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| | The name of the author is Richard Eldridge but people always misspell of which. His day job is a supervisor but soon he'll be by himself. Playing croquet is one of the points he loves most. Ohio is where I've been living and my family loves it.<br><br>Feel free to visit my web site: [http://www.reddit.com/user/AbrahamMicah/ Resume] |
| [[File:EnigmaMachineLabeled.jpg|thumb|Military Enigma machine]]
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| {{EnigmaSeries}}
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| An '''Enigma machine''' was any of a family of related [[Electromechanics|electro-mechanical]] [[rotor machine|rotor cipher machines]] used in the twentieth century for [[enciphering]] and deciphering secret messages. Enigma was invented by the [[Germans|German]] engineer [[Arthur Scherbius]] at the end of [[World War I]].<ref>{{Cite book| last=Singh|first=Simon|author-link=Simon Singh|publication-date=1999|title=[[The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography]]|publication-place=London|publisher= Fourth Estate|page=127|isbn=1-85702-879-1}}</ref> Early models were used commercially from the early 1920s, and adopted by military and government services of several countries — most notably by [[Nazi Germany]] before and during [[World War II]].<ref>{{cite web | last = Lord | first = Bob | title = 1937 Enigma Manual by: Jasper Rosal - English Translation | year = 1998–2010 | url = http://www.ilord.com/enigma-manual1937-english.html | accessdate =31 May 2011 | ref = harv | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}</ref> Several different Enigma models were produced, but the [[Wehrmacht|German military]] models are the most commonly discussed.
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| German military texts enciphered on the Enigma machine were first broken by the [[Polish Cipher Bureau]], beginning in December 1932. This success was a result of efforts by three Polish [[cryptologist]]s, [[Marian Rejewski]], [[Jerzy Różycki]] and [[Henryk Zygalski]], working for Polish military intelligence. Rejewski "[[reverse engineered|reverse-engineered]]" the device, using [[theoretical mathematics]] and material supplied by French military intelligence. Subsequently the three mathematicians designed mechanical devices for breaking Enigma ciphers, including the [[Bomba (cryptography)|cryptologic bomb]]. From 1938 onwards, additional complexity was repeatedly added to the Enigma machines, making decryption more difficult and necessitating larger numbers of equipment and personnel—more than the Poles could readily produce.
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| On 25 July 1939, in [[Warsaw]], the Poles initiated French and British [[military intelligence]] representatives into their [[Cryptanalysis of the Enigma|Enigma-decryption techniques]] and equipment, including [[Zygalski sheets]] and the [[Bomba (cryptography)|cryptologic bomb]], and promised each delegation a Polish-reconstructed Enigma. The demonstration represented a vital basis for the later British continuation and effort.<ref>[[Gordon Welchman]], who became head of [[Hut 6]] at Bletchley Park, has written: "Hut 6 [[Ultra]] would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use." [[Gordon Welchman]], ''The Hut Six Story'', 1982, p. 289.</ref> During the war, British [[cryptography#Cryptanalysis|cryptologist]]s decrypted a vast number of messages enciphered on Enigma. The [[Military intelligence|intelligence]] gleaned from this source, codenamed "[[Ultra]]" by the British, was a substantial aid to the [[Allies of World War II|Allied]] war effort.<ref>Much of the German cipher traffic was encrypted on the Enigma machine, hence the term "Ultra" has often been used almost synonymously with "[[Cryptanalysis of the Enigma|Enigma decrypts]]". However, Ultra also encompassed decrypts of the German [[Lorenz cipher|Lorenz SZ 40 and 42 machines]] that were used by the German High Command, and decrypts of [[C-36 (cipher machine)|Hagelin ciphers]] and of other Italian ciphers and codes, as well as of Japanese ciphers and codes such as [[Purple (cipher machine)|Purple]] and [[JN-25]].</ref>
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| Though Enigma had some cryptographic weaknesses, in practice it was German procedural flaws, operator mistakes, laziness, failure to systematically introduce changes in encipherment procedures, and Allied capture of key tables and hardware that, during the war, enabled Allied cryptologists to succeed.{{sfn|Kahn|1991}}{{sfn|Stripp|1993}}
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| The exact influence of Ultra on the course of the war is debated; an oft-repeated assessment is that decryption of German ciphers advanced the [[Victory in Europe Day|end of the European war]] by two years.{{sfn|Kahn|1991}}<ref name="engima_cryptographic_mathematics">{{Cite journal|url= http://www.nsa.gov/about/_files/cryptologic_heritage/publications/wwii/engima_cryptographic_mathematics.pdf|title=The Cryptographic Mathematics of Enigma|last= Miller|first=A. Ray|publisher=National Security Agency|year=2001|postscript=<!--None-->|ref= harv}}</ref><ref>[[Bletchley Park]] veteran and historian [[Harry Hinsley|F.H. Hinsley]] is often cited as an authority for the two-year estimate, yet his assessment in ''Codebreakers'' is much less definitive: "Would the [[Soviet Union|Soviets]] meanwhile have defeated [[Germany]], or Germany the Soviets, or would there have been stalemate on the eastern fronts? What would have been decided about the [[atom bomb]]? Not even [[Counter-factual history|counter-factual historians]] can answer such questions. They are questions which do not arise, because the war went as it did. But those historians who are concerned only with the war as it was must ask why it went as it did. And they need venture only a reasonable distance beyond the facts to recognise the extent to which the explanation lies in the influence of Ultra." [[Harry Hinsley|F.H. Hinsley]], "Introduction: The Influence of Ultra in the Second World War," ''Codebreakers: The Inside Story of Bletchley Park'', edited by F.H. Hinsley and Alan Stripp, Oxford University Press, 1993, pp. 12–13.</ref> [[Winston Churchill]] told the United Kingdom's King [[George VI]] after World War II: "It was thanks to Ultra that we won the war."<ref>{{cite web|url=http://www.history.co.uk/explore-history/ww2/code-breaking.html |title=Code Breaking – World War 2 on History |publisher=History.co.uk |date= |accessdate=2012-07-17}}</ref>
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| {{toclimit|3}}
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| ==Design==
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| [[File:Bundesarchiv Bild 183-2007-0705-502, Chiffriermaschine "Enigma".jpg|thumb|upright|Enigma in use, 1943]]
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| Like other rotor machines, the Enigma machine is a combination of mechanical and electrical subsystems. The mechanical subsystem consists of a [[alphanumeric keyboard|keyboard]]; a set of rotating disks called ''rotors'' arranged adjacently along a [[axle|spindle]]; and one of various stepping components to turn one or more rotor with each key press.
