right|thumbnail|320px|A disk cipher device of the Jefferson type from the 2nd quarter of the 19th century in the [[National Cryptologic Museum]]
The Jefferson disk, also called the Bazeries cylinder or wheel cypher, is a cipher system commonly attributed to Thomas Jefferson that uses a set of wheels or disks, each with letters of the alphabet arranged around their edge in an order, which is different for each disk and is usually ordered randomly.
Each disk is marked with a unique number, and a hole in the center of the disks allows them to be stacked on an axle. The disks are removable and can be mounted on the axle in any order desired. The order of the disks is the cipher key, and both sender and receiver must arrange the disks in the same predefined order. Jefferson's device had 36 disks while Bazeries' system had 20.
Once the disks have been placed on the axle in the agreed order, the sender rotates each disk up and down until a desired message is spelled out in one row. Then, the sender can copy down any row of text on the disks other than the one that contains the plaintext message. The recipient has to arrange the disks in the agreed-upon order, rotate the disks so they spell out the encrypted message on one row, and then look around the rows until they see the plaintext.
History
In the late 18th century combination locks, known in Europe since 15th century, were popularized by Edmé Régnier L'Aîné, and versions of them with letters have been suggested to be the origin of cipher machines.
The first prototype resembling the Jefferson disk was invented by Swedish baron Fredrik Gripenstierna in 1786, but it operated on a different principle: rather than substitute letters with letters, it used 57 disks to substitute letters entered by a cleared official on the one side of device with numbers on the other side of device visible to a clerk.
At some point in the 1790s (exact date is not clear) Thomas Jefferson described the device now named after him, with 26 letters on a wheel and estimated 36 to 48 wheels, and its operation in a manuscript. It's commonly claimed that he invented it himself but it is not backed by any evidence, and Jefferson himself didn't imply so in the text. The manuscript was apparently forgotten until it was discovered in 1922 (a year after M-94 entered service, see below) by historian Edmund C. Burnett studying the Continental Congress. It doesn't appear that the device was ever fabricated,
In the early 1980s NSA acquired for its museum a large incomplete device of Jefferson's type (picture 1 of this article) with 35 remnant disks (out of 40 originally) and 42 characters, including French letters, on each. However, it's not clear from this description whether the letters were in alphabetic or random order.
Basis for later military ciphers
A device mechanically similar to Jefferson's but somewhat improved was independently re-invented in 1891 by Commandant Etienne Bazeries, but did not become well known until he broke the Great Cipher, of Rossignols. In 1893, French mathematician Arthur Joseph Hermann (better known for founding Éditions Hermann) redesigned the device to use 18 flat wooden or cardboard strips.
One major weakness of the Bazeries cylinder is that the offset from the plaintext letter to the ciphertext letter for the cipher alphabet on each disk will be exactly the same. In the example shown above, this offset is six letters.
For example, if a cryptanalyst found a message encrypted on the ten-disk Bazeries cylinder described in the example above and has captured their own cylinder, they could decipher the message by entering it on their cylinder and rotating it until they found the message. Still, the number of possible permutations of the disks of the example Bazeries cylinder is . Due to the large size of this number, trial and error testing of the arrangement of the disks is difficult to perform by hand.