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Military History Companion:

Enigma

Enigma

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In 1919, Hugo Koch from the Netherlands invented an electronic enciphering machine that provided 22 million different combinations. It really began to be used in 1923 as a commercial product and by this time a German named Arthur Scherbius had taken over the development of the machine, which was aimed at business needs for secure communications. The German navy became interested in the machine and it was withdrawn from the civilian market and refined for military use.

In its developed form the Enigma machine had a keyboard, plugboard, three (army, air force) or four (navy) rotors, and a lamp table. The rotors were set to a ‘ground setting’ (grundstellung), usually changed daily. Each message would be preceded by an individual ‘key setting’. The message would be typed onto the keyboard, the rotors changed the cipher at each letter, and the enciphered letters would light up on the lamp table. After wireless transmission by Morse code the enciphered message would be typed by the receiver onto an Enigma machine having the same ground setting, the key setting entered, and the text deciphered automatically.

Three Polish mathematicians (Rejewski, Rozycki, and Zygalski) established the theoretical basis for breaking the output of German military Enigma machines in early 1933, through a process of combining mathematics, statistics, computational ability, and inspired guesswork. In July 1939, at a secret meeting with British representatives, the Polish government handed over their theoretical data on breaking Enigma and a replica Enigma machine. In August the Government Code and Cypher School (GC&CS) was moved to Bletchley Park, an estate 46 miles (75 km) from London. Chess masters, mathematicians, professors, and linguists were recruited from all over Britain, many from Cambridge University. The first Bombe machine (named after the ice cream, not explosive) permitted the British to read some traffic during the fall of France. This intelligence, dubbed ULTRA, was passed on to a very limited number of recipients, among whom the most voracious reader was certainly Churchill. ULTRA supplied advanced warning of Luftwaffe intentions during the battle of Britain in 1940 and was instrumental in the interdiction of Axis supplies in the Mediterranean, contributing substantially to the turning point at Alamein. Theoretical data was shared with the Americans even before they entered the war, although there were always reservations about their less stringent distribution and occasionally careless use of ULTRA.

The battle against Enigma was never completely won. Advances came from the capture of ground settings from German weather ships (taken in a ‘cutting out’ operation on suggestion from Bletchley Park) and a U-boat. First principle was the identification of a standard message such as ‘nothing to report’ and the possible key setting such as the operator's wife's name, from which it was possible to work back to the ground setting. The Bombe machine could then find the key settings for other messages in that ground setting. By 1944, over 4, 000 German messages were being decrypted daily at Bletchley Park.

The flood of SIGINT, of which the product from the attack on Enigma was only a part, crucially influenced the direction and outcome of WW II. The North Africa, Italian, and North-West Europe campaigns, but above all the battles of the Atlantic and the Pacific (though this latter did not involve Enigma), were heavily affected by the Allies' foreknowledge of Axis intentions. Never in a major war has one combatant had his intentions betrayed so comprehensively to his opponent. It is remarkable that the secret was entirely kept for 30 years and much of it for 50 years: the story is still unfolding.

Bibliography

  • Bauer, F. L., Decrypted Secrets: Methods and Maxims of Cryptology (New York, 1997).
  • Hinsley, H., et al., British Intelligence in the Second World War (London, 1979-88).
  • Hodges, Andrew, Alan Turing: The Enigma (London, 1992).
  • Kahn, David, The Codebreakers: The Story of Secret Writing (rev. edn., New York, 1996)

— Danny M. Johnson/Peter Jarvis

 
 
Britannica Concise Encyclopedia: Enigma

Device used by the German military to encode strategic messages before and during World War II. The Enigma code was first broken by the Poles in the early 1930s, so that German messages were eventually intercepted and deciphered by Allied code-breakers during the war. (See also Ultra.)

For more information on Enigma, visit Britannica.com.

 
Intelligence Encyclopedia: Enigma

Enigma was a ciphering (code communication) system used by the German military from 1926 until the end of World War II, and by several other nations for some years after. Enigma was the first mechanized message-encryption system to see wide use. Enigma produced such thoroughly scrambled messages that for many years its cipher was considered unbreakable both by the German military and its foes. Polish and British mathematicians, however, cracked the Enigma cipher in time to give the Allies access to most German military communications throughout World War II. The German government never knew that the Enigma cipher had been broken and that its military communications were often transparent, giving a significant advantage to the Allies on many occasions. The Japanese military also used a cipher related to Enigma during World War II. The Japanese version of Enigma was cracked by American cryptographers, providing a crucial advantage to the Allies in the Pacific theater. U.S. knowledge of secrete Japanese transmissions was essential, for example, to victory at the crucial battle at Midway, the Japanese navy's first major defeat in several centuries. Many military strategists and historians hold that Allied success in cracking the Enigma and related ciphers helped significantly shorten World War II.

Origin of Enigma. During World War I, cumbersome paper-and-pencil ciphers were still the rule, as they had been for centuries past. (A cipher is any scheme for transforming ordinary written language—plaintext—into a coded, but apparently random string of characters, ciphertext.) After World War I, several inventors turned their attention to the mechanization of ciphering, seeking to increase accuracy, speed, and security. The most successful of these inventors was German engineer Arthur Scherbius, who in 1918, created a cipher machine he named the Enigma. (This is not a translation; the word "enigma" is the same in German and English). Scherbius was unsuccessful in selling Enigma to commercial buyers. It was not until 1923 that Enigma was chosen by the German government as its standard ciphering system, as Germany had only just learned how much damage had been done by the breaking of its ciphers by the Allies in World War I. Between 1925 and 1945, the German military bought over 30,000 Enigma machines, deploying slightly different systems to its European armies, its army in North Africa, its air force, and its navy.

The Enigma cipher. The Enigma cipher is built upon the simplest of all cipher types, the substitution cipher. In a substitution cipher, one letter of the alphabet is substituted directly for another. A substitution cipher for a sixletter alphabet might appear as

Plaintext:     A B C D E F
Ciphertext:   F C A B D E

Using this cipher, the plaintext word BAD (for example) would produce the ciphertext word CFB. Such ciphers are easy to implement, but also contain easily broken code, as their ciphertext contains all the regularities of ordinary language: that is, double letters in plaintext appear as double letters in ciphertext, the ciphertext letter for "e" will appear in the ciphertext just as often as "e" appears in plaintext, and so forth. Such codes are weak because analyzing regularities is one of the primary means by which codebreakers attack codes.

