The Beaufort cipher, created by Sir
Francis Beaufort
Sir Francis Beaufort ( ; 27 May 1774 – 17 December 1857) was an Irish hydrographer and naval officer who created the Beaufort cipher and the Beaufort scale.
Early life
Francis Beaufort was descended from French Protestant Hugu ...
, is a
substitution cipher
In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, t ...
similar to the
Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key (crypt ...
, with a slightly modified enciphering mechanism and
tableau
Tableau (French for 'little table' literally, also used to mean 'picture'; : tableaux or, rarely, tableaus) may refer to:
Arts
* ''Tableau'', a series of four paintings by Piet Mondrian titled '' Tableau I'' through to ''Tableau IV''
* '' Tableau ...
. Its most famous application was in a rotor-based cipher machine, the
Hagelin M-209. The Beaufort cipher is based on the Beaufort square which is essentially the same as a Vigenère square but in reverse order starting with the letter "Z" in the first row, where the first row and the last column serve the same purpose.
Using the cipher
To encrypt, first choose the plaintext character from the top row of the tableau; call this column P. Secondly, travel down column P to the corresponding key letter K. Finally, move directly left from the key letter to the left edge of the tableau, the ciphertext encryption of plaintext P with key K will be there.
For example if encrypting plain text character "d" with key "m" the steps would be:
# find the column with "d" on the top,
# travel down that column to find key "m",
# travel to the left edge of the tableau to find the ciphertext letter ("K" in this case).
To decrypt, the process is reversed. Unlike the otherwise very similar
Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key (crypt ...
, the Beaufort cipher is a
reciprocal cipher
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between ...
, that is, decryption and encryption algorithms are the same. This obviously reduces errors in handling the table which makes it useful for encrypting larger volumes of messages by hand, for example in the manual DIANA crypto system, used by U.S. Special Forces during the Vietnam War (compare DIANA-table in the image).
In the above example in the column with "m" on top one would find in the reciprocal "d" row the ciphertext "K". The same is true for decryption where ciphertext "K" combined with key "m" results in plaintext "d" as well as combining "K" with "d" results in "m". This results in "trigram" combinations where two parts suffice to identify the third. After eliminating the identical trigrams only 126 of the initial 676 combinations remain (see below) and could be memorized in any order (e.g. AMN can be memorized as "man" and CIP as "pic") to speed up encoding and decoding.
AAZ ABY ACX ADW AEV AFU AGT AHS AIR AJQ AKP ALO AMN
BBX BCW BDV BEU BFT BGS BHR BIQ BJP BKO BLN BMM BZZ
CCV CDU CET CFS CGR CHQ CIP CJO CKN CLM CYZ
DDT DES DFR DGQ DHP DIO DJN DKM DLL DXZ DYY
EER EFQ EGP EHO EIN EJM EKL EWZ EXY
FFP FGO FHN FIM FJL FKK FVZ FWY FXX
GGN GHM GIL GJK GUZ GVY GWX
HHL HIK HJJ HTZ HUY HVX HWW
IIJ ISZ ITY IUX IVW
JRZ JSY JTX JUW JVV
KQZ KRY KSX KTW KUV
LPZ LQY LRX LSW LTV LUU
MOZ MPY MQX MRW MSV MTU
NNZ NOY NPX NQW NRV NSU NTT
OOX OPW OQV ORU OST
PPV PQU PRT PSS
QQT QRS
RRR
Algebraic description
The Beaufort cipher can be described algebraically. For example, using an encoding of the letters – as the numbers 0–25 and using addition
modulo
In computing and mathematics, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the latter being called the '' modulus'' of the operation.
Given two positive numbers and , mo ...
26, let
be the characters of the message,
be the characters of the cipher text and
be the characters of the key, repeated if necessary. Then Beaufort encryption
can be written,
:
.
Similarly, decryption
using the key
,
:
.
Decrypting as a Vigenere cipher
Due to the similarities between the Beaufort cipher and the
Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key (crypt ...
it is possible, after applying a transformation, to solve it as a
Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key (crypt ...
. By replacing every letter in the ciphertext and key with its opposite letter (such that 'a' becomes 'z', 'b' becomes 'y' etc.; i.e. an
Atbash
Atbash (; 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 collating order.
Encryption
The Atbash ciph ...
-transformation) it can be solved like a
Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key (crypt ...
.
Distinguished from 'variant Beaufort'
The Beaufort cipher should not be confused with the "variant Beaufort" cipher. In variant Beaufort, encryption is performed by performing the decryption step of the standard Vigenère cipher, and likewise decryption is performed by using Vigenère encryption.
References
{{DEFAULTSORT:Beaufort Cipher
Cryptographic algorithms
Classical ciphers