Jefferson disk

Last updated
A disk cipher device of the Jefferson type from the 2nd quarter of the 19th century in the National Cryptologic Museum Jefferson's disk cipher.jpg
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, [1] was 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.

Contents

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. [2] [3]

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. [4]

The first prototype resembling the Jefferson disk was invented by Swedish baron F. 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. [5]

At some point in the 1790s (exact date is not clear [6] ) 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. [7] 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. [8] 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. [9] It doesn't appear that the device was ever fabricated, [6] and Jefferson abandoned the idea after receiving a description of columnar transposition cipher from Robert Patterson in 1803, which he found more practical. [10]

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. [8] It was dated to the second quarter of the 19th century and it's not clear if it is related to Jefferson despite originating from West Virginia. [8]

When in 1854 Bristol dentist John H. B. Thwaites submitted a "new" cipher (which was in fact a variant of what we know as Vigenère cipher) to the Journal of the Society of the Arts, Charles Babbage mentioned in his response that he likes to use "rings of box-wood placed side by side on a cylinder, and having the twenty-six letters on the circumference of each". [11] 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. [12] In 1893, French mathematician Arthur Joseph Hermann (better known for founding Éditions Hermann) redesigned the device to use 18 flat wooden or cardboard strips. [4] Cryptologists in other countries also considered similar devices.

The Bazeries cylinder was the basis for the US "M-94" cipher machine, which was introduced in 1922 and remained in service until 1942. In 1914, Parker Hitt experimented with the Bazeries device, building one prototype using slides on a wooden frame, with the cipher alphabets printed twice consecutively on the slides, and then another using disks of wood. He forwarded his experiments up the Signal Corps chain of command, and in 1917 Joseph Mauborgne refined the scheme, with the final result being the M-94.

The M-94 used 25 aluminium disks on a spindle. It was used by the Army, Coast Guard, and the Radio Intelligence Division of the Federal Communications Commission until early in World War II. The Army changed back to Hitt's original slide scheme with the "M-138-A" cipher machine, which was introduced in the 1930s and was used by the US Navy and US State Department through World War II. The M-138-A featured 100 strips, with 30 selected for use in any one cipher session. It was an improvement in security for the State Department, which during the interwar years had used insecure codes, even in one case a standard commercial telegraph code.

Example of operation

To encrypt a message, the encrypter rotates the disks to produce the plaintext message along one "row" of the stack of disks, and then selects another row as the ciphertext. To decrypt the message, the decrypter rotates the disks on his cylinder to produce the ciphertext along a row. Decryption is easier if both the encrypter and the decrypter know the offset of the row, but not necessary since the decrypter can look around the cylinder to find a row that makes sense.

For example, a simplified "toy" Bazeries cylinder using only ten disks might be organized as shown below, with each disk "unwrapped" into a line and each marked with a designating number:

1:< ZWAXJGDLUBVIQHKYPNTCRMOSFE <
2:< KPBELNACZDTRXMJQOYHGVSFUWI <
3:< BDMAIZVRNSJUWFHTEQGYXPLOCK <
4:< RPLNDVHGFCUKTEBSXQYIZMJWAO <
5:< IHFRLABEUOTSGJVDKCPMNZQWXY <
6:< AMKGHIWPNYCJBFZDRUSLOQXVET <
7:< GWTHSPYBXIZULVKMRAFDCEONJQ <
8:< NOZUTWDCVRJLXKISEFAPMYGHBQ <
9:< XPLTDSRFHENYVUBMCQWAOIKZGJ <
10:< UDNAJFBOWTGVRSCZQKELMXYIHP <

If the "key", the sequence of disks, for this Bazeries cylinder is 7, 9, 5, 10, 1, 6, 3, 8, 2, 4 and the encrypter wants to send the message "retreat now" to the decrypter, the encrypter rearranges the disks as per the key and rotates each disk to obtain the plaintext, which is shown at the left, with spacing added for clarity:

7:< R AFDCE O NJQGWTHSPYBXIZULVKM <
9:< E NYVUB M CQWAOIKZGJXPLTDSRFH <
5:< T SGJVD K CPMNZQWXYIHFRLABEUO <
10:< R SCZQK E LMXYIHPUDNAJFBOWTGV <
1:< E ZWAXJ G DLUBVIQHKYPNTCRMOSF <
6:< A MKGHI W PNYCJBFZDRUSLOQXVET <
3:< T EQGYX P LOCKBDMAIZVRNSJUWFH <
8:< N OZUTW D CVRJLXKISEFAPMYGHBQ <
2:< O YHGVS F UWIKPBELNACZDTRXMJQ <
4:< W AORPL N DVHGFCUKTEBSXQYIZMJ <

The encrypter then selects the ciphertext from the sixth row of the cylinder up from the plaintext. This ciphertext is also highlighted above with spacing, and gives: OMKEGWPDFN. When the decrypter gets the ciphertext, they rearrange the disks on their cylinder to the key arrangement, rotate the disks to give the ciphertext, and then read the plaintext six rows down from the ciphertext, or look over the cylinder for a row that makes sense.

Cryptanalysis

The Bazeries cylinder was a relatively strong system at the time (compared to many other systems in use), and Etienne Bazeries, a French military cryptanalyst, is said to have regarded it as indecipherable. The "Pers Z S" code-breaking group of the German Foreign Office cracked the M-138-A in 1944. However, by that time the Americans had more sophisticated cipher systems in operation.

The French cryptographer Gaetan de Viaris (a.k.a. Marquis Gaetan Henri Leon Viarizio di Lesegno) who is famous for one of the first printing cipher devices (1874), solved the Bazeries cylinder in 1893. [13]

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 10! = 3,628,800. Due to the large size of this number, trial and error testing of the arrangement of the disks difficult to perform by hand.

Related Research Articles

<span class="mw-page-title-main">Cipher</span> Algorithm for encrypting and decrypting information

In cryptography, a cipher is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.

<span class="mw-page-title-main">Cryptanalysis</span> Study of analyzing information systems in order to discover their hidden aspects

Cryptanalysis refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.

<span class="mw-page-title-main">Enigma machine</span> German cipher machine

The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the German military. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages.

<span class="mw-page-title-main">One-time pad</span> Encryption technique

In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent. In this technique, a plaintext is paired with a random secret key. Then, each bit or character of the plaintext is encrypted by combining it with the corresponding bit or character from the pad using modular addition.

In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters, pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing the inverse substitution process to extract the original message.

<span class="mw-page-title-main">Transposition cipher</span> Method of encryption

In cryptography, a transposition cipher is a method of encryption which scrambles the positions of characters (transposition) without changing the characters themselves. Transposition ciphers reorder units of plaintext according to a regular system to produce a ciphertext which is a permutation of the plaintext. They differ from substitution ciphers, which do not change the position of units of plaintext but instead change the units themselves. Despite the difference between transposition and substitution operations, they are often combined, as in historical ciphers like the ADFGVX cipher or complex high-quality encryption methods like the modern Advanced Encryption Standard (AES).

<span class="mw-page-title-main">Vigenère cipher</span> Simple type of polyalphabetic encryption system

The Vigenère cipher is a method of encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key.

In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key, there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy.

<span class="mw-page-title-main">Scytale</span> Encryption tool used to perform a transposition cipher

In cryptography, a scytale is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment wound around it on which is written a message. The ancient Greeks, and the Spartans in particular, are said to have used this cipher to communicate during military campaigns.

<span class="mw-page-title-main">Autokey cipher</span> Classic polyalphabet encryption system

An autokey cipher is a cipher that incorporates the message into the key. The key is generated from the message in some automated fashion, sometimes by selecting certain letters from the text or, more commonly, by adding a short primer key to the front of the message.

<span class="mw-page-title-main">Tabula recta</span> Fundamental tool in cryptography

In cryptography, the tabula recta is a square table of alphabets, each row of which is made by shifting the previous one to the left. The term was invented by the German author and monk Johannes Trithemius in 1508, and used in his Trithemius cipher.

<span class="mw-page-title-main">Frequency analysis</span> Study of the frequency of letters or groups of letters in a ciphertext

In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.

<span class="mw-page-title-main">Ciphertext</span> Encrypted information

In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. This process prevents the loss of sensitive information via hacking. Decryption, the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with codetext because the latter is a result of a code, not a cipher.