However, by adding complications to this simple idea, a powerful code can be devised. Consider the following substitution cipher for a three-letter alphabet

Plaintext:     A B C
Ciphertext:   A C B

In this simple example, A is enciphered as itself. This cipher can be imagined as a physical device consisting of three disks or dials arranged in a row. The first (left-hand) and third (right-hand) disks, each of which has the alphabet ABC spaced evenly around its edge, are identical, and are aligned so that their letters are in the same positions; the third disk, which sandwiched between the other two, is different. It contains three wires that pass from its left side right through to its right, connecting the two alphabet disks so that the A of the left-hand disk is wired to the A of the right-hand disk, the B of the left-hand disk to the C of the right-hand disk, and the C of the left-hand disk to the B of the right-hand disk. In effect, the middle disk scrambles the alphabet. The result is a simple substitution cipher. If the middle disk, (the scrambler) is rotated, however, so that the wire which touched A on the plaintext disk now touches C on that disk, all the other letters on the plaintext and ciphertext disks will also be connected differently by the scrambler, producing the following substitution cipher

Plaintext:     A B C
Ciphertext:   B A C

This can be verified by describing the wires in the scrambler as a set of input-output rules, one for each wire

  1. Connect input position 1 to output position 1.
  2. Connect input position 2 to output position 3.
  3. Connect input position 3 to output position 2.

By rule 1, when scrambler input position 1 is lined up with the letter A on the left-hand (plaintext) disk, it is connected to output position 1, which is lined up with the letter A on the right-hand (ciphertext) disk. The other two substitutions are produced by the other two wires: B → C, C → B. When the scrambler is rotated so that its input 1 moves from A to C on the plaintext disk, its output 1 moves from A to C on the ciphertext disk. Now, instead of producing A → A, wire 1 produces C → C. The other two wires now produce the substitutions A → B, B → A. Thus, each time the scrambler is rotated by one letter position, a new different substitution code is produced. This continues until the scrambler returns to its starting position, whereupon the substitution codes produced by the device begin to repeat. In this example, repetition begins with the third shift of the scrambler.

Rotation of the scrambler can be used to make a cipher that is more formidable than a straightforward substitution. Consider a three-letter plaintext message is to be sent: ABA. First, A is enciphered with the scrambler in the first position described above: A → A. Before the second letter is encrypted, the scrambler disk is rotated by one letter-position. The second plaintext letter is then enciphered: B → A. The disk is rotated, and A is enciphered again: A → C. Although in this case one would start repeating substitutions after only three letters, the resulting cipher is significantly more complex, and thus harder to crack, than a static substitution cipher.

Decryption in this system is simple as long as the receiving party possesses an identical machine; the wires in the scrambler disk work equally well in either direction, so decryption is simply encryption run backwards. The receiver must, however, begin decrypting with their scrambler set to the same position as the sender's at the start of transmission, otherwise the substitution codes used by the receiver to decipher the message will be out of step with those used by the sender to encipher it, and decipherment will fail.

The Enigma system was based upon the scramblerdisk principle described above. Enigma used not a 3-letter, but a 26-character alphabet and not one, but four scrambler disks. The first scrambler scrambled plaintext or ciphertext, the second scrambler scrambled the outputs of the first scrambler, the third scrambled the outputs of the second, and the fourth fed back, or "reflected," the outputs of the third so that messages passed through the other three scramblers before the encrypted ciphertext (or decrypted plaintext) was read. Each letter was thus scrambled a total of seven times during its passage through the machine. Three of the scrambler disks could be rotated freely, but the fourth, the "reflector," was stationary.

In order to use an Enigma unit, its operator typed plaintext or ciphertext into a keyboard. For each keystroke typed, Enigma automatically shifted one or more of its scramblers and lit up a letter on a display board. The letter on the display board showed the output text for the typed input letter: ciphertext if plaintext was input, plaintext if ciphertext was input. To produce further scrambling between ciphertext and plaintext, each Enigma also had a built-in commutator or "plugboard" that enabled the operator to crisscross paired letters of the alphabet before their signals fed into the first scrambler disk. The result was that Enigma had over 1020 different "keys" or distinct settings of scramblers and plugboard. Simply guessing the correct key for a given message was, therefore, essentially impossible. Every day at midnight, all operators of a given Enigma system would switch to a new key; these initial daily keys were printed in a codebook that was distributed to the operators. For added security, the scrambler-disks part of the key was changed for every single message sent; this message-key information was transmitted twice at the beginning of every message. This technique was intended to prevent message loss due to transmission errors, but in fact reduced Enigma's effectiveness by introducing an element of predictability.

The defeat of Enigma. Enigma was long considered impossible to crack. However, in 1931, a disgruntled German exofficer gave drawings for the machine to the French secret service. The French, who considered Enigma too tough to crack even with this information in their possession, gave it to the Polish government. Polish mathematician Marian Rejewski (1905–1980) used it to devise automatic devices (specialized electromechanical calculators) for re-cracking the ever-changing Enigma cipher on a daily basis. Just before the fall of Poland in 1939, Rejewski's findings were transferred to the British government, which continued to improve them.

During World War II, the German military modified the Enigma system at intervals, requiring the British to continue re-cracking the cipher throughout the war. With the help of a motley team of crossword-puzzle experts, bridge devotees, chess champions, mathematicians, and linguists led by British mathematician and computing pioneer Alan Turing (1912–1954), the group succeeded. Tragically, however, Turing was persecuted after the war for his homosexuality. His security clearance was revoked, he was forced to undergo debilitating hormone treatments, and he was banned from the development of the digital computer. Turing committed suicide in 1954, some 20 years before his crucial contribution to the cracking of Enigma, and thus, to the Allied victory, was declassified.

Further Reading

Books

Churchouse, Robert. Codes and Ciphers. Cambridge, England: Cambridge University Press, 2002.

Singh, Simon. The Code Book. New York: Doubleday, 1999.

 
Wikipedia: Enigma machine
For a discussion of how Enigma-derived intelligence was put to use, see Ultra (WWII intelligence).
The plugboard, keyboard, lamps, and finger-wheels of the rotors emerging from the inner lid of a three-rotor German military Enigma machine
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The plugboard, keyboard, lamps, and finger-wheels of the rotors emerging from the inner lid of a three-rotor German military Enigma machine
Enigma-logo.jpg
The Enigma cipher machine

The Enigma machine was a cipher machine used to encrypt and decrypt secret messages. More precisely, Enigma was a family of related electro-mechanical rotor machines, comprising a variety of different models.