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| ===Electrical pathway===
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| [[File:Enigma wiring kleur.svg|thumb|left|upright=1.3|Enigma wiring diagram with arrows and the numbers 1 to 9 showing how current flows from key depression to a lamp being lit. The ''A'' key is encoded to the ''D'' lamp. D yields A, but A never yields A; this property was due to a patented feature unique to the Enigmas, and could be exploited by cryptanalysts in some situations.]]
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| The mechanical parts act in such a way as to form a varying [[electrical network|electrical circuit]]. When a key is pressed, a circuit is completed. Current flows through various components in their current configuration, ultimately lighting one display [[lamp (electrical component)|lamp]], revealing an output letter. For example, when encrypting a message starting ''ANX...'', the operator would first press the ''A'' key, and the ''Z'' lamp might light, so ''Z'' would be the first letter of the [[ciphertext]]. The operator would next press ''N'', and then ''X'' in the same fashion, and so on.
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| The detailed operation of Enigma is shown in the wiring diagram to the left. To simplify the example, only four components of a complete Enigma machine are shown. In reality, there are 26 lamps and keys, rotor wirings inside the rotors (of which there are either three or four) and between six and ten plug leads.
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| [[Image:Enigma-action.svg|thumb|upright|The scrambling action of Enigma's rotors is shown for two consecutive letters with the right-hand rotor moving one position between them.]]
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| Current flowed from the battery (1) through a depressed bi-directional keyboard switch (2) to the plugboard (3). Next, it passed through the (unused in this instance, so shown closed) plug "A" (3) via the entry wheel (4), through the wiring of the three (Wehrmacht Enigma) or four (''[[Kriegsmarine]]'' M4 and ''Abwehr'' variants) installed rotors (5), and entered the reflector (6). The reflector returned the current, via an entirely different path, back through the rotors (5) and entry wheel (4), proceeding through plug "S" (7) connected with a cable (8) to plug "D", and another bi-directional switch (9) to light the appropriate lamp.<ref name="Rijmenants">Rijmenants, Dirk; [http://users.telenet.be/d.rijmenants/en/enigmatech.htm Technical details of the Enigma machine] Cipher Machines & Cryptology</ref>
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| The repeated changes of electrical path through an Enigma scrambler implemented a [[polyalphabetic cipher|polyalphabetic substitution cipher]] that provided Enigma's security. The diagram on the right shows how the electrical pathway changed with each key depression, which caused rotation of at least the right-hand rotor. Current passed into the set of rotors, into and back out of the reflector, and out through the rotors again. The greyed-out lines are other possible paths within each rotor; these are hard-wired from one side of each rotor to the other. The 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. Eventually other rotors step with a key press.
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| ===Rotors===
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| [[File:Enigma rotors with alphabet rings.jpg|thumb|Enigma rotor assembly. In the Wehrmacht Enigma, the three installed movable rotors are sandwiched between two fixed wheels: the entry wheel, on the right, and the reflector on the left.]]
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| {{Main|Enigma rotor details}}
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| The rotors (alternatively ''wheels'' or ''drums'', ''Walzen'' in German) formed the heart of an Enigma machine. Each rotor was a disc approximately {{convert|10|cm|in|abbr=on}} in diameter made from hard [[rubber]] or [[bakelite]] with [[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 this description). When the rotors were mounted side-by-side on the spindle, the pins of one rotor rested against the contacts of the neighbouring rotor, forming an electrical connection. Inside the body of the rotor, 26 wires connected each pin on one side to a contact on the other in a complex pattern. Most of the rotors were identified by Roman numerals, and each issued copy of rotor I was wired identically to all others. The same was true for the special thin beta and gamma rotors used in the M4 naval variant.
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| [[Image:enigma-rotors.jpg|thumb|left|Three Enigma rotors and the shaft, on which they are placed when in use.]]
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| 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, and so on. Enigma's security came from using several rotors in series (usually three or four) and the regular stepping movement of the rotors, thus implementing a polyalphabetic substitution cipher.