<span class="mw-page-title-main">Rotor machine</span>

In cryptography, a rotor machine is an electro-mechanical stream cipher device used for encrypting and decrypting messages. Rotor machines were the cryptographic state-of-the-art for much of the 20th century; they were in widespread use in the 1920s–1970s. The most famous example is the German Enigma machine, the output of which was deciphered by the Allies during World War II, producing intelligence code-named Ultra.

<span class="mw-page-title-main">M-94</span> US cryptographic equipment

The M-94 was a piece of cryptographic equipment used by the United States Army, consisting of several lettered discs arranged as a cylinder. It was also employed by the US Navy, under the name CSP 488.

<span class="mw-page-title-main">M-209</span> Mechanical cipher machine

In cryptography, the M-209, designated CSP-1500 by the United States Navy is a portable, mechanical cipher machine used by the US military primarily in World War II, though it remained in active use through the Korean War. The M-209 was designed by Swedish cryptographer Boris Hagelin in response to a request for such a portable cipher machine, and was an improvement of an earlier machine, the C-36.

The Two-square cipher, also called double Playfair, is a manual symmetric encryption technique. It was developed to ease the cumbersome nature of the large encryption/decryption matrix used in the four-square cipher while still being slightly stronger than the single-square Playfair cipher.

In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet. The earliest known description is due to Jacopo Silvestri in 1526. His proposal was for a rectangular stencil allowing single letters, syllables, or words to be written, then later read, through its various apertures. The written fragments of the plaintext could be further disguised by filling the gaps between the fragments with anodyne words or letters. This variant is also an example of steganography, as are many of the grille ciphers.

<span class="mw-page-title-main">Alberti cipher</span> Polyalphabetic substitution encryption and decryption system

The Alberti Cipher, created in 1467 by Italian architect Leon Battista Alberti, was one of the first polyalphabetic ciphers. In the opening pages of his treatise De componendis cifris he explained how his conversation with the papal secretary Leonardo Dati about a recently developed movable type printing press led to the development of his cipher wheel.

The Chaocipher is a cipher method invented by John Francis Byrne in 1918 and described in his 1953 autobiographical Silent Years. He believed Chaocipher was simple, yet unbreakable. Byrne stated that the machine he used to encipher his messages could be fitted into a cigar box. He offered cash rewards for anyone who could solve it.

References

  1. "Wheel Cipher". The Jefferson Monticello. Retrieved 19 March 2022.
  2. Kahn 1967, p. 194.
  3. Bazeries, Etienne (1901). Les Chiffres Secrets Dévoilés. Paris: Librairie Charpentier et Fasquelle. p. 250. Retrieved 7 October 2023.
  4. 1 2 Kruh, Louis (October 1981). "The Genesis of the Jefferson/Bazeries Cipher Device". Cryptologia. 5 (4): 193–208. doi:10.1080/0161-118191856039. ISSN   0161-1194.
  5. Beckman, Bengt (April 2002). "An Early Cipher Device: Fredrik Gripenstierna's Machine". Cryptologia. 26 (2): 113–123. doi:10.1080/0161-110291890821. ISSN   0161-1194.
  6. 1 2 Jefferson, Thomas (1950). The Papers of Thomas Jefferson, Volume 37: 4 March to 30 June 1802. Princeton University Press. ISBN   978-0-691-15001-7.
  7. "Cipher Machines". ciphermachines.com. Retrieved 2024-01-13.
  8. 1 2 3 Gaddy, David W. (October 1995). "The Cylinder-Cipher". Cryptologia. 19 (4): 385–391. doi:10.1080/0161-119591884033. ISSN   0161-1194.
  9. Bedini, Silvio A. (1990). Thomas Jefferson: Statesman of Science. Macmillan. p. 242. ISBN   978-0-02-897041-7.
  10. "Thomas Jefferson's Codes and Ciphers: II (1790-1803)". cryptiana.web.fc2.com. Retrieved 2024-01-09.
  11. Journal of the Royal Society of Arts. Society of Arts. 1854.
  12. Friedman 1918, p. 225.
  13. de Viaris (1893). L'Art de Déchiffrer les Dépêches Secrètes. Paris: Gauthier-Villars et Fils. pp. 50–52, 99–109. Retrieved 7 October 2023.

Sources