The Enigma was used commercially from the early 1920s on, and was also adopted by the military and governmental services of a number of nations—most famously by Nazi Germany before and during World War II.

The German military model, the Wehrmacht Enigma, is the version most commonly discussed. The machine has gained notoriety because Allied cryptologists were able to decrypt a large number of messages that had been enciphered on the machine. Decryption was made possible in 1932 by Polish cryptographers Marian Rejewski, Jerzy Różycki and Henryk Zygalski from Cipher Bureau. In mid-1939 reconstruction and decryption methods were delivered from Poland to Britain and France. The intelligence gained through this source, codenamed ULTRA, was a significant aid to the Allied war effort. The exact influence of ULTRA is debated, but a typical assessment is that the end of the European war was hastened by two years because of the decryption of German ciphers.[citation needed]

Although the Enigma cipher has cryptographic weaknesses, in practice it was only in combination with other significant factors (mistakes by operators, procedural flaws, an occasional captured machine or codebook) that Allied codebreakers were able to decipher messages.[1]

Description

Enigma wiring diagram showing current flow. The 'A' key is encoded to the 'D' lamp. D yields A, but A never yields A.
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Enigma wiring diagram showing current flow. The 'A' key is encoded to the 'D' lamp. D yields A, but A never yields A.
The scrambling action of the Enigma rotors shown for two consecutive letters — current is passed into set of rotors, around the reflector, and back out through the rotors again. The greyed-out lines represent other possible circuits within each rotor, which are hard-wired to contacts on each rotor. Letter A encrypts differently with consecutive key presses, first to G, and then to C. This is because the right hand rotor has stepped, sending the signal on a completely different route.
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The scrambling action of the Enigma rotors shown for two consecutive letters — current is passed into set of rotors, around the reflector, and back out through the rotors again. The greyed-out lines represent other possible circuits within each rotor, which are hard-wired to contacts on each rotor. Letter A encrypts differently with consecutive key presses, first to G, and then to C. This is because the right hand rotor has stepped, sending the signal on a completely different route.

Like other rotor machines, the Enigma machine is a combination of mechanical and electrical systems. The mechanical mechanism consists of a keyboard; a set of rotating disks called rotors arranged adjacently along a spindle; and a stepping mechanism to turn one or more of the rotors with each key press. The exact mechanism varies, but the most common form is for the right-hand rotor to step once with every key stroke, and occasionally the motion of neighbouring rotors is triggered. The continual movement of the rotors results in a different cryptographic transformation after each key press.

The mechanical parts act in such a way as to form a varying electrical circuit — the actual encipherment of a letter is performed electrically. When a key is pressed, the circuit is completed; current flows through the various components and ultimately lights one of many lamps, indicating the output letter. For example, when encrypting a message starting ANX..., the operator would first press the A key, and the Z lamp might light; Z would be the first letter of the ciphertext. The operator would then proceed to encipher N in the same fashion, and so on.

To explain the Enigma, we use the wiring diagram on the left. To simplify the example, only four components of each are shown. In reality, there are 26 lamps, keys, plugs and wirings inside the rotors. The current flows from the battery (1) through the depressed bi-directional letter-switch (2) to the plugboard (3). The plugboard allows rewiring the connections between keyboard (2) and fixed entry wheel (4). Next, the current proceeds through the - unused, so closed - plug (3) via the entry wheel (4) through the wirings of the three (Wehrmacht Enigma) or four (Kriegsmarine M4 or Abwehr variant) rotors (5) and enters the reflector (6). The reflector returns the current, via a different path, back through the rotors (5) and entry wheel (4), and proceeds through plug 'S' connected with a cable (8) to plug 'D', and another bi-directional switch (9) to light-up the lamp.

The continual changing of electrical paths through the unit because of the rotation of the rotors (which cause the pin contacts to change with each letter typed) implements the polyalphabetic encryption which provided Enigma's high security.

Rotors

Main article: Enigma rotor details
The left side of an Enigma rotor, showing the flat electrical contacts. A single turnover notch is visible on the left edge of the rotor.
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The left side of an Enigma rotor, showing the flat electrical contacts. A single turnover notch is visible on the left edge of the rotor.
The right side of a rotor, showing the pin electrical contacts. The Roman numeral V identifies the wiring of the rotor.
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The right side of a rotor, showing the pin electrical contacts. The Roman numeral V identifies the wiring of the rotor.

The rotors (alternatively wheels or drums — Walzen in German) form the heart of an Enigma machine. Approximately 10 cm in diameter, each rotor is a disc made of hard rubber or bakelite with a series of brass spring-loaded pins on one face arranged in a circle; on the other side are a corresponding number of circular electrical contacts. The pins and contacts represent the alphabet — typically the 26 letters A–Z (this will be assumed for the rest of the description). When placed side-by-side, the pins of one rotor rest against the contacts of the neighbouring rotor, forming an electrical connection. Inside the body of the rotor, a set of 26 wires connects each pin on one side to a contact on the other in a complex pattern. The wiring differs for every rotor.

Three Enigma rotors and the shaft on which they are placed when in use.
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Three Enigma rotors and the shaft on which they are placed when in use.

By itself, a rotor performs only a very simple type of encryption — a simple substitution cipher. For example, the pin corresponding to the letter E might be wired to the contact for letter T on the opposite face. The complexity comes from the use of several rotors in series — usually three or four — and the regular movement of the rotors; this provides a much stronger type of encryption.

When placed in the machine, a rotor can be set to one of 26 positions. It can be turned by hand using a grooved finger-wheel which protrudes from the internal cover when closed, as shown in Figure 2. So that the operator knows the position, each rotor has an alphabet tyre (or letter ring) attached around the outside of the disk, with 26 letters or numbers; one of these can be seen through a window, indicating the position of the rotor to the operator. In early Enigma models, the alphabet ring is fixed; a complication introduced in later versions is the facility to adjust the alphabet ring relative to the core wiring. The position of the ring is known as the Ringstellung ("ring setting").

The rotors each contain a notch (sometimes multiple notches), used to control the stepping of the rotors. In the military versions, the notches are located on the alphabet ring.

