Atbash Cipher

The Atbash cipher (also called the mirror cipher or reverse alphabet) is a monoalphabetic substitution cipher in which each letter is replaced by its counterpart in the alphabet; thus, A becomes Z, B becomes Y, and so on.

This cipher takes its name and origins from the ancient Hebrew alphabet.

The Atbash cipher relies on an inverted alphabet that serves as a reversible substitution key.

The Latin alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ and its symmetrical inverse (mirror) ZYXWVUTSRQPONMLKJIHGFEDCBA are mapped in a substitution table:

Encryption consists in replacing letters from the first with letters from the other one, with is equivalent to replace the first letter of the alphabet A with the last one Z, the second one B with the penultimate Y etc.

Atbash decryption is identical to encryption, since the substitution (mirror) alphabet is reversible (due to the symmetry of the backwards alphabet).

An Atbash ciphertext has a coincidence index similar to an unencrypted text.

If the encryption used the classical latin alphabet, letters V,G,R,L,M appear the most frequently.

Otherwise the presence of Hebrew characters or a reference to the Dead Sea can be a clue.

The notions of mirror, reflection, opposite, axis, direction, word written in reverse (hsabta) are also clues.

The name Atbash comes from the method applied to the Hebrew alphabet:

— Aleph (first letter) ↔ Tav (last)

— Beth (second) ↔ Shin (penultimate)

The initials of these four letters (A-T-B-Sh) form the word Atbash.

The number Atbash is mentioned in the Hebrew Bible, notably in the book of Jeremiah (chapter 25, verse 26 and chapter 51, verse 41). It is used to replace names and places with their coded equivalents.

There are a small number of words that have an existing Atbash equivalent in the English dictionary.

In Hebrew, this situation is more common (notably because the alphabet has no vowels).

Atbash can be applied to any alphabet (Latin, Greek, Hebrew, Cyrillic, etc.)

Mathematically, it is a special case of the affine cipher where the multiplicative parameter is $ a = n-1 $ and the offset $ b = n-1 $ with $ n $ the size of the alphabet.

Atbash can be described as a monoalphabetic substitution using the reversed alphabet ZYXWVUTSRQPONMLKJIHGFEDCBA

The origins of the Atbash cipher date back to antiquity, probably around the 6th or 5th century BC, in Israel.

It is considered one of the earliest known cipher systems, used primarily for symbolic or religious purposes rather than for security.