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Abstract
:Thomas Jefferson's contributions to mathematics are often overshadowed by
his brilliance in government and love of agriculture and architecture.
As part of the Thomas Jefferson and Mathematics Seminar this past semester,
we have explored his lesser-known mathematical accomplishments for the purpose
of raising awareness of his intellectual dexterity. Among Jefferson’s
mathematical pursuits was an interest in cryptography, which led him to
the invention of the wheel cipher. The wheel cipher is a physical encryption
tool that can provide two end users with private communication. Due to
Jefferson’s lack of public documentation, the wheel cipher was reinvented
over a hundred years later by the military. As a testament to Jefferson’s
foresight, the military’s variation of the wheel cipher remained unbroken for
more than twenty years (through wartime) until a German code-breaking group
cracked it in 1944.
A wheel cipher is composed of free-spinning wood or metal discs on a spindle. Each disk contains the twenty-six letters of the alphabet arranged around the edge in a random order. The sender and receiver have identical discs arranged in the same order; this ordering is the cryptographic key. With the discs arranged in the agreed-upon order, the sender arranges the discs until the desired message appears. The sender then can choose any other row to send to the recipient to indicate the offset of each disc. Leo Battista Alberti first envisioned the concept of the wheel cipher in the fifteenth century, but it was never popularized. Unknowingly, Thomas Jefferson re-invented the tool and put it to use in settings where security was of importance. First employed when he was the ambassador to France, Jefferson created several variations of his cipher to pass on coded messages. With short messages and a secret password, the wheel cipher is nearly unbreakable. Since Jefferson never publicized his idea, French Major Etienne Bazeries and U.S. Colonel Parker Hitt each later invented it in 1901 and 1914, respectively. The U.S. Army used their version in the early twentieth century for military cryptanalytic purposes. This presentation will include the history of the wheel cipher, Thomas Jefferson’s particular inventions, and a demonstration of how to make and break the wheel cipher. We have built a functional wheel cipher for the purpose of exhibition and will step through the processes of encoding and decoding a message using the cipher. We will explain the mathematics behind the encryption technique and how, with a sufficiently long sample, the integrity of a cipher can be compromised. |