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| When placed in an Enigma, each rotor can be set to one of 26 possible positions. When inserted, it can be turned by hand using the grooved finger-wheel, which protrudes from the internal Enigma cover when closed. So that the operator can know the rotor's position, each had an ''alphabet tyre'' (or letter ring) attached to the outside of the rotor disk, with 26 characters (typically letters); one of these could be seen through the window, thus indicating the rotational position of the rotor. In early models, the alphabet ring was fixed to the rotor disk. A later improvement was the ability to adjust the alphabet ring relative to the rotor disk. The position of the ring was known as the ''Ringstellung'' ("ring setting"), and was a part of the initial setting prior to an operating session. In modern terms it was a part of the [[initialization vector]].
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| [[File:Enigma rotors and spindle showing contacts rachet and notch.jpg|thumb|left|Two Enigma rotors showing electrical contacts, stepping ratchet (on the left) and notch (on the right-hand rotor opposite '''D''').]]
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| Each rotor contained a notch (or more than one) that controlled rotor stepping. In the military variants, the notches are located on the alphabet ring.
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| The Army and Air Force Enigmas were used with several rotors, initially three. On 15 December 1938, this changed to five, from which three were chosen for a given session. Rotors 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 variation was probably intended as a security measure, but ultimately allowed the Polish [[Clock (cryptography)|Clock Method]] and British [[Banburismus]] attacks.
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| 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 marked VI, VII and VIII, all with different wiring, and had two notches, resulting in 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 one and by adding a thin fourth rotor. That fourth rotor was one of two types, ''Beta'' or ''Gamma'', and never stepped, but could be manually set to any of 26 positions. One of the 26 made the machine perform identically to the three-rotor machine.
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| ===Stepping===
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| To avoid merely implementing a simple (and easily breakable) substitution cipher, every key press caused one or more rotors to step by one twenty-sixth of a full rotation, before the electrical connections were made. This changed the substitution alphabet used for encryption, ensuring that the cryptographic substitution was different at each new rotor position, producing a more formidable polyalphabetic substitution cipher. The stepping mechanism varied slightly from model to model. The right-hand rotor stepped once with each keystroke, and other rotors stepped less frequently.
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| ===Turnover===
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| [[Image:Enigma ratchet.png|thumb|The Enigma stepping motion seen from the side away from the operator. All three ratchet pawls (green) push in unison as a key is depressed. For the first rotor (1), which to the operator is the right-hand rotor, the ratchet (red) is always engaged, and steps with each keypress. Here, the middle rotor (2) is engaged because the notch in the first rotor is aligned with the pawl; it will step (''turn over'') with the first rotor. The third rotor (3) is not engaged, because the notch in the second rotor is not aligned to the pawl, so it will not engage with the rachet.]]
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| The advancement of a rotor other than the left-hand one was called a ''turnover'' by the British. This was achieved by a [[ratchet and pawl]] mechanism. Each rotor had a ratchet with 26 teeth and every time a key was pressed, the set of spring-loaded pawls moved forward in unison, trying to engage with a ratchet. The alphabet ring of the rotor to the right normally prevented this. As this ring rotated with its rotor, a notch machined into it would eventually align itself with the pawl, allowing it to engage with the ratchet, and advance the rotor on its left. The right-hand pawl, having no rotor and ring to its right, stepped its rotor with every key depression.<ref name = "doublestepping"/> For a single-notch rotor in the right-hand position, the middle rotor stepped once for every 26 steps of the right-hand rotor. Similarly for rotors two and three. For a two-notch rotor, the rotor to its left would turn over twice for each rotation.
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| The first five rotors to be introduced (I–V) contained one notch each, while the additional naval rotors VI, VII and VIII each had two notches. The position of the notch on each rotor was determined by the letter ring which could be adjusted in relation to the core containing the interconnections. The points on the rings at which they caused the next wheel to move were as follows.<ref>{{cite web| last=Sale|first=Tony|authorlink=Anthony Sale|title=Technical specifications of the Enigma rotors| work=Technical Specification of the Enigma|url=http://www.codesandciphers.org.uk/enigma/rotorspec.htm|accessdate=15 November 2009}}</ref>
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| {|class="wikitable"|border=1|style="margin: 1em auto 1em auto"
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| |+ Position of turnover notches
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| |-
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| ! style="width:130pt;"| Rotor
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| ! style="width:130pt;"| Turnover position(s)
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| ! style="width:130pt;"| BP mnemonic
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| |- style="text-align:center;"
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| ||I|| style="text-align:center;"|R|| style="text-align:center;"|Royal
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| |- style="text-align:center;"
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| ||II|| style="text-align:center;"|F|| style="text-align:center;"|Flags
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| |- style="text-align:center;"
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| ||III|| style="text-align:center;"|W|| style="text-align:center;"|Wave
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| |- style="text-align:center;"
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| ||IV|| style="text-align:center;"|K|| style="text-align:center;"|Kings
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| |- style="text-align:center;"
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| ||V|| style="text-align:center;"|A|| style="text-align:center;"|Above
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| |-
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| | style="text-align:center;"|VI, VII and VIII|| style="text-align:center;"|A and N|||
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| |}
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| The design also included a feature known as ''double-stepping''. This occurred when each pawl aligned with both the ratchet of its rotor and the rotating notched ring of the neighbouring rotor. If a pawl engaged with a ratchet through alignment with a notch, as it moved forward it pushed against both the ratchet and the notch, advancing both rotors. In a three-rotor machine, double-stepping affected rotor two only. If in moving forward the ratchet of rotor three was engaged, rotor two would move again on the subsequent keystroke, resulting in two consecutive steps. Rotor two also pushes rotor one forward after 26 steps, but since rotor one moves forward with every keystroke anyway, there is no double-stepping.<ref name="doublestepping">David Hamer, "Enigma: Actions Involved in the 'Double-Stepping' of the Middle Rotor", ''Cryptologia'', 21(1), January 1997, pp. 47–50, [http://web.archive.org/web/20110719081659/http://www.eclipse.net/~dhamer/downloads/rotorpdf.zip Download (zipped PDF)]</ref> This double-stepping caused the rotors to deviate from [[odometer]]-style regular motion.
