Barbeu-Dubourg is known for translating Benjamin Franklin's work into French.
In his letter written from 10 June to 2 July 1776, he sent Franklin a cipher. It was a passage cipher whereby each letter of a key text is assigned sequential numbers. A similar scheme had been used between Franklin and Charles William Frederick Dumas.
The letter is in PCC (Papers of Continental Congress), (roll number?) p.70 and printed in Papers of Benjamin Franklin, vol.22, p.453-470.
The short specimen allows partial reconstruction of the original key text.
Such Barbeu-Dubourg's passage cipher is described in Weber (1979), United States Diplomatic Codes and Ciphers 1775-1938 and my article, "Benjamin Franklin's Codes and Ciphers" (2009). Actually, more is known from:
Leighton, A.C., Matyas, S.M. (1985). The History of Book Ciphers. In: Blakley, G.R., Chaum, D. (eds) Advances in Cryptology. CRYPTO 1984. Lecture Notes in Computer Science, vol 196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39568-7_11 p.105.
The example given by Barbeu-Dubourg is:
3,2,Β,19,5,23,16,12,γι,44,53,δ,10,51,4,61,θ,36,17,6,24,71,1,λ,42,28,37,33,μ,82,54,11,9,8,47,59,88,13,69,ξι,31,92,π,72,34,56,73,σ,6,94,4,20,φ,40,100,68,48,ψω
(The Greek letters are word breaks.)
The latter half of the example is left without decipherment. This kind of cipher cannot be deciphered without finding out the key text, but Leighton succeeded in extending the key text with the assistance of Dr. Eric Gans, who thought of extending the plaintext "Ma femme et deux filles vous" with "embrassent de tout leur etre".
3 2 * 19 5 23 16 12 * 44 53 * 10 51 4 61 * 36 17 6 24 71 1 * 42 28 37 33 * m a f e m m e e t d e u x f i l l e s v o u s 82 54 11 9 8 47 59 88 13 69 * 31 92 * 72 34 56 73 * 6 94 4 20 * 40 100 68 48 e m b r a s s a n t d e t o u t l e u r e t r e
It is remarkable that there are few repetitions. The mere two instances of consistent assignment 4=u and 6=l are hardly enough to justify the extension. But when these figures are sorted, a meaningful key text emerges.
(In the above image, highlighted cells are from the extension.)
It will be reasonable to read the beginning (SAMUEL_ARDBEN__MI_FR__ML__) as "Samuel Ward Benjamin Franklin" (M toward the last is an error for K). (Samuel Ward was a member of the Secret Committee of the Continental Congress (Rhode Island Historical Society, One Eternal Day (by Standfast)), of which Franklin was among the original members.)
The occurrence of these names hardly seem to be a coincidence and thus makes the extension plausible (at least for the part involved in these names).
It will be seen there are higher numbers yet unaccounted for. If someone can think of some plausible text to fill the gaps, I'd like to know, though it will be more difficult because known figures are sparse.
The following revisits Leighton's extension. Absence of highlight for "de tout" and "leur" indicates these may be altered without affecting the above discovery.
