Did Beaufort Really Use the Beaufort Cipher?

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.

Earlier Description by Sestri (1710)

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.

When Was the Beaufort Cipher Published?

Halfpenny Postcard Version (1870)

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)).

Becher's Version (1855)

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).)

The means of secret correspondence is an important power, which, like all others, may be well or badly applied. Something like a box of lucifer matches, it may be turned to a good or bad purpose as an ill or well designed person may please to apply it, as is very well exemplified by some discoveries made by a gentleman well known in the walks of science in one of our daily public journals. These discoveries were made by his arriving at a knowledge of the key, and although the annexed ingenious method has defied hitherto all attempts at such discovery, its improper application must not stand in the way of the good use to which it is equally applicable. It is not the first time it has been in print, having appeared many years ago in a scientific journal; but it is by no means commonly known, nor that the author of it is the late Hydrographer to the Admiralty, Rear-Admiral Sir Francis Beaufort, who has recently retired from that important station, after a lifetime of valuable contributions to the general store of knowledge, but more especially towards the improvement of navigation.
It will be seen by the method that a piece of paper and a pencil are all that is necessary to form the key previously agreed on between the two persons, who need carry nothing further, and that the key can always be varied at pleasure; -- but no doubt any common paper, with printed squares, such as used in worsted work, would materially facilitate the application of the method.

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.

William Morris' Version (1857?)

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).

Version in Babbage's Papers

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).

Vigenere vs. Beaufort

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 steps which have been taken
Vis count Melbo urne Visc ountM
Now look in the side column for the first letter of the text (t) and in the top or bottom column for the first letter (v); where these columns meet there will be found the letter (o) which is to be written for the beginning of the secret paragraph. Proceed in the same manner with the second letter, viz. (h) at the side and (i) at the top and the result will be (p.) The third letter will be (w) as found at the junction of the two columns of (e) and (s) and so on to the end of the dispatch, which will stand thus : -
opw uhycl iltdv brii wmwp huxxz

The halfpenny postcard version (apparently identical with the William Morris version in view of the quotations in Franksen (1993)) is as follows:

The steps which have been taken
Vis count Melbo urne Visc ountM
Now look in the side column for the first letter of the text (t) and run the eye across the table until it comes to the first letter of the key (v), then at the top of the column in which v stands will be found the letter c, which is to be written for the first letter of the cypher dispatch. Proceed in the same manner for every consecutive letter, and the resulting letters will stand thus: -

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.

Babbage paper version?Vigenere
Becher's version1855Vigenere
William Morris' version1857?Beaufort
Halfpenny postcard version1870Beaufort

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.

Ciphers Actually Used by Beaufort

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.

Correspondence with Brother William

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.)

Secret Private Life in Cipher Diary

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.)

Leap from Primitive Cipher to Polyalphabetic 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. )

My system has a complement in the Vigenère system, that is to say, in deciphering a message which can be identified as a double substitution of the Vigenère cipher, the whole mode of deciphering can be speeded up by drawing up a table of these complements. Thus, when deciphering, all that needs to be done is to set down the resulting letters and its complement, as either the one or the other will give the right solution.
14 July 1848, Beaufort to a Lieutenant R.P. Cator, R.N.

(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.

Additional Remarks (27 November 2021)

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.

References to the Beaufort's Cipher

The following is early references to the Beaufort's cipher.


The only cipher I have met with which appears to be absolutely untranslatable is that invented by the late Admiral Sir F. Beaufort. In this the cipher changes, and consequently a letter in the original may by chance be represented by half the letters of the alphabet in the same despatch, and, moreover, this change follows no rule. For instance, "Three times three," written twice consecutively, with the same key-word, is "Ulryj hzffw tbwsv mivey ygdxt xhljs."
The key-word may be any word (or words) or itself a cipher, and I think the above example shows that without it to translate would be impossible.
Beaufort's system is a card of letters in squares formed of two alphabets - one called the "top," the other the "side." You write your despatch and then interline it letter for letter with the key-word repeating this latter to the end. Then look in the side column for the first letter of the text, and in the top column for the first letter of the key-word, and where these two columns meet will be found the first letter on the secret paragraph; so on with the second and following letters. The translation is the reverse of this, the key-word being written under the secret paragraph.
English Mechanic and World of Science, no.552, Oct. 22, 1875, p.149 (Google)

The scheme is actually a Vigenere, with a keyword "beaufort".


The late Admiral Sir Francis Beaufort devised a useful card - which, after his decease, was published at a low price - for carrying on correspondence in a way which we should have thought would baffle any outsiders whatever. The card is full of alphabets, arranged in various ways; one letter is substituted for another in writing the message; the kind of substitution perpetually varies; and a key-word, known only to the two correspondents, shows in what fashion this variation takes place. The key-word and the card are used together, both by sender and receiver.
All the Year Round (1876) (a weekly magazine founded by Charles Dickens), February 26, 1876, p.511 (Google)

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.