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| <!--{|
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| |AFU
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| 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 × 26 × 26, because of double-stepping).<ref name="doublestepping" /> Historically, messages were limited to a few hundred letters, and so there was no chance of repeating any combined rotor position during a single session, denying cryptanalysts valuable clues.
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| To make room for the Naval fourth rotors, the reflector was made much thinner. The fourth rotor fit into the space made available. No other changes were made, which eased the changeover. Since there were only three pawls, the fourth rotor never stepped, but could be manually set into one of 26 possible positions.
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| A device that was designed, but not implemented before the war's end, was the ''Lückenfüllerwalze'' (gap-fill wheel) that implemented irregular stepping. It allowed field configuration of notches in all 26 positions. If the number of notches was a relative [[Prime number|prime]] of 26 and the number of notches were different for each wheel, the stepping would be more unpredictable. Like the Umkehrwalze-D it also allowed the internal wiring to be reconfigured.<ref>{{cite web|url=http://www.cryptomuseum.com/crypto/enigma/lf/index.htm |title=Lückenfüllerwalze |publisher=Cryptomuseum.com |date= |accessdate=2012-07-17}}</ref>{{-}}
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| ===Entry wheel===
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| The current entry wheel (''Eintrittswalze'' in German), or entry [[stator]], connects the [[plugboard]] to the rotor assembly. If the plugboard is not present, the entry wheel instead connects the keyboard and lampboard to the rotor assembly. While the exact wiring used is of comparatively little importance to security, it proved an obstacle to Rejewski's progress during his study of the rotor wirings. The commercial Enigma connects the keys in the order of their sequence on the keyboard: ''Q''<math>\rightarrow</math>''A'', ''W''<math>\rightarrow</math>''B'', ''E''<math>\rightarrow</math>''C'' and so on. However, the military Enigma connects them in straight alphabetical order: ''A''<math>\rightarrow</math>''A'', ''B''<math>\rightarrow</math>''B'', ''C''<math>\rightarrow</math>''C'', and so on. It took inspired guesswork for Rejewski to penetrate the modification.
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| ===Reflector===
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| With the exception of models '''A''' and '''B''', the last rotor came before a ''reflector'' (German: ''Umkehrwalze'', meaning ''reversal rotor''), a patented feature unique to Enigma among the period's various rotor machines. 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 [[Involution (mathematics)|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.
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| In 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.
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| 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]].<ref name="ukwd-1">Philip Marks, "Umkehrwalze D: Enigma's Rewirable Reflector — Part I", Cryptologia 25(2), April 2001, pp. 101–141</ref> 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.{{-}}
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| ===Plugboard===
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| [[Image:Enigma-plugboard.jpg|right|thumbnail|The plugboard (''Steckerbrett'') was positioned at the front of the machine, below the keys. When in use during World War II, there were ten connections. In this photograph, just two pairs of letters have been swapped (A↔J and S↔O).]]
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| 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. The plugboard contributed more cryptographic strength than an extra rotor. Enigma without a plugboard (known as ''unsteckered Enigma'') can be solved relatively straightforwardly using hand methods; these techniques are generally defeated by the plugboard, driving Allied cryptanalysts to special machines to solve it.
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| A cable placed onto the plugboard connected letters 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. Up to 13 steckered pairs might be used at one time, although only 10 were normally used.
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| Current flowed from the keyboard through the plugboard, and proceeded to the entry-rotor or ''Eintrittswalze''. Each letter on the plugboard had two jacks. Inserting a plug disconnected 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.
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| ===Accessories===
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| [[Image:Enigma-printer-2.jpg|left|thumbnail|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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| [[Image:Enigma-uhr-box.jpg|right|thumbnail|upright|The Enigma Uhr attachment]]
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| Other features made various Enigma machines more secure or more convenient.<ref>{{cite web | last = Reuvers | first = Paul | title = Enigma accessories |year = 2008 | url = http://www.jproc.ca/crypto/enigma_acc.html | accessdate =22 July 2010 | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. --> }}</ref>
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| Some M4 Enigmas used the ''Schreibmax'', a small [[Computer printer|printer]] that could print the 26 letters on a narrow paper ribbon. This eliminated the need for a second operator to read the lamps and transcribe the letters. 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 light bulbs had to be removed. It improved both convenience and operational security; the printer could be installed remotely such that the signal officer operating the machine no longer had to see the decrypted [[plaintext]].
