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| The Enigma cipher machine |
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| Enigma machine |
| Breaking Enigma |
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This article contains technical details about the rotors of the Enigma machine. Understanding the way the machine encrypts requires taking into account the current position of each rotor, the ring setting and its internal wiring.
| Exploded view of an Enigma rotor | Three rotors in sequence | ||
|---|---|---|---|
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No letter can map to itself, a cryptographic weakness caused by the same wires being used for forwards and backwards legs.
The effect of rotation on the rotors can be demonstrated with some examples.
As an example, let us take rotor type I of Enigma I (see table below) without any ring setting offset. It can be seen that an A is encoded as an E, a B encoded as a K, and a K is encoded as an N. Notice that every letter is encoded into another.
In the case of the reflectors, in this example Wide B is taken (Reflector B in the table below) where an A is returned as a Y and the Y is returned as an A. Notice that the wirings are connected as a loop between two letters.
When a rotor has stepped, the offset must be taken into account to know what the output is, and where it enters the next rotor.
If for example rotor I is in the B-position, an A enters at the letter B which is wired to the K. Because of the offset this K enters the next rotor in the J position.
With the rotors I, II and III (from left to right), wide B-reflector, all ring settings in A-position, and start position AAA, typing AAAAA will produce the encoded sequence BDZGO[ citation needed ].
The ring settings, or Ringstellung, are used to change the position of the alphabet ring relative to the internal wiring. Notch and alphabet ring are fixed together. Changing the ring setting will therefore change the positions of the wiring, relative to the turnover-point and start position.
The ring setting will rotate the wiring. Where rotor I in the A-position normally encodes an A into an E, with a ring setting offset B-02 it will be encoded into K
As mentioned before these encodings only happen after the key is pressed and the rotor has turned. Tracing the signal on the rotors AAA is therefore only possible if a key is pressed while the rotors were in the position AAZ and the ring settings are all on 01 or A.
With the rotors I, II, III (from left to right), wide B-reflector, all ring settings in B-position, and start position AAA, typing AAAAA will produce the encoded sequence EWTYX.
This table shows how the internal wiring connects the right side of the rotor (with the spring-loaded contacts) to the left side. Each rotor is a simple substitution cipher. The letters are listed as connected to alphabet order. If the first letter of a rotor is E, this means that the A is wired to the E. This does not mean that E is wired to A; such looped wiring is only the case with the reflectors.
| Rotor # | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Date Introduced | Model Name & Number |
|---|---|---|---|
| IC | DMTWSILRUYQNKFEJCAZBPGXOHV | 1924 | Commercial Enigma A, B |
| IIC | HQZGPJTMOBLNCIFDYAWVEUSRKX | 1924 | Commercial Enigma A, B |
| IIIC | UQNTLSZFMREHDPXKIBVYGJCWOA | 1924 | Commercial Enigma A, B |
| Rotor # | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Date Introduced | Model Name & Number |
| I | JGDQOXUSCAMIFRVTPNEWKBLZYH | 7 February 1941 | German Railway (Rocket) |
| II | NTZPSFBOKMWRCJDIVLAEYUXHGQ | 7 February 1941 | German Railway (Rocket) |
| III | JVIUBHTCDYAKEQZPOSGXNRMWFL | 7 February 1941 | German Railway (Rocket) |
| UKW | QYHOGNECVPUZTFDJAXWMKISRBL | 7 February 1941 | German Railway (Rocket) |
| ETW | QWERTZUIOASDFGHJKPYXCVBNML | 7 February 1941 | German Railway (Rocket) |
| Rotor # | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Date Introduced | Model Name & Number |
| I-K | PEZUOHXSCVFMTBGLRINQJWAYDK | February 1939 | Swiss K |
| II-K | ZOUESYDKFWPCIQXHMVBLGNJRAT | February 1939 | Swiss K |
| III-K | EHRVXGAOBQUSIMZFLYNWKTPDJC | February 1939 | Swiss K |
| UKW-K | IMETCGFRAYSQBZXWLHKDVUPOJN | February 1939 | Swiss K |
| ETW-K | QWERTZUIOASDFGHJKPYXCVBNML | February 1939 | Swiss K |
| Rotor # | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Date Introduced | Model Name & Number |
| I | EKMFLGDQVZNTOWYHXUSPAIBRCJ | 1930 | Enigma I |
| II | AJDKSIRUXBLHWTMCQGZNPYFVOE | 1930 | Enigma I |
| III | BDFHJLCPRTXVZNYEIWGAKMUSQO | 1930 | Enigma I |
| IV | ESOVPZJAYQUIRHXLNFTGKDCMWB | December 1938 | M3 Army |
| V | VZBRGITYUPSDNHLXAWMJQOFECK | December 1938 | M3 Army |
| VI | JPGVOUMFYQBENHZRDKASXLICTW | 1939 | M3 & M4 Naval (FEB 1942) |
| VII | NZJHGRCXMYSWBOUFAIVLPEKQDT | 1939 | M3 & M4 Naval (FEB 1942) |
| VIII | FKQHTLXOCBJSPDZRAMEWNIUYGV | 1939 | M3 & M4 Naval (FEB 1942) |
| Rotor # | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Date Introduced | Model Name & Number |
| Beta | LEYJVCNIXWPBQMDRTAKZGFUHOS | Spring 1941 | M4 R2 |
| Gamma | FSOKANUERHMBTIYCWLQPZXVGJD | Spring 1942 | M4 R2 |
| Reflector A | EJMZALYXVBWFCRQUONTSPIKHGD | ||
| Reflector B | YRUHQSLDPXNGOKMIEBFZCWVJAT | ||
| Reflector C | FVPJIAOYEDRZXWGCTKUQSBNMHL | ||
| Reflector B Thin | ENKQAUYWJICOPBLMDXZVFTHRGS | 1940 | M4 R1 (M3 + Thin) |
| Reflector C Thin | RDOBJNTKVEHMLFCWZAXGYIPSUQ | 1940 | M4 R1 (M3 + Thin) |
| ETW | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Enigma I | |
Technical comments related to Enigma modifications 1939-1945.
