Cryptology - Unofficial St. Mary's College of California Web Site

10.13. EXERCISES 217
4. (which is the most essential property) It should be absolutely
inscrutable to all unacquainted with the particular key or secret for
decyphering
Patterson believed he had discovered one method that satisfied his first
three requirements and was “absolutely impossible, even for one perfectly
acquainted with the general system, ever to decypher the writing of another
without his key.”
In the same letter he sent what we will call Patterson’s Cipher. As revised
by Jefferson and himself, and slightly modified to fit our manner of doing
things, the cipher works as follows.
(a) Choose two keywords of the same number of letters.
letters alphabetically:
B e n j a m i n
2 3 7 5 2 6 4 8
Number the
F r a n k l i n
2 7 1 6 4 5 3 8
(Repeated letters are thought of as occurring in a “second” alphabet.)
(b) Write the message (ignoring non-alphabetic characters and spaces)
in rows, using a consistent number of letters per row (the last row
may have fewer).
(c) Cyclically number the columns in order, with the largest number
being the number of letters in the keyword.
(d) Take the columns off in the numerical order indicated by the line
keyword. Before transcribing them in rows insert as many nulls as
the letter keyword indicates. Add some number of nulls at the end.
As Patterson further explained
It will be proper that the supplementary letters used at the beginning
and end of the lies, should be nearly in the same relative proportion
to each other in which they occur in the cypher itself, so that no clue
may be afforded for distinguishing between them and the significant
letters.
On calculating the number of changes, and combinations, of which the
above cypher is susceptible even supposing that neither the number of
lines in a section, nore the number of arbitrary letters at the beginning
of the lines, should ever exceed nine, it will be found to amount to
upwards of ninety millions of millions ... nearly equal to the number
of seconds in three millions of years! Hence I presume the utter
impossibility of decyphering will be readily acknowledged.
Jefferson responded on 22 March, 1802 that
I have thoroughly considered your cypher, and find it is much more
convenient in practice than my wheel cypher, that I am proposing it
to the secretary of state for use in his office