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| Another accessory was the remote lamp panel ''Fernlesegerät''. For machines equipped with the extra panel, the wooden case of the Enigma was wider and could store the extra panel. A lamp panel version could be connected afterwards, but that required, as with the ''Schreibmax'', that the lamp panel and lightbulbs be removed.<ref name="Rijmenants"/> The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it.
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| In 1944, the ''Luftwaffe'' introduced a plugboard switch, called the ''Uhr'' (clock), a small box containing a switch with 40 positions. It replaced the standard plugs. After connecting the plugs, as determined in the daily key sheet, the operator turned the switch into one of the 40 positions, each producing a different combination of plug wiring. Most of these plug connections were, unlike the default plugs, not pair-wise.<ref name="Rijmenants"/> In one switch position, the ''Uhr'' did not swap letters, but simply emulated the 13 stecker wires with plugs.
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| === Mathematical analysis ===
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| The Enigma transformation for each letter can be specified mathematically as a product of [[permutation]]s.{{sfn|Rejewski|1980}} Assuming a three-rotor German Army/Air Force Enigma, let <math>P</math> denote the plugboard transformation, <math>U</math> denote that of the reflector, and <math>L, M, R</math> denote those of the left, middle and right rotors respectively. Then the encryption <math>E</math> can be expressed as
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| :<math>E = PRMLUL^{-1}M^{-1}R^{-1}P^{-1}</math>.
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| After each key press, the rotors turn, changing the transformation. For example, if the right-hand rotor <math>R</math> is rotated <math>i</math> positions, the transformation becomes <math>\rho^iR\rho^{-i}</math>, where <math>\rho</math> 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 <math>j</math> and <math>k</math> rotations of <math>M</math> and <math>L</math>. The encryption transformation can then be described as
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| :<math>E = P(\rho^iR\rho^{-i})(\rho^{j}M\rho^{-j})(\rho^{k}L\rho^{-k})U(\rho^kL^{-1}\rho^{-k})(\rho^{j}M^{-1}\rho^{-j})(\rho^{i}R^{-1}\rho^{-i})P^{-1}</math>.
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| Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (158 [[quintillion]]) different settings.<ref>{{youtube|id=G2_Q9FoD-oQ|title=158,962,555,217,826,360,000 - Numberphile}}</ref>
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| ==Operation==
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| [[Image:Kenngruppenheft.jpg|thumb|German Kenngruppenheft (a U-boat [[codebook]] with grouped key codes)]]In use, the Enigma required a list of daily key settings and auxiliary documents. The procedures for German Naval Enigma were more elaborate and more secure than those in other services. Navy [[codebook]]s were printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were endangered.
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| In German military practice, communications were divided into separate networks, each using different settings. These communication nets were termed ''keys'' at [[Bletchley Park]], and were assigned [[code name]]s, such as ''Red'', ''Chaffinch'', and ''Shark''. Each unit operating in 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 configure their Enigma in the same way; rotor selection and order, starting position and plugboard connections must be identical. All these settings (together the [[key (cryptography)|key]] in modern terms) were established beforehand, distributed in [[codebook]]s.
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| An Enigma machine's initial state, the [[Key (cryptography)|cryptographic key]], has several aspects:
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| * Wheel order (''Walzenlage'') – the choice of rotors and the order in which they are fitted.
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| * Initial position of the rotors – chosen by the operator, different for each message.
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| * Ring settings (''Ringstellung'') – the position of the alphabet ring relative to the rotor wiring.
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| * Plug connections (''Steckerverbindungen'') – the connections of the plugs in the plugboard.
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| * In very late versions, the wiring of the reconfigurable reflector.
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| Note that although the ''ringstellung'' was a required part of the setup, they did not affect encryption because the rotors were positioned independently of the rings. The ring settings were only necessary to determine the initial rotor position based on the ''message setting'' that was transmitted at the beginning of a message, as described in the "Indicators" section, below. Once the receiver's rotors were set to the indicated positions, the ring settings no longer played any role.
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| In modern cryptographic language, the ring settings did not actually contribute [[Information entropy|entropy]] to the key used for encrypting the message. Rather, the ring settings were part of a separate key (along with the rest of the setup such as wheel order and plug settings) used to encrypt an ''initialization vector'' for the message. The session key consisted of the complete setup ''except for'' the ring settings, plus the initial rotor positions chosen arbitrarily by the sender (the ''message setting''). The important part of this session key was the rotor positions, not the ring positions. However, by ''encoding'' the rotor position into the ring position using the ring settings, additional variability was added to the encryption of the initialization vector.
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| Enigma was designed to be secure even if the rotor wiring was known to an opponent, although in practice considerable effort protected the wiring configuration. If the wiring is secret, the total number of possible configurations has been calculated to be around 10<sup>114</sup> (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around 10<sup>23</sup> (76 bits).<ref name="engima_cryptographic_mathematics"/> 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 a [[brute force attack]].
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| ===Indicator===
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| Most of the key was kept constant for a set time period, typically a day. However, a different initial rotor position was used for each message, a concept similar to an [[Initialization vector|initialisation vector]] in modern cryptography. The reason is that encrypting many messages with identical or near-identical settings (termed in cryptanalysis as being ''in depth''), would enable an attack using a statistical procedure such as [[William F. Friedman|Friedman's]] [[Index of coincidence]].<ref>{{cite book|last=Friedman| first=W.F.|authorlink=William F. Friedman|title=The index of coincidence and its applications in cryptology|series=Department of Ciphers. Publ 22|publisher=Riverbank Laboratories|location=Geneva, Illinois, USA|oclc=55786052|year=1922}}</ref> The starting position for the rotors was transmitted just before the ciphertext, usually after having been enciphered. The exact method used was termed the ''indicator procedure''. Design weakness and operator sloppiness in these indicator procedures were two of the main weakness that made cracking Enigma possible.
