Atbash is a simple
substitution cipher for the
Hebrew alphabet. It consists in substituting
aleph (the first letter) for
tav (the last),
beth (the second) for
shin (one before last), and so on,
reversing the
alphabet.
In the Book of Jeremiah, Lev Kamai (51:1)
is Atbash for Kasdim (Chaldeans), and Sheshakh
(25:26; 51:41) is Atbash for Bavel (Babylon). It
has been associated with the esoteric methodologies of
Jewish mysticism's interpretations of
Hebrew religious texts as in
the
Kabbalah.
An Atbash cipher for the
Roman
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
Atbash can also be used to mean the same thing in any other
alphabet as well. This is a very simple substitution cipher.
For example, in Atbash, the letters "nlmvb" indicate the word
"money".
A few English words 'Atbash' into other English words. For example,
"hob"="sly", "hold"="slow", "holy"="slob", "horn"="slim",
"zoo"="all", "irk"="rip", "low"="old", "glow"="told", and
"grog"="tilt".
It is a very weak cipher because it only has one possible key, and
it is a simple monoalphabetic substitution cipher. However, this
may not have been an issue in the cipher's time.
The Atbash cipher is referenced in
Google's
Da Vinci Code Quest, in which participants must decode a common
word from Atbash.
The Atbash Cipher as an Affine cipher
The Atbash cipher can be seen as a special case of the
Affine cipher.
If you define the first letter of the alphabet to be 0, the second
letter to be 1 and so on up to the last letter of the alphabet
being the number of letters in the alphabet-1; then the Atbash
cipher may be enciphered & deciphered using the encryption
function for an Affine cipher:
f(x)=(ax+b)\mod{m}
Where, for the Atbash cipher: a=b=(m-1) in which m is the number of
letters in the alphabet (m = 26 for monocase
English).
This may be simplified to:
\begin{align}f(x) & = (m-1)(x+1)\mod{m} \\
& = -(x+1)\mod{m} \\
\end{align}
If, instead, the first letter of the alphabet is defined to be 1,
the second letter to be 2 and so on, the encryption function for
the Affine Cipher becomes:
f(x)=((ax+b-1)\mod{m})+1
Where, for the Atbash cipher: a=(m-1), b=1 in which m is the length
of the alphabet.
This may be simplified to:
\begin{align}f(x) & = (x(m-1)\mod{m})+1 \\
& = (-x\mod{m})+1 \\
\end{align}
See also
External links