Dumas' Cipher -- Benjamin Franklin's Favorite Cipher

The founding fathers used various ciphers in their correspondence. Benjamin Franklin occasionally used Dumas' cipher, devised by Charles William Frederick Dumas [Charles Guillaumes Frédéric Dumas] residing in the Netherlands. Being an ardent supporter of the American cause, he was commissioned as an American agent. In his letter dated April 30, 1776, he expressed his gratitude and conveyed this cipher system to Franklin (head of the Committee of Secret Correspondence) in Philadelphia. The letter is printed in Sparks (ed.), The Diplomatic Correspondence of the American Revolution or Wharton (ed.), The Revolutionary Diplomatic Correspondence of the United States. These volumes, however, do not reproduce the detailed explanation of the cipher. The present article uses the document in Papers of Continental Congress (PCC) to see how Dumas described his cipher system to Franklin.

Dumas' cipher

Dumas' cipher is a heavily homophonic simple substitution system. An enciphering table is found in PCC, Roll 72.

Each letter is enciphered as a number from 1 to 682 ("simple substitution"). Most letters have many numbers assigned to it ("heavily homophonic") and any one of such assigned numbers may be used. Thus, "BED" can be enciphered as "118 5 20" but there are numerous other ways to represent "BED" such as "163 13 325", "118 13 20", etc.

Besides alphabetical letters, the table includes such symbols as the ampersand (&), the apostrophe ('), the comma (,), the interrogation (?), the full stop (.), the division or hyphen (=), and the reference (*).

When the letters and characters are arranged in the order of the number as V(1), O(2), U(3), L(4), ..., they make a passage in French. The full passage reads as follows:

(1) Voulez=vous sentir la difference? Jettez les yeux sur le continent (57)
septentrional de l'amerique. Dans les resolutions vigoureuses de (114)
ces braves colons vous reconnoitrez la voix de la vraie liberte * (168)
aux prises avec l'oppression. Vous fremirez, vous vous revolte= (223)
rez contre la morgue & la durete inconcevable de ceux, qui, jaloux (278)
a l'extreme de leur propre liberte, pensent de pouvoir devenir plus (335)
puissants, de pouvoir rester libres eux=memes en asservissant leurs (394)
freres. Vous ne pourrez vous empecher de faire votre cause de (445)
celle de ces peuples, de leur savoir gre de leur fermete, de trem= (499)
bler qu'ils ne suciombent sous la massue levee du pouvoir, qui veut (555)
ou les gouverner arbitrairement, ou les ecraser, en fin de leur sou= (612)
haiter avec le genereux d. der. tout le succes possible dans leur (666)
juste resistance. (682)
[The numbers in parentheses will be referred to in Dumas' letter translated below.]

This passage is taken from the introduction Dumas wrote of a book he sent to Franklin: Emerich de Vattel's Le droit des gens (Law of Nations). Dumas had reprinted this work with his introduction and notes that applied its principles to the situation in America and had sent three copies to Franklin in 1775 (Franklin acknowledges it in his letter of December 19, 1775).

Since Dumas' cipher is based on a passage in French, each letter has as many homophones as proportional to its frequency in French and K and W, not used in French, are not assigned a number. While the table illustrated above shows numbers 684-694 for W, these are struck out with a note "make use of two vs". As for K, there is an instruction "use C".

Dumas' Letter of April 30, 1776

Dumas' Letter of April 30, 1776 (PCC, Roll 121, Page 18) includes the following detailed explanation (in French) of Dumas' cipher, which is not printed in Sparks or Wharton.

The following paragraphs come after the opening paragraph ending with "This promise on my part is in fact an oath of allegiance, which I spontaneously take to Congress; receive it as such."

(Page 18)
After these declarations and protestations made
once and for all, I begin by observing
that it is absolutely necessary that we establish
a cipher between us so that, even if some of
our letters are intercepted in the course, our secrets
are not compromised. I will save you
the pain of making this cipher by sending you
a copy of the one I have already prepared to this purpose
for my use. But, if the present letter does not reach you by
mishap and this copy and my original
are useless, it would be necessary to make another and I
cannot use it from now on. The passage
on which I composed the cipher is in the book I
sent you last. I am the editor of the book and, at the beginning,
I wrote on a blank page my idea on the government
(Page 19)
and the royalty, of which you remark that it
is not displeasing. I indicate it to you enough, I think. You
will find this passage in my letter to Mr. ***, which follows immediately
the title page III, IV, and V. That is,
page III. the 3 last lines of the text
page IV the 7 lines of the text
page V. the 3 first lines of the text
13 lines in all
The first letter of the 1st of these 13 lines is 1. And the last 57
The last letter of the 2nd line is -- ------------------- 114
----- ----- of the 3rd ----- ----- ------ ------ ------ 168
----- ----- of the 4th ----- ----- ------ ------ ------ 223
----- ----- of the 5th ----- ----- ------ ------ ------ 278
----- ----- of the 6th ----- ----- ------ ------ ------ 335
----- ----- of the 7th ----- ----- ------ ------ ------ 394
----- ----- of the 8th ----- ----- ------ ------ ------ 445
----- ----- of the 9th ----- ----- ------ ------ ------ 499
----- ----- of the 10th ---- ----- ------ ------ ------ 555
----- ----- of the 11th ---- ----- ------ ------ ------ 612
----- ----- of the 12th ---- ----- ------ ------ ------ 666
----- ----- of the 13th ---- ----- ------ ------ ------ 682
All has its number therein, even the ' or apostrophe,
the - or hyphens, the commas, the full-stops, the ampersands,
and the references or (*).
To make this operation easier for you, I had
a series of past 1000 numbers printed, of which herein
are several sheets. You have only to take one of those sheets,
and write along the columns, from 1 to 682 (this
is a full-stop), the letters or characters of the indicated 13 lines,
each character next to its number. Further, as, when writing to me, you
will need K and W, which are not used
in French, you have only to put 5 or 6 of each
next to as many numbers that follow the 682th.
Or, what will be still better, make do C in the cipher
without distinction for C or for K and make do V for
V or for W. It will not embarrass me in any way in
deciphering. In order to prevent any misunderstanding, you will find
appended herewith a model of cipher on another passage,
which will serve you as an example for the method of constructing
the one which we will make use of and of which I indicated to you the
passage in the above. Nevertheless, you may keep this model
(Page 20)
for unexpected situations, for example, if the other cipher was
discovered. For the time being, we will call it the small cipher
for distinction from the great. I also keep a copy of it
here.
To begin with, by using the great cipher of the 13 lines, I tell you that

