Beaufort Cipher

The Beaufort Cipher is a polyalphabetic substitution cipher closely related to the Vigenère Cipher. Invented by Sir Francis Beaufort in the 19th century, it uses a reversed encryption mechanism compared to Vigenère: instead of adding key values to plaintext letters, the plaintext letters are subtracted from the key letters modulo 26. This results in a symmetric system where encryption and decryption processes are identical, simplifying usage while retaining polyalphabetic complexity.

Like other polyalphabetic ciphers, the Beaufort Cipher reduces the risk of frequency analysis inherent in monoalphabetic systems such as the Simple Substitution Cipher. Its unique inversion of the standard Vigenère algorithm gives it distinct cryptographic properties and makes it an instructive example in the study of historical ciphers.

Beaufort Cipher: Encoding

To encrypt a message, each plaintext letter is subtracted from the corresponding key letter, modulo 26. Using the keyword KEY to encrypt “HELLO”:

Plaintext:  H  E  L  L  O
Key:        K  E  Y  K  E
Numeric:    H=7, E=4, L=11, L=11, O=14
            K=10, E=4, Y=24, K=10, E=4
Subtraction (Key - Plaintext) mod 26:
            (10-7) = 3 → D
            (4-4)  = 0 → A
            (24-11)=13 → N
            (10-11)=25 → Z
            (4-14) =16 → Q

Ciphertext: DANZQ

Beaufort Cipher: Decoding

Due to the symmetric nature of the cipher, decoding uses the same process as encoding. Using the same keyword and subtracting the ciphertext letters from the key letters modulo 26 reproduces the original plaintext:

Ciphertext: D  A  N  Z  Q
Key:        K  E  Y  K  E
Subtraction (Key - Ciphertext) mod 26:
            (10-3) = 7 → H
            (4-0)  = 4 → E
            (24-13)=11 → L
            (10-25)=11 → L
            (4-16) =14 → O

Plaintext: HELLO

Beaufort Cipher: Notes

The Beaufort Cipher demonstrates how slight modifications of the Vigenère mechanism can produce a symmetric, reversible polyalphabetic system. Its design allows easier decryption without needing a separate decryption formula, unlike standard Vigenère. It is historically significant and conceptually related to other polyalphabetic systems like the Autokey Cipher, illustrating the evolution of techniques designed to resist frequency analysis while remaining human-operable.