Two Centuries On, a Cryptologist Cracks a Presidential Code

The cryptic message was sent to President Jefferson in December 1801 by his friend and frequent correspondent, Robert Patterson, a mathematics professor at the University of Pennsylvania. President Jefferson and Mr. Patterson were both officials at the American Philosophical Society -- a group that promoted scholarly research in the sciences and humanities -- and were enthusiasts of ciphers and other codes, regularly exchanging letters about them.

In this message, Mr. Patterson set out to show the president and primary author of the Declaration of Independence what he deemed to be a nearly flawless cipher. "The art of secret writing," or writing in cipher, has "engaged the attention both of the states-man & philosopher for many ages," Mr. Patterson wrote. But, he added, most ciphers fall "far short of perfection."

To Mr. Patterson's view, a perfect code had four properties: It should be adaptable to all languages; it should be simple to learn and memorize; it should be easy to write and to read; and most important of all, "it should be absolutely inscrutable to all unacquainted with the particular key or secret for decyphering."

Mr. Patterson then included in the letter an example of a message in his cipher, one that would be so difficult to decode that it would "defy the united ingenuity of the whole human race," he wrote.

There is no evidence that Jefferson, or anyone else for that matter, ever solved the code. But Jefferson did believe the cipher was so inscrutable that he considered having the State Department use it, and passed it on to the ambassador to France, Robert Livingston.

The cipher finally met its match in Lawren Smithline, a 36-year-old mathematician. Dr. Smithline has a Ph.D. in mathematics and now works professionally with cryptology, or code-breaking, at the Center for Communications Research in Princeton, N.J., a division of the Institute for Defense Analyses.

A couple of years ago, Dr. Smithline's neighbor, who was working on a Jefferson project at Princeton University, told Dr. Smithline of Mr. Patterson's mysterious cipher.

Dr. Smithline, intrigued, decided to take a look. "A problem like this cipher can keep me up at night," he says. After unlocking its hidden message in 2007, Dr. Smithline articulated his puzzle-solving techniques in a recent paper in the magazine American Scientist and also in a profile in Harvard Magazine, his Alma mater's alumni journal.

The code, Mr. Patterson made clear in his letter, was not a simple substitution cipher. That's when you replace one letter of the alphabet with another. The problem with substitution ciphers is that they can be cracked by using what's termed frequency analysis, or studying the number of times that a particular letter occurs in a message. For instance, the letter "e" is the most common letter in English, so if a code is sufficiently long, whatever letter appears most often is likely a substitute for "e."

Because frequency analysis was already well known in the 19th century, cryptographers of the time turned to other techniques. One was called the nomenclator: a catalog of numbers, each standing for a word, syllable, phrase or letter. Mr. Jefferson's correspondence shows that he used several code books of nomenclators. An issue with these tools, according to Mr. Patterson's criteria, is that a nomenclator is too tough to memorize.

Jefferson even wrote about his own ingenious code, a model of which is at his home, Monticello, in Charlottesville, Va. Called the wheel cipher, the device consisted of cylindrical pieces, threaded onto an iron spindle, with letters inscribed on the edge of each wheel in a random order. Users could scramble and unscramble words simply by turning the wheels.

But Mr. Patterson had a few more tricks up his sleeve. He wrote the message text vertically, in columns from left to right, using no capital letters or spaces. The writing formed a grid, in this case of about 40 lines of some 60 letters each...MORE...

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