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Beaufort cipher

A cousin of Vigenère that subtracts instead of adding, so encoding and decoding are the same job.

Conversion

Beaufort is its own inverse. Run the cipher text through with the same key and the message comes back.

20 characters
Updates as you type

Show the steps
  1. Write the key FORTIFICATION over the message, repeating it as often as needed.
  2. For each letter take the key letter minus the message letter, counting A as 0, and wrap round below 0 by adding 26.
  3. F − D = 5 − 3 → C; O − E = 14 − 4 → K; R − F = 17 − 5 → M; T − E = 19 − 4 → P; I − N = 8 − 13 → V; F − D = 5 − 3 → C…
  4. Because key − (key − plain) = plain, the same sum turns the cipher text back. Encoding and decoding are one step.

Using the Beaufort tool

Type a key and your message. The result is the Beaufort cipher text, in capitals, with spaces and punctuation left out. To decode, paste the cipher text in with the same key. You get the message back, because the cipher undoes itself.

Any word or phrase will do as a key. Longer keys that don't repeat a pattern are harder to break.

How it works

Number the letters from A = 0 to Z = 25 and write the key over the message, repeating it as often as needed. Each cipher letter is the key letter minus the message letter, wrapped round by adding 26 when the answer goes below zero.

With the key KEY, the message DCODE comes out as HCKHA. K is 10 and D is 3, and 10 − 3 = 7, which is H.

Vigenère adds the key to the message. Beaufort takes the message away from the key, and that swap is what makes it reciprocal. Take the cipher letter away from the key again and you land back on the message letter.

Admiral Beaufort and a cipher machine

The cipher is credited to Sir Francis Beaufort, though who first thought of it is less certain. dCode notes that it was published after his death by his brother in 1857, and that some writings suggest the variant was known as early as 1710.

Its best-known use came much later, inside a machine. The Hagelin M-209, a rotor-based cipher machine, worked on the Beaufort principle. The US National Security Agency also used it as the basis of a one-time pad format code-named DIANA, which US Special Forces used by hand during the Vietnam War.

Related conversions

The Vigenère cipher is the same table of shifted alphabets, read the other way round. The Porta cipher is another reciprocal key cipher, with only 13 alphabets instead of 26.

Questions

Is the Beaufort cipher the same as Vigenère?

Close but not the same. Vigenère adds the key to the message, and Beaufort subtracts the message from the key. That makes Beaufort its own inverse.

How do I decode a Beaufort cipher?

Run the cipher text through again with the same key. Key minus cipher gives you the message, so there is no separate decode step.

Is the Beaufort cipher secure?

Not with a short repeating key. It falls to the same attacks as Vigenère. With a truly random key as long as the message, used once, it becomes a one-time pad.

Sources

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