The Beaufort cipher is a variant of the Vigenere cipher. Whereas the Vigenere cipher can be represented as C = P + K, the Beaufort cipher corresponds to C = K - P (P: plaintext, K: key, C: ciphertext). Cryptologically, the difference is minor, but, in practice, the Beaufort cipher has an advantage that enciphering and deciphering can be done with the same operation.
Although Admiral Francis Beaufort (1774-1857) is remembered with this polyalphabetic cipher scheme (in addition to the Beaufort Wind Scale, which is closer to his profession as the Hydrographer of the Navy), the cipher he used in private was a simpler cipher.
The Beaufort cipher had already been described in Giovanni Sestri (1710), Metodo Brevissimo & assoluto per scrivere occulto in tutto le lingue ... (Roma: Bernabò) (Kahn p.1011), but rediscovery of cipher schemes is common enough. Writer and mathematician Lewis Carroll also invented the same cipher. When I read Lewis Carroll may have known of the Beaufort cipher (see another article (in Japanese)), I was induced to check the timeline.
Anyway, Sestri's work was largely ignored and is unlikely to have influenced Beaufort's invention.
The Beaufort cipher was published under the title Cryptography, a system of secret writing by the late Admiral Sir Francis Beaufort, K. C. B. , adapted for telegrams, and the new half-penny postage cards (Duke University Libraries). It is generally a square sheet of paper folded to form four pages. The inside pages (pp.2-3) print the cipher table, and the back cover (p.4) gives an explanation of its use.
This is not dated, but it is advertised on the 22 October 1870 issue of The Athenaeum (No. 2243) (Google) (also listed in Books in Print (?1894)). The "new half-penny postage cards" in the title also indicates the year 1870, when the postcards were introduced in Britain (History Today, Postal Museum). Beaufort's short biography also dates this as 1870 (Hercock (2000)).
This was not the first publication of the Beaufort cipher (Friendly, p.282).
It was published in August 1855 in The Nautical Magazine, p.431 (Internet Archive). (The editor of the magazine was A. B. Becher, who was assistant to Beaufort in the office of the Hydrographer of the Navy (Wikipedia).)
This says the cipher had been anonymously published in a scientific journal "many years ago", but no trace has been found of the earlier publication.
Friendly describes another version titled "Cryptography, a system of Secret Writing. By the late Admiral Sir Francis Beaufort, KCB, adapted for Telegrams, and Postage Cards" on folded stiff paper. It seems similar to the 1870 version mentioned above, but the title is slightly different (no "new halfpenny"). Friendly says this was probably published soon after Beaufort's death in 1857 (Friendly was aware that postcards were a later invention, but he says it "was coming into its own"). The backside of this edition has a text by his son, William Morris Beaufort (1823-1907 (Wikisource)) stating it was "invented and published many years ago by my father ... and I have been induced to republish it in a cheap and portable form, to affirm and to preserve the claim of the inventor, which has recently overlooked or disregarded."
A copy is in the Mendelsohn Collection of the University of Pennsylvania Library, and Kahn adopts the date 1857 given by Galland (Kahn p.1011). Franksen (1993) questions this dating, and points out William Morris departed for duty with the Indian Civil Service three months after his father's death in 1857, not to return until twelve years later (p.332). In the first place, given that Beaufort died on 17 December 1857, it seems more likely that people just assumed the year of the admiral's death as the publication date. As early as 1883, Kerckhoffs dates this 1857, but no records have been found that referred to the Beaufort cipher before 1870 (see below).
According to Franksen (1993), the mathematician Charles Babbage's papers contain a cipher table and "Explanation of the Table." It is textually identical to Becher's version but is printed in entirely different font and layout. This may be the earlier publication mentioned by Becher's version as well as William Morris' version, but a possibility that this was privately printed for Babbage is not excluded (p.335).
Franksen (1993) (p.335-336) points out the explanation of the cipher in Becher's version and the Babbage papers version actually corresponds to the traditional Vigenere cipher, whereas William Morris's version indeed corresponds to what is known as the Beaufort cipher today.
