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.

History

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

The Atbash cipher for the modernHebrew Alpha betwould be:

◢→	Aleph	Bet	Gimel	Daleth	Heh	Vav	Zayin	Het	Tet	Yodh	Kaph	Lamed	Mem	Nun	Samech	Ayin	Peh	Tzady	Koof	Reish	Shin	Taw
Plain	א	ב	ג	ד	ה	ו	ז	ח	ט	י	כ	ל	מ	נ	ס	ע	פ	צ	ק	ר	ש	ת
◢←	Taw	Shin	Reish	Koof	Tzady	Peh	Ayin	Samech	Nun	Mem	Lamed	Kaph	Yodh	Tet	Het	Zayin	Vav	Heh	Daleth	Gimel	Bet	Aleph
Cipher	ת	ש	ר	ק	צ	פ	ע	ס	נ	מ	ל	כ	י	ט	ח	ז	ו	ה	ד	ג	ב	א

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

In the Bible

Severalbiblicalwords are described by commentatorsas being examples of Atbash:

• Jeremiah 25:26– "The king ofSheshachshall drink after them "– Sheshach meaningBabylonin Atbash (בבל‎bbl→ששך‎ššk).
• Jeremiah 51:1– "Behold, I will raise up against Babylon, and against the inhabitants ofLev-kamai,a destroying wind. "– Lev-kamai meaningChaldeans(כשדים‎kśdym→לבקמי‎lbqmy).
• Jeremiah 51:41– "How hasSheshachbeen captured! and the praise of the whole earth taken! How has Babylon become a curse among the nations! "– Sheshach meaning Babylon (בבל‎bbl→ששך‎ššk).

Regarding a potential Atbash switch of a single letter:

• Exodus 20:20- "Any placeIwill mention My name "(אזכיר‎) → "Any placeyouwill mention My name "(תזכיר‎) (a → t), according toYom Tov Asevilli

Relationship to the affine cipher

The Atbash cipher can be seen as a special case of theaffine cipher.

Under the standard affine convention, an Alpha bet ofmletters is mapped to the numbers0, 1,...,m− 1.(The Hebrew Alpha bet hasm= 22,and the standard Latin Alpha bet hasm= 26).The Atbash cipher may then be enciphered and deciphered using the encryption function for an affine cipher by settinga=b= (m− 1):

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

This may be simplified to

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

If, instead, themletters of the Alpha bet are mapped to1, 2,...,m,then the encryption and decryption function for the Atbash cipher becomes

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

See also

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

References

• Paul Y. Hoskisson."Jeremiah's Game".Insights.Archived fromthe originalon 1 July 2013.Retrieved30 March2013.

External links

• Online Atbash decoder