Exploded view of an Enigma rotor   Three rotors in sequence
Enigma_rotor_exploded_view.png
  1. notched ring
  2. marking dot for "A" contact
  3. alphabet ring
  4. plate contacts
  5. wire connections
  6. pin contacts
  7. spring-loaded ring adjusting lever
  8. hub
  9. finger wheel
  10. ratchet wheel
 Enigma_rotor_set.png

The Army and Air Force Enigmas came equipped with several rotors; when first issued there were only three. On 15 December 1938 this changed to five, from which three were chosen for insertion in the machine. These were marked with Roman numerals to distinguish them: I, II, III, IV and V, all with single notches located at different points on the alphabet ring. This must have been intended as a security measure, but ultimately allowed the Polish Clock Method and British Banburismus attacks.

The Naval version of the Wehrmacht Enigma had always been issued with more rotors than the other services: at first, six, then seven and finally eight. The additional rotors were named VI, VII and VIII, all with different wiring, and had two notches cut into them at 'N' and 'A', resulting in a more frequent turnover.

The four-rotor Naval Enigma (M4) machine accommodated an extra rotor in the same space as the three-rotor version. This was accomplished by replacing the original reflector with a thinner reflector and adding a special fourth rotor. The fourth rotor can be one of two types, Beta or Gamma, and never steps, but it can be manually placed in any of the 26 positions.

Stepping motion

Stepping motion of the Enigma. All three ratchet pawls (green) push in unison. In the first rotor (1), the ratchet (red) is always engaged, and steps with each keypress. Here, the second rotor (2) is engaged because the notch in the first rotor is aligned with the pawl; it will step with the next keypress. The third rotor (3) is not engaged, because the notch in the second rotor is not aligned; the pawl will simply slide over the curved ring.
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Stepping motion of the Enigma. All three ratchet pawls (green) push in unison. In the first rotor (1), the ratchet (red) is always engaged, and steps with each keypress. Here, the second rotor (2) is engaged because the notch in the first rotor is aligned with the pawl; it will step with the next keypress. The third rotor (3) is not engaged, because the notch in the second rotor is not aligned; the pawl will simply slide over the curved ring.

To avoid merely implementing a simple (and easily breakable) substitution cipher, some rotors turned with consecutive presses of a key. This ensured the cryptographic substitution would be different at each position, producing a formidable polyalphabetic substitution cipher.

The most common arrangement used a ratchet and pawl mechanism. Each rotor had a ratchet with 26 teeth; a group of pawls engage the teeth of the ratchet. The pawls pushed forward in unison with each keypress on the machine. If a pawl engaged the teeth of a ratchet, that rotor advanced by one step.

In the Wehrmacht Enigma, each rotor had an adjustable notched ring. The five basic rotors (I-V) had one notch each, while the additional naval rotors VI, VII and VIII had two notches. At a certain point, a rotor's notch eventually aligned with the pawl, allowing it to engage the ratchet of the next rotor with the subsequent key press. When a pawl was not aligned with the notch, it simply slid over the surface of the ring without engaging the ratchet. In a single-notch rotor system, the second rotor advanced one position every 26 advances of the first rotor. Similarly, the third rotor advanced one position for every 26 advances of the second rotor. The second rotor also advanced at the same time as the third rotor, meaning the second rotor can step twice on subsequent key presses — "double stepping" — resulting in a reduced period.[2]

This double stepping caused the rotors to deviate from a normal odometer. A double step occurred as follows: the first rotor stepped, and took the second rotor one step further. If the second rotor moved by this step into its own notch-position, the third pawl drops down. On the next step this pawl would push the ratchet of the third rotor and advance it, but pushed into the second rotor's notch, advancing the second rotor a second time in a row.

With three wheels and only single notches in the first and second wheels, the machine had a period of 26 × 25 × 26 = 16,900 (not 26 X 26 X 26 because of the double stepping of the second rotor, see bottom of page in the references section, for a link to a PDF file on this 'double stepping'). Historically, messages were limited to a couple of hundred letters, and so there was very little risk of repeating any position within a single message.

To make room for the naval fourth rotors "Beta" and "Gamma", introduced in 1942, the reflector was changed, by making it much thinner and the special thin fourth rotor was placed against it. No changes were made to rest of the mechanism. Since there were only three pawls, the fourth rotor never stepped, but could be manually set into one of its 26 positions.

When pressing a key, the rotors stepped before the electrical circuit is connected.

The Enigma rotor assembly. The three movable rotors are sandwiched between two fixed wheels: the entry wheel on the right and the reflector (here marked "B") on the left.
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The Enigma rotor assembly. The three movable rotors are sandwiched between two fixed wheels: the entry wheel on the right and the reflector (here marked "B") on the left.

Entry wheel

The entry wheel (Eintrittswalze in German), or entry stator, connects the plugboard, if present, or otherwise the keyboard and lampboard, to the rotor assembly. While the exact wiring used is of comparatively little importance to the security, it proved an obstacle in the progress of Polish cryptanalyst Marian Rejewski during his deduction of the rotor wirings. The commercial Enigma connects the keys in the order of their sequence on the keyboard: Q→A, W→B, E→C and so on. However, the military Enigma connects them in straight alphabetical order: A→A, B→B, C→C etc. It took an inspired piece of guesswork for Rejewski to realise the modification, and he was then able to solve his even more inspired equations.

Reflector

With the exception of the early models A and B, the last rotor came before a reflector (German: Umkehrwalze), a patented feature distinctive of the Enigma family amongst the various rotor machines designed in the period. The reflector connected outputs of the last rotor in pairs, redirecting current back through the rotors by a different route. The reflector ensured that Enigma is self-reciprocal: conveniently, encryption was the same as decryption. However, the reflector also gave Enigma the property that no letter ever encrypted to itself. This was a severe conceptual flaw and a cryptological mistake subsequently exploited by codebreakers.

In the commercial Enigma model C, the reflector could be inserted in one of two different positions. In Model D the reflector could be set in 26 possible positions, although it did not move during encryption. In the Abwehr Enigma, the reflector stepped during encryption in a manner like the other wheels.

In the German Army and Air Force Enigma, the reflector was fixed and did not rotate; there were four versions. The original version was marked A, and was replaced by Umkehrwalze B on 1 November 1937. A third version, Umkehrwalze C was used briefly in 1940, possibly by mistake, and was solved by Hut 6.[3] The fourth version, first observed on 2 January 1944 had a rewireable reflector, called Umkehrwalze D, allowing the Enigma operator to alter the connections as part of the key settings.

Plugboard

The plugboard (Steckerbrett) was positioned at the front of the machine, below the keys. When in use, there were up to 13 connections. In the above photograph, two pairs of letters have been swapped (S-O and J-A).
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The plugboard (Steckerbrett) was positioned at the front of the machine, below the keys. When in use, there were up to 13 connections. In the above photograph, two pairs of letters have been swapped (S-O and J-A).