Works on Cryptography
The following titles, &c., chronologically arranged, are in part taken from my own possession, ....
Wheatstone, Profr. Interpretation of an important Document in Cipher. (Instructions [by Charles I] pour le Sieur de Goffe.) Philobiblon Society, 1862, 8vo.
Beaufort, W.M. Cryptography, a System of Secret Writing, by the late Admiral Sir Francis Beaufort, K.C.B. Adapted for Telegrams, and the New Halfpenny Postage Cards. Price Sixpence. London, Edward Stanford. (About 1870.)
Leslie, L.C. Postal Cryptograms. A complete System of Secret Writing and Cypher Communication, especially adapted for the purposes of correspondence by the new halfpenny postage cards; to which are added other Cryptographic Codes...... London, J. Neal & Co., 8vo. (About 1870.)
Notes and Queries (1877) (Google) p.169-172

Britannica, 9th Edition (1877)

Complications have been introduced into ciphers by the employment of "dummy" letters, "nulls and insignificants," as Bacon terms them. Other devices have been introduced to perplex the decipherer, such as spelling words, backwards making false divisions between words, &c. The greatest security against the decipherer has been found in the use of elaborate tables of letters, arranged in the form of the multiplication table, the message being constructed by the aid of preconcerted key-words. Details of the working of these ciphers may be found in the treatises named in this article....
An excellent modification of the key word principle was constructed by the late admiral sir Francis Beaufort; it has been recently published in view of its adaptation to telegrams and post-cards.
Enyclopaedia Britannica, ninth edition, vol.6 (1877), p.671 (National Library of Scotland, reprint (1898) at Google)

Chambers (1880)

[The substance of the above is from Enyclopaedia Britannica, ninth edition.]
Library of Universal Knowledge: A Reprint of the Last (1880) Edinburgh and London Edition of Chambers Encyclopaedia (Google) An 1871 edition (Internet Archive, p.346) does not have a corresponding reference.

The relevant description is identical with Britannica's above. (So only the credit line is quoted in the above.)

Kerckhoffs (1883)

d. Système de Beaufort
Une modification assez ingénieuse a été apportée au chiffre carré par l amiral anglais Francis Beaufort (1857). Quoiqu'elle paraisse au premier abord n'affecter que le maniement du tableau, elle altère assez sensiblement le texte cryptographique pour lui donner aux yeux des non-initiés un véritable air d'indéchiffrabilité. Voici d'abord le tableau de Beaufort:
Les déchiffreurs anglais, que le système de Beaufort a tant émerveillés, ne se doutaient certainement pas qu'on pût obtenir le inême résultat avec les systèmes de Vigenère ou de Saint-Cyr en retournant tout simplement l'alphabet normal.1
1 Il est probable que l'amiral anglais lui même n'a jamais cru à la possibilité de transformer son système en chiffre carré ordinaire; on ne s'expliquerait pas, sans cela, que M. Morris Beaufort réclame encore énergiquement en ce moment, pour son illustre père, l'honneur d'avoir doté son pays d'un système de cryptographie indéchiffrable (Cryptography a system of secret writing by the late admiral sir Francis Beaufort).
Auguste Kerckhoffs (1883), La cryptographie militaire (Google), p.30-31

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).

Génie Civil (1886)

(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.


Cryptography: Beaufort System
From an interesting series of articles on Cryptography, in Le Génie Civil, we extract the following for the benefit of the curious in such matters:
This cryptogram is a modification of the "square table," and was suggested in 1857 by Admiral Francis Beaufort, R. N.; it was long regarded as indecipherable.
Engineering News, vol.xvi (1886), p.172 (Google)

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.

W.W. Rouse Ball (1892/1914)

The Beaufort Cipher, introduced in the British Navy by Admiral Beaufort in 1857, is of the St Cyr type. Its inventor thought it insoluble, but French writers have shown that no special difficulties occur in the discovery of the key word in the solution, though the analysis is tedious.
A far better system of this kind is the Playfair Cipher....
W. W. Rouse Ball, Mathematical Recreations and Essays (1892 1st ed.,1914 6th ed.) (Internet Archive)

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.

Bazeries (1899)

Pièce No.353
Bazeries Étienne, 53 ans, ...
(Entendu le 23 septembre 1899 par M. Bérenger. Serment prèté.)
Quelques jours après, et après des recherches, je pus déchiffrer les dépèches de M. Buffet au duc d Orléans qui, également avait comme clef le jour la date et le mois. Exemple: lundi 12 xe. Mais au lieu d'être faites comme celles de M. de Chevilly avec le chiffre de Vigener elles étaient faites avec le chiffre de Beaufort qui n'en est qu'une variante
Haute Cour de Justice (1899), Affaire buffet, déroulède, guérin et autres inculpés de complot: Dépositions des témoins, p.6 (Google)

This is a testimony of Bazeries about how he deciphered ciphers in the Duke of Orleans' correspondence.

Etienne Bazeries, Les Chiffres Secrets Dévoilés (1901)

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)"

©2021 S.Tomokiyo
First posted on 29 October 2021. Last modified on 27 November 2021.
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