In 1941 it became known to the Swiss that some of their Enigma traffic was being read by the French. It was decided to make some design modifications.
Swiss Army Enigma machines were the only machines modified. The surviving Swiss Air Force machines do not show any signs of modification. Machines used by the diplomatic service apparently were not altered either.
The single turnover notch positioned on the left side (plate connector side) of the rotor triggers the stepping motion by engaging the ratchet teeth of the wheel to the left. Later rotors had two turnover notches. The table below lists the turnover notch point of each rotor.
| Rotor | Notch | Effect |
|---|---|---|
| I | Q | If rotor steps from Q to R, the next rotor is advanced |
| II | E | If rotor steps from E to F, the next rotor is advanced |
| III | V | If rotor steps from V to W, the next rotor is advanced |
| IV | J | If rotor steps from J to K, the next rotor is advanced |
| V | Z | If rotor steps from Z to A, the next rotor is advanced |
| VI, VII, VIII | Z+M | If rotor steps from Z to A, or from M to N the next rotor is advanced |
In the following examples you can observe a normal step sequence and a double step sequence. The used rotors are (from left to right) I, II, III, with turnovers on Q, E and V. It is the right rotor's behavior we observe here (turnover V).
The introduction of the fourth rotor was anticipated because captured material dated January 1941 had made reference to the development of a fourth rotor wheel; [2] indeed, the wiring of the new fourth rotor had already been worked out.
On 1 February 1942, the Enigma messages began to be encoded using a new Enigma version that had been brought into use. The previous 3-rotor Enigma model had been modified with the old reflector replaced by a thin rotor and a new thin reflector. Breaking Shark on 3-rotor bombes would have taken 50 to 100 times as long as an average Air Force or Army message. It seemed, therefore, that effective, fast, 4-rotor bombes were the only way forward. Encoding mistakes by cipher clerks allowed the British to determine the wiring of the new reflector and its rotor. [2]
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In the history of cryptography, Typex machines were British cipher machines used from 1937. It was an adaptation of the commercial German Enigma with a number of enhancements that greatly increased its security. The cipher machine was used until the mid-1950s when other more modern military encryption systems came into use.
In the history of cryptography, the ECM Mark II was a cipher machine used by the United States for message encryption from World War II until the 1950s. The machine was also known as the SIGABA or Converter M-134 by the Army, or CSP-888/889 by the Navy, and a modified Navy version was termed the CSP-2900.
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.
Hans-Thilo Schmidt codenamed Asché or Source D, was a spy who sold secrets about the German Enigma machine to the French during World War II. The materials he provided facilitated Polish mathematician Marian Rejewski's reconstruction of the wiring in the Enigma's rotors and reflector; thereafter the Poles were able to read a large proportion of Enigma-enciphered traffic.
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Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra.
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The card catalog, or "catalog of characteristics," in cryptography, was a system designed by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski, and first completed about 1935 or 1936, to facilitate decrypting German Enigma ciphers.
The grill method, in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau in decrypting German Enigma machine ciphers. The Enigma rotor cipher machine changes plaintext characters into cipher text using a different permutation for each character, and so implements a polyalphabetic substitution cipher.
John William Jamieson Herivel was a British science historian and World War II codebreaker at Bletchley Park.
Marian Adam Rejewski was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen Nazi German military Enigma cipher machine, aided by limited documents obtained by French military intelligence. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski developed and used techniques and equipment to decrypt the German machine ciphers, even as the Germans introduced modifications to their equipment and encryption procedures.
The Schlüsselgerät 39 (SG-39) was an electrically operated rotor cipher machine, invented by the German Fritz Menzer during World War II. The device was the evolution of the Enigma rotors coupled with three Hagelin pin wheels to provide variable stepping of the rotors. All three wheels stepped once with each encipherment. Rotors stepped according to normal Enigma rules, except that an active pin at the reading station for a pin wheel prevented the coupled rotor from stepping. The cycle for a normal Enigma was 17,576 characters. When the Schlüsselgerät 39 was correctly configured, its cycle length was characters, which was more than 15,000 times longer than a standard Enigma. The Schlüsselgerät 39 was fully automatic, in that when a key was pressed, the plain and cipher letters were printed on separate paper tapes, divided into five-digit groups. The Schlüsselgerät 39 was abandoned by German forces in favour of the Schlüsselgerät 41.
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