The plugboard (Steckerbrett in German) permitted variable wiring that could be reconfigured by the operator (visible on the front panel of Figure 1; some of the patch cords can be seen in the lid). It was introduced on German Army versions in 1930 and was soon adopted by the Navy as well. The plugboard contributed a great deal to the strength of the machine's encryption: more than an extra rotor would have done. Enigma without a plugboard — "unsteckered" Enigma — can be solved relatively straightforwardly using hand methods; these techniques are generally defeated by the addition of a plugboard, and Allied cryptanalysts resorted to special machines to solve it.

A cable placed onto the plugboard connected letters up in pairs, for example, E and Q might be a "steckered" pair. The effect was to swap those letters before and after the main rotor scrambling unit. For example, when an operator presses E, the signal was diverted to Q before entering the rotors. Several such steckered pairs, up to 13, might be used at one time.

Current flowed from the keyboard through the plugboard, and proceeds to the entry-rotor or Eintrittswalze. Each letter on the plugboard had two jacks. Inserting a plug disconnects the upper jack (from the keyboard) and the lower jack (to the entry-rotor) of that letter. The plug at the other end of the crosswired cable was inserted into another letter's jacks, thus switching the connections of the two letters.

The "Schreibmax" was a printing unit which could be attached to the Enigma, removing the need for laboriously writing down the letters indicated on the light panel.
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The "Schreibmax" was a printing unit which could be attached to the Enigma, removing the need for laboriously writing down the letters indicated on the light panel.

Accessories

The Enigma Uhr attachment
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The Enigma Uhr attachment

A feature that was used on the M4 Enigma was the "Schreibmax", a little printer which could print the 26 letters on a small paper ribbon. This did away with the need for a second operator to read the lamps and write the letters down. The Schreibmax was placed on top of the Enigma machine and was connected to the lamp panel. To install the printer, the lamp cover and all lightbulbs had to be removed. Besides its convenience, it could improve operational security; the printer could be installed remotely such that the signal officer operating the machine no longer had to see the decrypted plaintext information.

Another accessory was the remote lamp panel. If the machine was equipped with an extra panel, the wooden case of the Enigma was wider and could store the extra panel. There was a lamp panel version that could be connected afterwards, but that required, just as with the Schreibmax, that the lamp panel and lightbulbs be removed. The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it.

In 1944 the Luftwaffe introduced an extra plugboard switch, called the Uhr (clock). There was a little box, containing a switch with 40 positions. It replaced the default plugs. After connecting the plugs, as determined in the daily key sheet, the operator turned the switch into one of the 40 positions, each position producing a different combination of plug wiring. Most of these plug connections were, unlike the default plugs, not pair-wise.

Mathematical description

The Enigma transformation for each letter can be specified mathematically as a product of permutations. Assuming a three-rotor German Army/Air Force Enigma, let P denote the plugboard transformation, U denote the reflector, and L,M,R denote the actions of the left, middle and right rotors. Then the encryption E can be expressed as

E = PRMLUL - 1M - 1R - 1P - 1

After each key press the rotors turn, changing the transformation. For example, if the right hand rotor R is rotated i positions, the transformation becomes ρiRρ - i, where ρ is the cyclic permutation mapping A to B, B to C, and so forth. Similarly, the middle and left-hand rotors can be represented as j and k rotations of M and L. The encryption function can then be described as:

E = P(ρiRρ - i)(ρjMρ - j)(ρkLρ - k)U(ρkL - 1ρ - k)(ρjM - 1ρ - j)(ρiR - 1ρ - i)P - 1

Procedures for using the Enigma

In use, the Enigma required a list of daily key settings as well as a number of auxiliary documents. The procedures for German Naval Enigma were more elaborate, and secure, than the procedures used in other services. The Navy codebooks were also printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were at risk of being seized by the enemy. The above codebook was taken from captured U-boat U-505.
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In use, the Enigma required a list of daily key settings as well as a number of auxiliary documents. The procedures for German Naval Enigma were more elaborate, and secure, than the procedures used in other services. The Navy codebooks were also printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were at risk of being seized by the enemy. The above codebook was taken from captured U-boat U-505.

In German military usage, communications were divided up into a number of different networks, all using different settings for their Enigma machines. These communication nets were termed keys at Bletchley Park, and were assigned codenames, such as Red, Chaffinch and Shark. Each unit operating on a network was assigned a settings list for its Enigma for a period of time. For a message to be correctly encrypted and decrypted, both sender and receiver had to set up their Enigma in the same way; the rotor selection and order, the starting position and the plugboard connections must be identical. All these settings (together the key in modern terms) must have been established beforehand, and were distributed in codebooks.

An Enigma machine's initial state, the cryptographic key, has several aspects:

  • Wheel order (Walzenlage) — the choice of rotors and the order in which they are fitted.
  • Initial position of the rotors: — chosen by the operator, different for each message.
  • Ring settings (Ringstellung) — the position of the alphabet ring relative to the rotor wiring.
  • Plug settings (Steckerverbindungen) — the connections of the plugs in the plugboard.
  • In very late versions, the wiring of the reconfigurable reflector.

Enigma was designed to be secure even if the rotor wiring was known to an opponent, although in practice there was considerable effort to keep the wiring secret. If the wiring is secret, the total number of possible configurations has been calculated to be around 10114 (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around 1023 (76 bits).[4] Users of Enigma were confident of its security because of the large number of possibilities; it was not then feasible for an adversary to even begin to try every possible configuration in a brute force attack.

Indicators

Most of the keys were kept constant for a set time period, typically a day. However, a different initial rotor position was chosen for each message, a concept similar to an initialisation vector in modern cryptography, because if a number of messages are sent encrypted with identical or near-identical settings a cryptanalyst, with several messages "in depth", might be able to attack the messages using frequency analysis. The starting position was transmitted just before the ciphertext. The exact method used was termed the "indicator procedure" — weak indicator procedures allowed the initial breaks into Enigma.

Figure 2. With the inner lid down, the Enigma was ready for use. The finger wheels of the rotors protruded through the lid, allowing the operator to set the rotors, and their current position — here RDKP — was visible to the operator through a set of windows.
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Figure 2. With the inner lid down, the Enigma was ready for use. The finger wheels of the rotors protruded through the lid, allowing the operator to set the rotors, and their current position — here RDKP — was visible to the operator through a set of windows.