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| [[Image:Enigma-rotor-windows.jpg|left|thumbnail|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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| 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 (the ''Grundstellung'', meaning ''ground setting''), say, ''AOH''. 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 these 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.
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| 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. After moving his rotors to ''EIN'', the receiving operator then typed in the rest of the ciphertext, deciphering the message.
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| 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 procedure.
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| During World War II, codebooks were only used each day to set up the rotors, their ring settings and the plugboard. For each message, the operator selected a random start position, let's say ''WZA'', and a 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 to 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.<ref>Rijmenants, Dirk; [http://users.telenet.be/d.rijmenants/en/enigmaproc.htm Enigma message procedures] Cipher Machines & Cryptology</ref>
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| 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 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, for example, 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.<ref>Rijmenants, Dirk; [http://users.telenet.be/d.rijmenants/en/kurzsignale.htm Kurzsignalen on German U-boats] Cipher Machines & Cryptology</ref>
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| ===Additional details===
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| The Army Enigma machine used only the 26 alphabet characters. Signs were replaced with rare character combinations. A space was omitted or replaced with an X. The X was generally used as point or full-stop.
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| Some signs were different in other parts of the armed forces. The ''Wehrmacht'' replaced a comma with ZZ and the question sign with FRAGE or FRAQ.
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| The ''Kriegsmarine'' replaced the comma with Y and the question sign with UD. The combination CH, as in "Acht" (eight) or "Richtung" (direction), was replaced with Q (AQT, RIQTUNG). Two, three and four zeros were replaced with CENTA, MILLE and MYRIA.
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| The ''Wehrmacht'' and the ''Luftwaffe'' transmitted messages in groups of five characters.
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| The ''Kriegsmarine'', using the four rotor Enigma, had four-character groups. Frequently used names or words were varied as much as possible. Words like ''Minensuchboot'' (minesweeper) could be written as MINENSUCHBOOT, MINBOOT, MMMBOOT or MMM354. To make cryptanalysis harder, messages were limited to 250 characters. Longer messages were divided into several parts, each using a different message key.<ref>{{cite web|url=http://www.codesandciphers.org.uk/documents/egenproc/eniggnix.htm|title=The translated 1940 ''Enigma General Procedure''|publisher=codesandciphers.org.uk|accessdate=16 October 2006}}</ref><ref>{{cite web|url=http://www.codesandciphers.org.uk/documents/officer/officerx.htm|title=The translated 1940 ''Enigma Officer and Staff Procedure''| publisher=codesandciphers.org.uk|accessdate=16 October 2006}}</ref>{{-}}
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| == History ==
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| The Enigma family included multiple designs. The earliest were commercial models dating from the early 1920s. Starting in the mid-1920s, the German military began to use Enigma, making a number of security-related changes. Various nations either adopted or adapted the design for their own cipher machines.
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| {|style="margin: 1em auto 0 auto;"
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| |-
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| |[[Image:Enigmas.jpg|upright=2.0|thumbnail|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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| |}
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| ===Commercial Enigma===
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| [[Image:Scherbius-1928-patent.png|thumb|Scherbius's Enigma patent—{{US patent|1657411}}, granted in 1928.]]
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| On 23 February 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.
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| Chiffriermaschinen AG began advertising a rotor machine — ''Enigma model A'' — which was exhibited at the Congress of the [[Universal Postal Union|International Postal Union]] in 1923-1924. The machine was heavy and bulky, incorporating a [[typewriter]]. It measured 65×45×35 cm and weighed about {{convert|50|kg|lb|}}.
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| [[Image:Enigma-8-rotor.jpg|right|thumbnail|A rare 8-rotor printing Enigma.]]
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| In 1925 Enigma ''model B'' was introduced, and was of a similar construction.<ref>{{cite web|url=http://www.armyradio.com/publish/Articles/The_Enigma_Code_Breach/Pictures/enigma_type_b.jpg|title=image of Enigma Type B}}</ref> 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.
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| The reflector — suggested by Scherbius's colleague [[Willi Korn]] — was introduced in ''Enigma C'' (1926).
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| ''Model C'' was smaller and more portable than its predecessors. It lacked a typewriter, relying on the operator; hence the informal name of "glowlamp Enigma" to distinguish it from models ''A'' and ''B''.
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| The ''Enigma C'' quickly gave way to ''Enigma D'' (1927). This version was widely used, with shipments to Sweden, the Netherlands, United Kingdom, Japan, Italy, Spain, United States and Poland.
