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## The Breaking of the "Jefferson" Code

In December, 1801, Robert Patterson, a University of Pennsylvania Math Professor, sent his friend President Thomas Jefferson a letter with a coded message. It was not solved for more than 200 years.

Patterson's intent was share his almost flawless cipher, which in his view had to have these traits:

• Be adaptable to all languages
• Be simple to learn and memorize
• Be easy to write and to read
• Be "absolutely inscrutable to all unacquainted with the particular key or secret for decyphering"
In his letter, Patterson sent an example of the use of his cipher, so difficult that it would "defy the united ingenuity of the whole human race." Apparently, Jefferson did not solve it.

After 200 years, Lawren Smithline, a mathematical cryptologist, became aware of the letter's existence...and solved the code. He published his results in the American Scientist.

If you know something about cryptology, the following should make sense. Rather than a simple substitution cipher, Patterson used a nomenclator, or special catalog of numbers to represent words, syllables, phrases or letters. He then increased its complexity by writing the message text in vertical column, creating a 40 x 60 grid of letters (with some random letters added on each end). After sectioning the grid into groups of nine numbered lines (1-9), Patterson transformed each line to form a new grid that scrambled the order of the numbered lines within each section.

Smithline's solution was his discovery that the code's key was a series of two-digit pairs, indicating the line number within a section and the number of letters added to the beginning of that row. For instance, an initial key of 43 implied that fourth row was moved to the first line of a section and three random letters were added at the start of the line. He then searched for patterns involving highly-probable digraphs, made some educated guesses, and accessed the power of computer-based dynamic programming. After just shy of 100,000 calculations and several weeks of work, Smithline had solved Patternson's code.

For a visual overview of this whole process, please see this WSJ video. It also reveals the "unexpected" message that Patterson had sent President Jefferson.

Source: Rachel Silverman's "Two Centuries On, a Cryptologist Cracks a Presidential Code," Wall Street Journal, (7/2/2009)