One of the earliest indicator procedures was used by Polish cryptanalysts to make the initial breaks into the Enigma. The procedure was for the operator to set up his machine in accordance with his settings list, which included a global initial position for the rotors (Grundstellung — "ground setting"), AOH, perhaps. The operator turned his rotors until AOH was visible through the rotor windows. At that point, the operator chose his own, arbitrary, starting position for that particular message. An operator might select EIN, and this became the message settings for that encryption session. The operator then typed EIN into the machine, twice, to allow for detection of transmission errors. The results were an encrypted indicator — the EIN typed twice might turn into XHTLOA, which would be transmitted along with the message. Finally, the operator then spun the rotors to his message settings, EIN in this example, and typed the plaintext of the message.

At the receiving end, the operation was reversed. The operator set the machine to the initial settings and typed in the first six letters of the message (XHTLOA). In this example, EINEIN emerged on the lamps. By moving his rotors to EIN, the receiving operator then typed in the rest of the ciphertext, deciphering the message.

The weakness in this indicator scheme came from two factors. First, use of a global ground setting — this was later changed so the operator selected his initial position to encrypt the indicator, and sent the initial position in the clear. The second problem was the repetition of the indicator, which was a serious security flaw. The message setting was encoded twice, resulting in a relation between first and fourth, second and fifth, and third and sixth character. This security problem enabled the Polish Cipher Bureau to break into the pre-war Enigma system as early as 1932. However, from 1940 on, the Germans changed the procedures to increase the security.

During World War II codebooks were used only to set up the rotors and ring settings. For each message, the operator selected a random start position, let's say WZA, and random message key, perhaps SXT. He moved the rotors to the WZA start position and encoded the message key SXT. Assume the result was UHL. He then set up the message key SXT as the start position and encrypted the message. Next, he transmitted the start position WZA, the encoded message key UHL and then the ciphertext. The receiver set up the start position according the first trigram, WZA and decoded the second trigram, UHL, to obtain the SXT message setting. Next, he used this SXT message setting as the start position to decrypt the message. This way, each ground setting was different and the new procedure avoided the security flaw of double encoded message settings.

This procedure was used by Wehrmacht and Luftwaffe only. The Kriegsmarine procedures on sending messages with the Enigma were far more complex and elaborate. Prior to encryption with the Enigma, the message was encoded using the Kurzsignalheft code book. The Kurzsignalheft contained tables to convert sentences into four-letter groups. A great many choices were included, e.g. logistic matters such as refueling and rendezvous with supply ships, positions and grid lists, harbor names, countries, weapons, weather conditions, enemy positions and ships, date and time tables. Another codebook contained the Kenngruppen and Spruchschlüssel: the key identification and message key. More details on Kurzsignale on German U-Boats

Abbreviations and guidelines

The Army Enigma machine only used the 26 alphabet characters. Signs were replaced by rare character combinations. A space was omitted or replaced by an X. The X was generally used as point or full stop. Some signs were different in other parts of the armed forces. The Wehrmacht replaced a comma by ZZ and the question sign by FRAGE or FRAQ. The Kriegsmarine however, replaced the comma by Y and the question sign by UD. The combination CH, as in Acht (eight) or Richtung (direction) were replaced by Q (AQT, RIQTUNG). Two, three and four zeros were replaced by CENTA, MILLE and MYRIA.

The Wehrmacht and the Luftwaffe transmitted messages in groups of five characters. The Kriegsmarine, using the four rotor Enigma, had four-character groups. Frequently used names or words were to be varied as much as possible. Words like Minensuchboot (minesweeper) could be written as MINENSUCHBOOT, MINBOOT, MMMBOOT or MMM354. To make cryptanalysis harder, more than 250 characters in one message were forbidden. Longer messages were divided in several parts, each using its own message key. For more details see Tony Sale's translations of "General Procedure"[5] and "Officer and Staff procedure".[6]

History and development of the machine

Far from being a single design, there are numerous models and variants of the Enigma family. The earliest Enigma machines were commercial models dating from the early 1920s. Starting in the mid-1920s, the various branches of the German military began to use Enigma, making a number of changes in order to increase its security. In addition, a number of other nations either adopted or adapted the Enigma design for their own cipher machines.

A selection of seven Enigma machines and paraphernalia exhibited at the USA's National Cryptologic Museum. From left to right, the models are: 1) Commercial Enigma; 2) Enigma T; 3) Enigma G; 4) Unidentified; 5) Luftwaffe (Air Force) Enigma; 6) Heer (Army) Enigma; 7) Kriegsmarine (Naval) Enigma — M4.
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A selection of seven Enigma machines and paraphernalia exhibited at the USA's National Cryptologic Museum. From left to right, the models are: 1) Commercial Enigma; 2) Enigma T; 3) Enigma G; 4) Unidentified; 5) Luftwaffe (Air Force) Enigma; 6) Heer (Army) Enigma; 7) Kriegsmarine (Naval) Enigma — M4.

Commercial Enigma

Scherbius' Enigma patent — U.S. Patent  , granted in 1928
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Scherbius' Enigma patent — U.S. Patent  , granted in 1928

On February 23, 1918, German engineer Arthur Scherbius applied for a patent for a cipher machine using rotors, and, with E. Richard Ritter, founded the firm of Scherbius & Ritter. They approached the German Navy and Foreign Office with their design, but neither was interested. They then assigned the patent rights to Gewerkschaft Securitas, who founded the Chiffriermaschinen Aktien-Gesellschaft (Cipher Machines Stock Corporation) on 9 July 1923; Scherbius and Ritter were on the board of directors.

The Enigma logo
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The Enigma logo

Chiffriermaschinen AG began advertising a rotor machine — Enigma model A — which was exhibited at the Congress of the International Postal Union in 1923 and 1924. The machine was heavy and bulky, incorporating a typewriter. It measured 65×45×35 cm and weighed about 50 kg. A model B was introduced, and was of a similar construction.[7] While bearing the Enigma name, both models A and B were quite unlike later versions: they differed in physical size and shape, but also cryptographically, in that they lacked the reflector.

The reflector — an idea suggested by Scherbius' colleague Willi Korn — was first introduced in the Enigma C (1926) model. The reflector is a key feature of the Enigma machines.

A rare 8-rotor printing Enigma.
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A rare 8-rotor printing Enigma.