Becher's version (identical with the Babbage papers version) explains as follows:
The halfpenny postcard version (apparently identical with the William Morris version in view of the quotations in Franksen (1993)) is as follows:
The plaintext letter is located on the left side in both cases, but the key letter is found on the top row in Becher's version, while the halfpenny postcard version finds it on the same row as the plaintext letter. So, even though both explanations use the same plaintext and the same keyword ("Viscount Melbourne") as an example, the resulting ciphertext is different.
| version | date | scheme |
|---|---|---|
| Babbage paper version | ? | Vigenere |
| Becher's version | 1855 | Vigenere |
| William Morris' version | 1857? | Beaufort |
| Halfpenny postcard version | 1870 | Beaufort |
A possible explanation (Franksen (1993) p.346) is: Beaufort did describe the Vigenere cipher, which ended up among Babbage's papers. When Becher reprinted it in 1855, he misunderstood that Beaufort invented it. Possibly, Beaufort could not correct the error, but told his son of the mistake.
There is no record that shows Beaufort actually used the Beaufort cipher. He does not even mention his invention of a cipher in his pocket diaries (1835-1857) (Friendly p.283). He did use cipher in his correspondence with his brother as well as in his diary, but the cipher was a more primitive one.
Beaufort used cipher in his letters to William, his elder brother. It was a simple substitution cipher in which various symbols ("Greek letters, astronomical symbols and invented squiggles") are in one-to-one correspondence with the letters of the alphabet. A typical example is seen on a page he kept at sea (21 April 1793). (Friendly p.50-51; The reference in Wikipedia in German to a Vigenere variant in this context seems wrong.)
Beaufort's pocket diary in cipher revealed Beaufort's scandalous relation with his sister Harriet. After Beaufort lost his first wife in 1834, his spinster sister Harriet came to London in 1835 from home in Ireland to take care of the children. Beaufort's ever close relationship with her grew into intimacy. His diary includes thirteen entries in cipher that refer to sexual acts explicitly or implicitly. The first is on 26 November 1835: "Fresh hor[r]ors with Har[r]iet, O Lord forgive us." Two months later, "Again I employed Har[r]iet O Lord take pity upon me and strengthen my mind now." The relation lasted for three years before his second marriage in 1838. (Friendly p.270)
(I have not seen the ciphertext, but doubt Wikipedia's description as if Beaufort used the Beaufort cipher. It gives Friendly as the source, but Friendly does not seem to mention the kind of cipher used in these diary entries. In discussing the Beaufort cipher, both Friendly and Franksen (1993) wonder how Beaufort could have devised it (see below). Their tone cannot be explained if these authors had found use of the Beaufort cipher in the diary. Irish Examiner, 7 March 2014 says the cipher used in the diary consisted of "Greek letters, astronomical symbols and invented squiggles", but this seems to repeat Friendly's description of Beaufort's cipher with his brother. Irish Times, 27 May 1996 does not specify the kind of cipher.)
Friendly wonders the "enormous step forward" from the simple substitution cipher with his brother to the polyalphabetic cipher now attributed to him. He even says Beaufort did not have a creative mathematical mind, and points out that mathematician Charles Babbage and physicist Charles Wheatstone, both known to have been involved in codebreaking, were his frequent companions (p.283).
Franksen (1993) also suggests Beaufort owed insight to Babbage's works (p.364, 338, 348).
Franksen (1993) (p.345) presents one piece of evidence that clearly tells Beaufort's deep knowledge of polyalphabetic ciphers. It is taken from A History of British Secret Service (1969, revised 1985) by Richard Deacon (pseudonym of Donald McCormick (Wikipedia)). Franksen was told by McCormick that the year 1868 in the book was a misprint for 1848, and that the letter is now lost. (McCormick, author of many historical books about secret services, acquired papers of Captain R. P. Cator, but later cleared out most of them because of lack of space. )
(The term "double substitution" probably refers to the two-step table lookup involved in the Vigenere/Beaufort cipher. The Vigenere cipher can be represented as C = P + K, while the relation is C = K - P with the Beaufort cipher. This means if one applies the Beaufort table lookup process to ciphertext enciphered in Vigenere, the complement of the plaintext (-P) is obtained. In other words, if the left side of the table is labelled with the complementary alphabet (Z, Y, X, ..., B, A) as well as the ordinary alphabet, application of the Beaufort table to a given ciphertext in either Vigenere or Beaufort results in two readings: the correct reading and its complement. This can speed up the deciphering when one does not know which system is used.)
