Beaufort and Running Key Ciphers

The Beaufort cipher is a variant of the Vigenère cipher with a key difference in the encryption formula. Where Vigenère computes C = (P + K) mod 26, Beaufort computes C = (K - P) mod 26.

This small change gives the Beaufort cipher a remarkable property: it is its own inverse. The same operation with the same key encrypts and decrypts, a property called being a reciprocal cipher.

Because encryption and decryption are the same operation in Beaufort, the cipher is called "self-reciprocal" or "involutory". To decrypt, you run exactly the same procedure you used to encrypt.

This was practically useful in the pre-computer era: military operators only needed to learn one procedure instead of two separate encrypt and decrypt procedures, reducing training time and human error.