Model C was smaller and more portable than its predecessors. It lacked a typewriter, relying instead on the operator reading the lamps; hence the alternative name of "glowlamp Enigma" to distinguish from models A and B. The Enigma C quickly became extinct, giving way to the Enigma D (1927). This version was widely used, with examples going to Sweden, the Netherlands, United Kingdom, Japan, Italy, Spain, United States and Poland.

Military Enigma

The Navy was the first branch of the German military to adopt Enigma. This version, named Funkschlüssel C (Radio cipher C), had been put into production by 1925 and was introduced into service in 1926.[8] The keyboard and lampboard contained 29 letters — A-Z, Ä, Ö and Ü — which were arranged alphabetically, as opposed to the QWERTZU ordering.[9] The rotors had 28 contacts, with the letter X wired to bypass the rotors unencrypted.[10] Three rotors were chosen from a set of five[11] and the reflector could be inserted in one of four different positions, denoted α, β, γ and δ.[12] The machine was revised slightly in July 1933.[13]

By 15 July 1928,[14] the German Army (Reichswehr) had introduced their own version of the Enigma — the Enigma G, revised to the Enigma I by June 1930.[15] Enigma I is also known as the Wehrmacht, or Services Enigma, and was used extensively by the German military services and other government organisations (such as the railways[16]), both before and during World War II. The major difference between Enigma I and commercial Enigma models was the addition of a plugboard to swap pairs of letters, greatly increasing the cryptographic strength of the machine. Other differences included the use of a fixed reflector, and the relocation of the stepping notches from the rotor body to the movable letter rings[15] The Navy eventually agreed and in 1934[17] brought into service the Navy version of the Army Enigma, designated Funkschlüssel M or M3. While the Army used only three rotors at that time, for greater security the Navy specified a choice of three from a possible five.[18]

In December 1938, the Army issued two extra rotors so that the three rotors were chosen from a set of five.[15] In 1938, the Navy added two more rotors, and then another in 1939 to allow a choice of three rotors from a set of eight.[18] In August 1935, the Air Force also introduced the Wehrmacht Enigma for their communications.[15] A four-rotor Enigma was introduced by the Navy for U-boat traffic on 1 February 1942, called M4 (the network was known as Triton, or Shark to the Allies). The extra rotor was fitted in the same space by splitting the reflector into a combination of a thin reflector and a thin fourth rotor.

There was also a large, eight-rotor printing model, the Enigma II. During 1933, Polish codebreakers detected that it was in use for high-level military communications, but that it was soon withdrawn from use after it was found to be unreliable and jam frequently.[19]

Enigma G, used by the Abwehr, had four rotors, no plugboard, and multiple notches on the rotors.
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Enigma G, used by the Abwehr, had four rotors, no plugboard, and multiple notches on the rotors.

The Abwehr used the Enigma G (the Abwehr Enigma). This Enigma variant was a four-wheel unsteckered machine with multiple notches on the rotors. This model was equipped with a counter which incremented upon each key press, and so is also known as the counter machine or the Zählwerk Enigma.

The four-wheel Swiss Enigma K, made in Germany, used re-wired rotors.
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The four-wheel Swiss Enigma K, made in Germany, used re-wired rotors.

Other countries also used Enigma machines. The Italian Navy adopted the commercial Enigma as "Navy Cipher D"; the Spanish also used commercial Enigma during their Civil War. British codebreakers succeeded in breaking these machines, which lacked a plugboard. The Swiss used a version of Enigma called model K or Swiss K for military and diplomatic use, which was very similar to the commercial Enigma D. The machine was broken by a number of parties, including Poland, France, Britain and the United States (the latter codenamed it INDIGO). An Enigma T model (codenamed Tirpitz) was manufactured for use by the Japanese.

The Enigma wasn't perfect, especially after the Allies got hold of it, thus allowing the Allies to decode the German messages, which proved vital in the Battle of the Atlantic.

It has been estimated that 100,000 Enigma machines were constructed.[20] After the end of the Second World War, the Allies sold captured Enigma machines, still widely considered secure, to a number of developing countries.[20]

Surviving Enigmas

Enigma machine on display in Warsaw.
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Enigma machine on display in Warsaw.

The effort to break the Enigma was not disclosed until the 1970s. Since then, interest in the Enigma machine has grown considerably and a number of Enigmas are on public display in museums in the U.S. and Europe. The Deutsches Museum in Munich has both the three and four-wheel German military variants, as well as several older civilian versions. A functional Enigma is on display in the NSA's National Cryptologic Museum at Fort Meade, Maryland, where visitors can try their hand at encrypting messages and deciphering code. The Armémuseum in Stockholm in Sweden currently has an Enigma on display. There are also examples at the Computer History Museum in the United States, at Bletchley Park in the United Kingdom, at the Australian War Memorial, and in foyer of the Defence Signals Directorate, both located at Canberra in Australia, as well as a number of other locations in Germany, the U.S., the UK and elsewhere. The now-defunct San Diego Computer Museum had an Enigma in its collection, which has since been given to the San Diego State University Library. A number are also in private hands. Occasionally, Enigma machines are sold at auction; prices of US$20,000 are not unusual.[21][22]

Replicas of the machine are available in various forms, including an exact reconstructed copy of the Naval M4 model, an Enigma implemented in electronics (Enigma-E), various computer software simulators and paper-and-scissors analogues.

A rare Abwehr Enigma machine, designated G312, was stolen from the Bletchley Park museum on 1 April, 2000. In September, a man identifying himself as "The Master" sent a note demanding £25,000 and threatened to destroy the machine if the ransom was not paid. In early October 2000, Bletchley Park officials announced that they would pay the ransom but the stated deadline passed with no word from the blackmailer. Shortly afterwards the machine was sent anonymously to BBC journalist Jeremy Paxman, but three rotors were missing. In November 2000, an antiques dealer named Dennis Yates was arrested after telephoning The Sunday Times to arrange the return of the missing parts. The Enigma machine was returned to Bletchley Park after the incident. In October 2001, Yates was sentenced to ten months in prison after admitting handling the stolen machine and blackmailing Bletchley Park Trust director Christine Large, although he maintained that he was acting as an intermediary for a third party. Yates was released from prison after serving three months.