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| {{-}}
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| ===Military Enigma===
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| [[Image:Bundesarchiv Bild 101I-241-2173-09, Russland, Verschlüsselungsgerät Enigma.jpg|thumb|Enigma in use on the Russian front]]
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| The Navy was the first military branch 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.{{sfn|Kahn|1991|pp=39–41, 299}}
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| The keyboard and lampboard contained 29 letters—A-Z, Ä, Ö and Ü—which were arranged alphabetically, as opposed to the QWERTZU ordering.{{sfn|Ulbricht|2005|p=4}} The rotors had 28 contacts, with the letter ''X'' wired to bypass the rotors unencrypted.{{sfn|Stripp|1993}}
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| Three rotors were chosen from a set of five{{sfn|Kahn|1991|pp=40, 299}} and the reflector could be inserted in one of four different positions, denoted α, β, γ and δ.{{sfn|Bauer|2000|p=108}} The machine was revised slightly in July 1933.{{sfn|Stripp|1993|loc=plate 3}}
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| By 15 July 1928,{{sfn|Kahn|1991|pp=41, 299}} the German Army (''[[Reichswehr]]'') had introduced their own version of the Enigma—the ''Enigma G'', revised to the ''Enigma I'' by June 1930.{{sfn|Kruh|Deavours|2002|p=97}} Enigma I is also known as the ''Wehrmacht'', or "Services" Enigma, and was used extensively by German military services and other government organisations (such as the [[Deutsche Reichsbahn-Gesellschaft|railways]]<ref>Michael Smith ''Station X'', Channel Four books (Macmillan) 1998, Paperback 2000, ISBN 0-7522-7148-2, Page 73</ref>), before and during [[World War II]].
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| The major difference between ''Enigma I'' and commercial Enigma models was the addition of a plugboard to swap pairs of letters, greatly increasing cryptographic strength. 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. The machine measured 28×34×15 cm (11 in×13.5 in×6 in) and weighed around {{convert|12|kg|lb|abbr=on}}.<ref name="Stripp">Stripp, 1993</ref>
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| By 1930, the Army had suggested that the Navy adopt their machine, citing the benefits of increased security (with the plugboard) and easier interservice communications.{{sfn|Kahn|1991|p=43}} The Navy eventually agreed and in 1934<ref>{{harvnb|Kahn|1991|p=43}} says August 1934. {{harvnb|Kruh|Deavours|2002|p=15}} say October 2004.</ref> brought into service the Navy version of the Army Enigma, designated ''Funkschlüssel'' ' or ''M3''. While the Army used only three rotors at that time, the Navy specified a choice of three from a possible five.{{sfn|Kruh|Deavours|2002|p=98}}
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| [[File:Bundesarchiv Bild 101I-769-0229-10A, Frankreich, Guderian, "Enigma" croppped.jpg|thumb|200px|[[Heinz Guderian]] in the [[Battle of France]], with an Enigma machine]]
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| In December 1938, the Army issued two extra rotors so that the three rotors were chosen from a set of five.{{sfn|Kruh|Deavours|2002|p=97}} 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.{{sfn|Kruh|Deavours|2002|p=98}} In August 1935, the Air Force introduced the Wehrmacht Enigma for their communications.{{sfn|Kruh|Deavours|2002|p=97}}
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| 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.
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| There was also a large, eight-rotor printing model, the ''Enigma II''. In 1933 the [[Polish Cipher Bureau]] detected that it was in use for high-level military communications, but that it was soon withdrawn, as it was unreliable and jammed frequently.{{sfn|Kozaczuk|1984|p=28}}
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| 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.
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| During World War II the Abwehr used these machines to control and report the locations of submarines in the Atlantic and to pass information about bombing raids, the movement of military units, and the location and cargo of military supply ships. Before Enigma Britain was in danger of being starved into submission and after it the roles were virtually reversed. The British moved one step ahead of the Germans and began sinking submarines faster than they could be built.<ref>{{cite journal|last=Adamy|first=Dave|title=Bletchley Park|journal=Journal of Electronic Defense|date=July 2003|page=16|ref=harv}}</ref>
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| ====Other countries====
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| Other countries used Enigma machines. The Italian Navy adopted the commercial Enigma as "Navy Cipher D". The Spanish also used commercial Enigma during their [[Spanish Civil War|Civil War]]. British codebreakers succeeded in breaking these machines, which lacked a plugboard.{{sfn|Smith|2006|p=23}} Not only militaries used the Enigma, they were also used by diplomatic services.
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| The Swiss used a version of Enigma called ''model K'' or ''Swiss K'' for military and diplomatic use, which was very similar to commercial Enigma D. The machine was cracked by Poland, France, the United Kingdom and the United States (the latter codenamed it INDIGO). An ''Enigma T'' model (codenamed ''Tirpitz'') was used by Japan.
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| An estimated 100,000 Enigma machines were constructed. After the end of World War II, the Allies sold captured Enigma machines, still widely considered secure, to a number of developing countries.{{sfn|Bauer|2000|p=112}} As these countries did not know that the machine had been broken, their supposedly secure communications were in fact being read regularly by the major Western intelligence agencies.
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| <center><gallery perrow="3">
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| File:Enigma-G.jpg|Enigma G, used by the ''[[Abwehr]]'', had four rotors, no plugboard, and multiple notches on the rotors.
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| File:Enigma-IMG 0484-black.jpg|The Enigma-K used by the Swiss Army sported three rotors and a reflector, and no plugboard. It was made in Germany, but had locally re-wired rotors and an additional lamp panel.
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| File:four-rotor-enigma.jpg|An Enigma model T (Tirpitz)—a modified commercial Enigma K manufactured for use by the Japanese.