In short, Dumas gives instructions about preparation of the deciphering table. As he tells it, he prepared sheets with sequential numbers from 1 to 682 (and upwards) printed on it (cf. PCC, Roll 72, Page 154). Franklin would refer to the book he was given and write the letters of the passage V-O-U-L-... besides each number:

1	V
2	O
3	U
4	L
5	E
6	Z
7	=

When this is completed, the recipient of the cipher message can find out what letter or character is represented by each number.

After the above paragraphs come the pages of the printed letter: "When I remarked, in my last letter to you, ..."

At the end of the entry of that day (i.e., before "May 9"), Dumas continues his explanation of the cipher.

(Page 27)
To revert to the cipher, when you have put
the 13 lines letter by letter (the apostrophes,
commas, full-stops, etc. included therein) in column on one of the
sheets herein (as it is necessary to begin there),
for deciphering easily and quickly all
that is in cipher in my letter, you have only to
have the sheet at hand and write above each number
of my letter the character that you find next to
the same number on the sheet. I do
this operation quick enough alone and without aid, though
for the first time in my life.
You will understand why I do not sign my name.
As to letters you write to me
in the future, do not put anything above other than
those three words for Mr. Uryman
and thereupon an envelope to the address
of Mr. M. M. Rey, Bookhandler in Amsterdam,
if you use the way of
Saint Eustatius or to the address of Mr. A. Stuckey,
Merchant in Rotterdam, if you write to me in
line of Philadelphia or by
France. By this way, your letters
reach me surely.

Another Explanation

PCC Roll 121, Page 30 is a summary of the letter of "April 30, 1776 and of the subsequent 7 to 8 days", which includes some further material.
After summarising his complimentary first paragraph, Dumas proceeds to repeat the same explanation of the cipher with slightly modified expressions. His explanation after the table goes so far as to explain how to make an enciphering sheet.

(Page 30)
To make this operation easier for you, I had a series of past
one thousand numbers printed. Herein are several sheets. It is necessary to
take one of those sheets and write along the columns, from 1 to 682, the letters
or characters of those 13 lines, each character next to its
number. This will be the key you use for deciphering
my letters by writing, above the lines, above each number
the letter or character corresponding to the number in the sheet that serves as the key.
Then, take one blank sheet, in which you write in one
column at the left from top to bottom the letters of the alphabet,
an apostrophe, a comma, a full-stop, and &, next to each letter
(Page 31)
or character you write in succession from the left to the right
all the numbers that express this letter in the key.
This will be the cipher you will use for enciphering the
letters you write to me, taking care to represent as infrequently as possible
the same letters by the same numbers, above all, the vowels,
in particular E. By this precaution, our cipher
will be impossible to penetrate. To begin to use the cipher, I
will tell you that

After the above paragraphs come the same pages of the printed letter with some omission (notably the first 14 lines). After the pages in cipher, the experience of Mr. Story is briefly summarised and receipt of a further letter is reported as of May 9.

While Franklin was in Paris as a commissioner of the thirteen United States to the French court, he was given another cipher, James Lovell's polyalphabetic cipher (PCC, Roll 72, Page 144). However, he found it troublesome and expressed his preference to Dumas' cipher.

In his letter to Lovell dated August 10, 1780, he wrote "The cypher you have communicated, either from some defect in your explanation, or in my comprehension, is not yet of use to me; for I cannot understand by it the little specimen you have written in it. If you have that of M. Dumas, which I left with Mr Morris, we may correspond by it when a few sentences are required only to be written in cypher, but it is too tedious for a whole letter."

On June 25, 1782, he wrote to Robert Livingston, "I have made the addition you directed to the cypher. I rather prefer the old one of Dumas, perhaps because I am more used to it."

In their struggle for a new nation, the founding fathers were also trying to establish a way of secure communication.