Enigma derivatives

The Enigma was influential in the field of cipher machine design, and a number of other rotor machines are derived from it. The British Typex was originally derived from the Enigma patents — Typex even includes features from the patent descriptions that were omitted from the actual Enigma machine. Owing to the need for secrecy about its cipher systems, no royalties were paid for the use of the patents by the British government. A Japanese Enigma clone was codenamed GREEN by American cryptographers. Little used, it contained four rotors mounted vertically. In the U.S., cryptologist William Friedman designed the M-325, a machine similar to Enigma in logical operation, although not in construction

A unique rotor machine was constructed in 2002 by Netherlands-based Tatjana van Vark.[23] This unusual device was inspired by Enigma but makes use of 40-point rotors, allowing letters, numbers and some punctuation to be used; each rotor contains 509 parts.[24]

The Japanese developed an Enigma clone, codenamed GREEN by American cryptographers, although it was little used.
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The Japanese developed an Enigma clone, codenamed GREEN by American cryptographers, although it was little used.
Tatjana van Vark's Enigma-inspired rotor machine, constructed in 2002. The rotors of this machine contain 40 contacts, compared to the original Enigma's 26.
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Tatjana van Vark's Enigma-inspired rotor machine, constructed in 2002. The rotors of this machine contain 40 contacts, compared to the original Enigma's 26.

Fiction

The play, Breaking the Code, by Hugh Whitemore is about the life and death of Alan Turing, who was the central force in breaking the Enigma in Britain during World War II. Turing was played by Derek Jacobi, who also played Turing in a 1996 television adaptation of the play. The television adaptation is generally available (though currently only on VHS). Although it is a drama and thus takes artistic license, it is nonetheless a fundamentally accurate account. It contains a two-minute, stutteringly-nervous speech by Jacobi that comes very close to encapsulating the entire Enigma codebreaking effort.

Robert Harris' 1996 novel Enigma is set against the backdrop of World War II Bletchley Park and cryptologists working to read Enigma. The book was made into the 2001 film, Enigma, directed by Michael Apted and starring Kate Winslet and Dougray Scott; the film has been criticized for many historical inaccuracies and neglecting the role of Biuro Szyfrów in breaking the Enigma code. An earlier Polish film dealing with the Polish aspects of the subject was the 1979 Sekret Enigmy (The Enigma Secret).[25]

Neal Stephenson's novel Cryptonomicon also features World War II military cryptography, including the Enigma and Bletchley Park. It takes considerable historical liberties.

The 1989 Doctor Who story The Curse of Fenric features British cryptographers, including a character based on Alan Turing, using a similar device called ULTIMA.

An interactive fiction game Jigsaw by Graham Nelson contains a puzzle in which the player must decrypt a message with a simplified version of the Enigma. The puzzle is generally accepted as the most annoying in the game, which is perhaps some measure of how hard it was to decrypt messages produced by the original machine(s).

Jonathan Mostow's 2000 film U-571 describes a fictional patrol by American submariners who have hijacked a German submarine to obtain an Enigma machine. The machine used in the film was an authentic Enigma obtained from a collector. The historical liberties taken are large, for the Polish breaks into Enigma (beginning in December 1932) did not require a captured machine, the Royal Navy captured several Enigmas or parts before the U.S. entered the war, and the U.S. capture of a U-boat occurred only days before D-Day in 1944. The film caused considerable protests when it was released in Britain, since it effectively transferred the exploits of the real life HMS Bulldog to a fictional American boat.

Friedrich Kittler's 1986 (trans. 1999) Gramophone, Film, Typewriter examines the use of the Enigma and similar devices in relation to the Symbolic order of Jacques Lacan.

Wolfgang Petersen's 1981 film Das Boot includes an Enigma machine which is evidently a four-rotor Kriegsmarine variant. It appears in many scenes which probably capture well the flavour of day-to-day Enigma use aboard a World War II U-Boat.

The Beast, the online puzzle-solving alternate reality game (ARG) created by a team at Microsoft to promote the Steven Spielberg film A.I.: Artificial Intelligence, required players to use an online Enigma simulator to solve one of the puzzles.

See also

Crypto_key.svg Cryptography Portal

World War II Era Encryption Devices:

"World War II Era Decryption:"

References

  • Bauer, 2000, p. 108, Bauer, 2000, p. 112 .
  • Hamer, David H.; Sullivan, Geoff; Weierud, Frode; Enigma Variations: an Extended Family of Machines; Cryptologia 22(3), July 1998. Online version (PDF).
  • Hinsley and Stripp, Alan; (eds.); Codebreakers: The Inside Story of Bletchley Park; 1993; pp. 83–88. Section by Alan; Stripp The Enigma Machine: Its Mechanism and Use
  • Kahn, David; Seizing the Enigma: The Race to Break the German U-Boats Codes, 1939-194; (1991)
  • Kozaczuk, Wladyslaw; The origins of the Enigma/ULTRA
  • Kruh, Louis; Deavours, Cipher; The Commercial Enigma: Beginnings of Machine Cryptography; Cryptologia, 26(1), pp. 1–16, 2002. Online version (PDF).
  • Marks, Philip; Weierud Frode; Recovering the Wiring of Enigma's Umkehrwalz A; Cryptologia 24(1), January 2000, pp55–66.
  • Ranshofen-Wertheimer, Egon; The German Enigma (Chapter V of "Victory is not enough")
  • Smith, Michael Station X; 4 books (macmillan) 1998; Paperback 2000; ISBN 0-7522-7148-2
  • Ulbricht, Heinz; Die Chiffriermaschine Enigma — Trügerische Sicherheit: Ein Beitrag zur Geschichte der Nachrichtendienste, PhD Thesis, 2005. Online version.(German)

Further reading

Wikimedia Commons has media related to:
  • Andy Carlson, About Enigma and Its Decryption
  • Christine Large, Hijacking Enigma, 2003, ISBN 0-470-86347-1.
  • Philip Marks, "Umkehrwalze D: Enigma's Rewirable Reflector — Part I", Cryptologia 25(2), April 2001, pp. 101–141.
  • Philip Marks, "Umkehrwalze D: Enigma's Rewirable Reflector — Part II", Cryptologia 25(3), July 2001, pp. 177–212.
  • Philip Marks, "Umkehrwalze D: Enigma's Rewirable Reflector — Part III", Cryptologia 25(4), October 2001, pp. 296–310.
  • Tom Perera, The Story of the ENIGMA: History, Technology and Deciphering, 2nd Edition, CD-ROM, 2004, Artifax Books, ISBN 1-890024-06-6 sample pages
  • Arturo Quirantes, "Model Z: A Numbers-Only Enigma Version", Cryptologia 28(2), April 2004.
  • Heinz Ulbricht, Enigma Uhr, Cryptologia, 23(3), April 1999, pp. 194–205
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