Beaufort cipher

How it works

Named after Admiral Francis Beaufort (of the wind scale), this cipher uses a repeated key like Vigenère but computes $c_i = (k_i - p_i) \bmod 26$. Solving for the plaintext gives $p_i = (k_i - c_i) \bmod 26$, the same formula: the cipher is reciprocal, and the Hagelin M-209 machine of the US Army used it for that reason.

The variant Beaufort, $c_i = (p_i - k_i) \bmod 26$, is simply Vigenère decryption used to encrypt. Both are polyalphabetic ciphers with a repeating key.

They are broken exactly like Vigenère: the key length shows up in repeated fragments (Kasiski) and in the index of coincidence, and each column of letters is then a reversed Caesar alphabet, solved by frequencies.