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Communications of the ACM

Signature simulation and certain cryptographic codes


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Three cyphers allegedly authored by Thomas Jefferson Beale in 1822 have been the subject of intensive study for over 100 years. Generations of cryptanalysts have expended untold man-years, thus far without success, attempting to decode them; vast armies of fortune hunters and treasure seekers have devoted Herculean labors to digging up the rolling hills of Virginia trying to locate the promised bonanza. The history of pertinent activities would fill volumes, yet serious students of cryptography have always had nagging doubts about the cyphers' authenticity. It has been alleged that the “known solution” to Cypher Number Two: 115, 73, 24, 818, 37, 52, 49, … (“I have deposited in the County of Bedford about four miles from Buford's in an excavation or vault…”) with the aid of an unsanitized version of the Declaration of Independence was merely a superb, imaginative, and grandiose hoax perpetrated ages ago for whatever reasons. Modern computer technology could obviously perform signature analyses on the Beale cyphers and could also, in fact, simulate the process of encoding itself so as to yield new clues and deeper insights into their construction. For the benefit of the uninitiated, the encoding method used in the second cypher employs a specified document whose words are simply numbered consecutively, and first letters of these words are sought out at random to match the letters of the cleartext or message. The sequence of numbers corresponding to these matches is then written down as the final code. While primitive, the process has the advantage of relative security until the source document becomes known; at that moment the cypher can be decoded even by second graders. The work now completed with the help of our UNIVAC 1108 includes numerous analytical studies of the Beale cyphers and various types of simulations. For example, we have turned the entire process of simulated encoding by various schemes over to the machine and analyzed the signatures of these synthetic codes; we have also encoded various messages by hand, using different texts and a variety of methods to obtain their signatures. These simulations provide convincing evidence that the signatures are both process and data dependent; they indicate also very strongly that Mr. Beale's cyphers are for real and that it is merely a matter of time before someone finds the correct source document and locates the right vault in the Commonwealth of Virginia.

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