Beaufort cipher

The Beaufort cipher was described by British Rear Admiral Francis Beaufort (yes, the one of the wind scale) in the 19th century. It’s an involutive variant of Vigenère: the same operation encrypts and decrypts. It was implemented in pocket cipher machines (notably the American M-209) thanks to this symmetry, which simplified the mechanism.

Principle

Where Vigenère applies C = (P + K) mod 26, Beaufort applies:

C = (K − P) mod 26

Put differently: to encrypt P with key K, find P in row K of the Vigenère table and read the column. To decrypt, apply the same rule: the operation is its own inverse, because (K − (K − P)) mod 26 = P.

The key is a word repeated cyclically, as in Vigenère.

Example

Plaintext CIPHERCHRONICLE with key KEY (cycled):

C + K → (10 − 2)  mod 26 = 8  → I
I + E → (4 − 8)   mod 26 = 22 → W
P + Y → (24 − 15) mod 26 = 9  → J
H + K → (10 − 7)  mod 26 = 3  → D
E + E → (4 − 4)   mod 26 = 0  → A

Result: IWJDAHIXHWRQITU. Applying the same operation (same key) to that result restores CIPHERCHRONICLE.

Variants

• German Beaufort variant — C = (P − K) mod 26, non-involutive but close.
• Classic Vigenère — C = (P + K) mod 26, non-involutive.
• Vernam / OTP — Beaufort with a single random key: provably unbreakable.

Weaknesses

The attacks that break Vigenère apply to Beaufort:

• Kasiski analysis to determine key length.
• Index of coincidence to confirm the period.
• Once the period is known, each column is a single-letter Beaufort — equivalent to a Caesar — solvable by frequency analysis.

The only practical difference from Vigenère is that an attacker who identifies the method (Beaufort vs. Vigenère) must change the attack formula. Recognizing the right variant takes a small extra hypothesis test.

In CipherChronicle

Beaufort is an elegant pedagogical trap: players trained on Vigenère apply the wrong formula and get noise. Grids can require identifying the variant before attacking — an extra layer of meta-cryptanalysis.