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Burr's cipher, sir: The 1807 treason case that featured in the Apple/FBI conflict

Glenn Fleishman | March 29, 2016
The damned fool who shot Alexander Hamilton in a duel also, some historians believe, wanted to set himself up as the Emperor of Mexico. Coded dispatches led to his downfall, but not conviction.

Burr was known to use code in his letters as early as 1774 at the age of 18. (He was a prodigy, like Hamilton.) The letter between Burr and the governor of the Lousiana Territory, James Wilkinson, that prompted treason charges contained three distinct methods:

  • Codes or what were termed “hieroglyphics” at the time: Symbols that referred to a specific thing or person, and which each party had a codebook with those correspondences. It also included some numeric codes for certain terms and for people. (At least two separate code systems may have been mixed together, or possibly three.)

  • A book or dictionary cipher, in which numbers referred to pages and columns in a standard reference work. This is an “out-of-band” element, something parties who encoded and decoded could have on hand that might not be unique, but didn’t pass over the same channel as the message. In this case, the 1800 edition of Entick’s Spelling Dictionary was the source.

  • A substitution cipher, in which each letter has a replacement with a symbol, apparently used as a fallback when parties couldn’t access the spelling dictionary, and for speed. Many ciphers swap one letter for another, instead. A more complicated substitution cipher was used by others who corresponded with Wilkinson, and relied on a commonly known word, like “cuba” or “france,” each letter of which seeded a separate substitution cipher which was used in sequence. One had to know the word to take the numbers used in the encoded text to restore them. (Jefferson used a more advanced and user friendly multiple-cipher version that relied on wooden disks.)

A codebook is the most resistent of all methods, because it is entirely arbitrary. Without the correspondence being discovered, a codebreaker would need to assemble enough material to find patterns.

The book-based method could be seen as foolhardy, because both this particular book (across multiple editions) had already been used, and those intercepting a message would recognize the form in which references to pages and columns were made. Obtaining a copy of the book on demand or trying multiple potential books would be time consuming, however.

Substitution ciphers are the easiest to break, because letter-frequency analysis of text of any modest length reveals most of the letters. It can be performed by hand. Even the rotation method (not employed in the so-called “treason letter”) isn’t resistent to frequency analysis, because patterns still emerge that can be broken down.

The greatest flaw in this and similar letters is mixing code types, as once the simpler encryptions are broken, this often reveals enough context to break the harder ones, such as the codebook method.


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