Editing Atbash

{{short description|Substitution cipher}}
{{One source|date=August 2015}}
[[File:Atbash.png|thumb|The Hebrew alphabet, run through Atbash.]]
'''Atbash''' ({{langx|he|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 [[collation|collating order]].

== Encryption ==
The Atbash cipher is a particular type of [[Substitution cipher|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 [[ISO basic Latin alphabet]] would work like this:
{{Aligned table|cols=27|class=wikitable|col1header=on
|  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
}}

Because there is only one way to perform this, the Atbash cipher provides no [[communications security]], as it lacks any sort of [[Key (cryptography)|key]]. If multiple [[collation|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.

== History ==

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

The Atbash cipher for the modern [[Hebrew alphabet]] would be:
{{Aligned table|cols=23|class=wikitable|col1header=on|rowstyle=text-align:center;
|◢→|{{small|Aleph}}|{{small|Bet}}|{{small|Gimel}}|{{small|Daleth}}|{{small|Heh}}|{{small|Vav}}|{{small|Zayin}}|{{small|Het}}|{{small|Tet}}|{{small|Yodh}}|{{small|Kaph}}|{{small|Lamed}}|{{small|Mem}}|{{small|Nun}}|{{small|Samech}}|{{small|Ayin}}|{{small|Peh}}|{{small|Tzady}}|{{small|Koof}}|{{small|Reish}}|{{small|Shin}}|{{small|Taw}}
|Plain |א|ב|ג|ד|ה|ו|ז|ח|ט|י|כ|ל|מ|נ|ס|ע|פ|צ|ק|ר|ש|ת
|◢←|{{small|Taw}}|{{small|Shin}}|{{small|Reish}}|{{small|Koof}}|{{small|Tzady}}|{{small|Peh}}|{{small|Ayin}}|{{small|Samech}}|{{small|Nun}}|{{small|Mem}}|{{small|Lamed}}|{{small|Kaph}}|{{small|Yodh}}|{{small|Tet}}|{{small|Het}}|{{small|Zayin}}|{{small|Vav}}|{{small|Heh}}|{{small|Daleth}}|{{small|Gimel}}|{{small|Bet}}|{{small|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 variant '''Batgash''' (named for Bet–Taw–[[Gimel]]–Shin) or '''Ashbar''' (for Aleph–Shin–Bet–[[Resh|Reish]]).  Either alternative mapping leaves one letter unsubstituted; respectively Aleph and Taw.

=== In the Bible===
Several [[biblical]] words are described by commentators<ref group=n>[[Rashi]] and [[Radak]] on each of the first three verses. Also other commentators.</ref> as being examples of Atbash:<ref>{{Cite book |url=https://books.google.com/books?id=2fnKNa7cfOoC&q=Atbash++&pg=PT1996 |title=The Moody Bible Commentary |first1=Michael |last1=Rydelnik |first2=Michael |last2=Vanlaningham |date=March 15, 2014 |publisher=Moody Publishers |isbn=9780802490186 |via=Google Books}}</ref><ref>{{Cite book |last=Helmbold |first=A. K. |title=The Zondervan Encyclopedia of the Bible, Volume 1 |publisher=Zondervan |year=2009 |isbn=9780310876960 |editor-last=Silva |editor-first=Moisés |edition=Revised |location=Grand Rapids |pages=430}}</ref><ref>{{Cite journal |last=Leuchter |first=Mark |date=2004 |title=Jeremiah's 70-Year Prophecy and the ימק בל/ךשש Atbash Codes |url=https://www.jstor.org/stable/42614548 |journal=Biblica |volume=85 |issue=4 |pages=503–522 |jstor=42614548 |issn=0006-0887}}</ref>
* [[Jeremiah 25:26]] – "The king of ''[[Sheshach]]'' shall drink after them" – Sheshach meaning [[Babylon]] in Atbash ({{Script/Hebrew|בבל}} ''bbl'' → {{Script/Hebrew|ששך}} ''ššk'').
* [[Jeremiah 51:1]] – "Behold, I will raise up against Babylon, and against the inhabitants of ''Lev-kamai'', a destroying wind." – Lev-kamai meaning [[Chaldea]]ns ({{Script/Hebrew|כשדים}} ''kśdym'' → {{Script/Hebrew|לבקמי}} ''lbqmy'').
* [[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 ({{Script/Hebrew|בבל}} ''bbl'' → {{Script/Hebrew|ששך}} ''ššk'').
Regarding a potential Atbash switch of a single letter:
* {{Bibleverse|Exodus|20:20|HE}} - "Any place ''I'' will mention My name" ({{Script/Hebrew|אזכיר}}) → "Any place ''you'' will mention My name" ({{Script/Hebrew|תזכיר}}) (a → t), according to [[Yom Tov Asevilli]]<ref>[https://www.sefaria.org.il/Midrash_Shmuel_on_Avot.3.6.1?lang=bi&with=all&lang2=en Midrash Shmuel on Avot 3:6]; see discussion in [[David Zvi Hoffmann]] [https://mg.alhatorah.org/Parshan/R._David_Zvi_Hoffmann/Shemot/20.20#m7e0n6 to Exodus 20:20]</ref>

== 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 {{nowrap|0, 1, ... , ''m'' − 1.}} (The Hebrew alphabet has {{nowrap|1=''m'' = 22,}} and the standard Latin alphabet has {{nowrap|1=''m'' = 26).}} The Atbash cipher may then be enciphered and deciphered using the encryption function for an affine cipher by setting {{nowrap|1=''a'' = ''b'' = (''m'' − 1):}}

: <math>\mathrm{E}(x) = \mathrm{D}(x) = \big((m - 1) x + (m - 1)\big) \bmod m.</math>

This may be simplified to
:<math>
\begin{align}
 \mathrm{E}(x) &= (m - 1)(x + 1) \bmod m \\
               &= -(x + 1) \bmod m.
\end{align}
</math>

If, instead, the ''m'' letters of the alphabet are mapped to {{nowrap|1, 2, ..., ''m'',}} then the encryption and decryption function for the Atbash cipher becomes
: <math>\mathrm{E}(x) = (-x \bmod m) + 1.</math>

==See also==
* [[Temurah (Kabbalah)]]
* [[Gematria]]
* [[Hebrew language]]
* [[ROT13]]

==Notes==
<references group=n />

==References==
{{Reflist}}
* {{cite web|author=Paul Y. Hoskisson|title=Jeremiah's Game|work=Insights|volume=30|issue=1|access-date=30 March 2013|url=http://maxwellinstitute.byu.edu/publications/insights/?vol=30&num=1&id=895|archive-url=https://web.archive.org/web/20130701184123/http://maxwellinstitute.byu.edu/publications/insights/?vol=30&num=1&id=895|archive-date=1 July 2013|url-status=dead}}

==External links==
*[http://rumkin.com/tools/cipher/atbash.php Online Atbash decoder]

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