Franksen (1993) (p.346-347) describes circumstantial information provided by McCormick. Cator submitted a detailed memorandum on ciphers to the Admiralty, which Beaufort may have studied. In one of Cator's letters, Beaufort reportedly praised Edgar Allan Poe's cryptographic skills: "Poe has been of more help to British Intelligence than the whole pack of informers we employ." (Actually, Poe's codebreaking skill was almost limited to monoalphabetic ciphers, and his greatest contribution to cryptology was to raise a public interest in cryptography through his writings in 1839-1841, culminating in The Gold Bug (1843). So, if this quotation is authentic, it shows Beaufort's lack of understanding at the time.) So, Franksen (1993) accepts Cator's letters and suggest Beaufort learned of polyalphabetic cipher in the period 1841-1848, possibly from Babbage.
The above quotation from Cator's papers indeed does not seem to be a mere fabrication. Still, the dating, if not the authorship, may be still worth further verification. (I note the term "the Vigenere system." I have not seen use of this term as of 1848.)
From Becher's wording, it seems certain that Beaufort at least knew polyalphabetic cipher "many years ago" from 1855.
Something was bothering me when I saw "the Vigenère system" in the letter above ascribed to Cator. I examined when the terms such as "the Vigenère cipher" or "the Vigenère system" came into use, and I now think Vigenere's name was associated with the scheme by Kerckhoffs (1883), in which the terms "Chiffre carré de Vigenère" and "Systèmes de Beaufort" are used in a classified description of polyalphabetic ciphers (see another article at Academia.edu). The dating of Beaufort's cipher at 1857 also appears to be due to him.
I now think the authenticity of Cator's letter as well as the dating of Beaufort's cipher before 1870 are yet to be established.
The following is early references to the Beaufort's cipher.
The scheme is actually a Vigenere, with a keyword "beaufort".
This does not provide a specific scheme. It is noted that this, as well as the previous quotation, does not distinguish between Vigenere and Beaufort.
By the way, the above paragraph is followed by one describing a tablet employed by Mr. Flamm, which seems to be a turning grille.
The relevant description is identical with Britannica's above. (So only the credit line is quoted in the above.)
Kerckhoffs proudly points out that the Beaufort system is equivalent to the Vigenere cipher or the Saint-Cyr cipher.
It is noted that the Beaufort cipher is dated 1857, but the phrase "en ce moment" indicates William Morris' publication was a near past from 1883. Langie and Soudart, Traite de Cryptographie cites publications of "Cryptography, a system of secret writing, by the late Admiral Sir Francis Beaufort" of 1883 and 1893 (Gallica p.VIII, p.67).
(Google) A serial "LA CRYPTOGRAPHIE" by Henri Mamy in the issue of 7 August 1886 describes "Système de Beaufort." It says Beaufort devised it in 1857 ("En 1857, l'amiral anglais Francis Beaufort a imaginé une modification assez curieuse du tableau carré."), which seems to be second-hand information.
This is a Beaufort (though the rows and columns are reversed), and the author recognizes that it is a modification of the "square table." Also, the publication date of 1857 is recognized.
The description "introduced in the British Navy" in this maths book seems wrong. But at least this shows "Vigenere" was not in the common vocabularly in this context.
This is a testimony of Bazeries about how he deciphered ciphers in the Duke of Orleans' correspondence.
Bazeries describes that "chiffre carré" is called "chiffre de Vigenè" or "chiffre de Beaufort" depending on the method used. He dates Beaufort's work at 1857 (p.51).
Alfred Friendly (1977), Beaufort of the Admiralty: The Life of Sir Francis Beaufort, 1774-1857
Marion Hercock (2000), Francis Beaufort, RN: 1774-1857 In P.H. Armstrong & G.J. Martin (Eds.). Geographers Biobibliographical Studies (Geographers: Biobibliographical Studies, pp. 1-15). London: Mansell. Retrieved October 18, 2021, from http://dx.doi.org/10.5040/9781474226776.0005
Biographical Sketches, 1852-1875 (Google)
Ole Immanuel Franksen (1985), Mr. Babbage's Secret (Internet Archive)
Ole Immanuel Franksen (1993), "Babbage and cryptography. Or, the mystery of Admiral Beaufort's cipher", Mathematics and Computers in Simulation 35, pp.327-367
Sir Francis Beaufort Papers: Finding Aid (OAC) ... catalogue information of Beaufort's papers at Huntington Library. Mentions "Friendly Alfred. Solution to Sir Francis Beaufort's cipher. 1974 (1 page)"