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| File:Enigma Decoder Machine.jpg|An Enigma machine in the UK's Imperial War Museum
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| File:Bundesarchiv Bild 101I-241-2173-06, Russland, Verschlüsselungsgerät Enigma.jpg|Enigma in use in Russia (image Bundesarchiv)
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| File:Bundesarchiv Bild 146-2006-0188, Verschlüsselungsgerät "Enigma".jpg|Enigma
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| </gallery></center>
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| ==Breaking Enigma==
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| {{Main|Cryptanalysis of the Enigma}}
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| ==Surviving machines==
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| [[Image:US M1 enigma analog 3.jpg|thumb|US Enigma replica on display at the [[National Cryptologic Museum]] in Fort Meade, Maryland, USA.]]
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| [[File:Kriegsmarine Enigma.png|thumb|A four–rotor ''[[Kriegsmarine]]'' (German Navy, 1935 to 1945) Enigma machine on display at the US National Cryptologic Museum]]
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| The effort to break the Enigma was not disclosed until the 1970s. Since then, interest in the Enigma machine has grown. Enigmas are on public display in museums around the world.
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| The [[Deutsches Museum]] in [[Munich]] has both the three- and four-rotor German military variants, as well as several civilian versions. Enigma machines are exhibited at the National Codes Centre in [[Bletchley Park]], the [[Government Communications Headquarters]], the [[Science Museum (London)|Science Museum]] in [[London]], the [[Polish Institute and Sikorski Museum]] in London, the [[Polish Army Museum]] in Warsaw, the ''[[Swedish Army Museum|Armémuseum]]'' (Swedish Army Museum) in [[Stockholm]], the National Signals Museum in [[Finland]], and at the [[Australian War Memorial]] and in the foyer of the [[Defence Signals Directorate]], both in [[Canberra]], Australia.
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| In the United States, Enigma machines can be seen at the [[Computer History Museum]] in [[Mountain View, California]], and at the [[National Security Agency|National Security Agency's]] [[National Cryptologic Museum]] in [[Fort George G. Meade|Fort Meade]], Maryland, where visitors can try their hand at enciphering and deciphering messages. Two machines that were acquired after the capture of {{Ship|German submarine|U-505||2}} during World War II are on display at the [[Museum of Science and Industry (Chicago)|Museum of Science and Industry]] in [[Chicago]], Illinois. The [[San Diego State University]] Library has a machine. A four rotor device is on display in the ANZUS Corridor of the [[The Pentagon]] on the second floor, A ring, between corridors 9 and 10. This machine is on loan from Australia.
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| In Canada, a Swiss Army issue Enigma-K, is in Calgary, Alberta. It is on permanent display at the Naval Museum of Alberta inside the Military Museums of Calgary. A 3-rotor Enigma machine is on display at the Communications and Electronics Engineering (CELE) Museum in Kingston, Ontario, at Canadian Forces Base (CFB) Kingston.
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| Occasionally, Enigma machines are sold at auction; prices have in recent years ranged from US$40,000<ref>Hamer, David; ''[http://www.eclipse.net/~dhamer/location.htm Enigma machines – known locations*]''</ref><ref>Hamer, David; ''[http://www.eclipse.net/~dhamer/enigma_p.htm Selling prices of Enigma and NEMA - all prices converted to US$]''</ref> to US$203,000<ref>Christi's; ''[http://www.christies.com/lotFinder/lot_details.aspx?intObjectID=5480138 3 Rotor enigma auction]''</ref> in 2011. Replicas are available in various forms, including an exact reconstructed copy of the Naval M4 model, an Enigma implemented in electronics (Enigma-E), various simulators and paper-and-scissors analogues.
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| 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 threatening to destroy the machine if the ransom were 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 afterward, the machine was sent anonymously to BBC journalist [[Jeremy Paxman]], missing three rotors.
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| 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 10 months in prison and served three months.<ref>{{cite news|url=http://news.bbc.co.uk/1/hi/uk/1609168.stm|work=BBC News|title=Man jailed over Enigma machine|date=19 October 2001|accessdate=2 May 2010}}</ref>
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| In October 2008, the Spanish daily newspaper ''[[El País]]'' reported that 28 Enigma machines had been discovered by chance in an attic of Army headquarters in Madrid. These 4-rotor commercial machines had helped Franco's Nationalists win the [[Spanish Civil War]] because, though the British cryptologist [[Alfred Dilwyn Knox]] in 1937 broke the cipher generated by Franco's Enigma machines, this was not disclosed to the Republicans, who failed to break the cipher. The Nationalist government continued using its 50 Enigmas into the 1950s. Some machines have gone on display in Spanish military museums,<ref>Graham Keeley. ''[http://www.timesonline.co.uk/tol/news/world/europe/article5003411.ece Nazi Enigma machines helped General Franco in Spanish Civil War]'', [[The Times]], 24 October 2008, p. 47.</ref><!--for the whole paragraph--><ref>{{cite web|url=http://www.cripto.es/museo/enigma-esp-fotos.htm |title=Taller de Criptografía - Enigmas españolas |publisher=Cripto.es |date= |accessdate=2013-09-08}}</ref> including one at the National Museum of Science and Technology (MUNCYT) in A Coruña. Two have been given to Britain's GCHQ.<ref>{{cite web|author=Posted on March 26, 2012 at 6:38 AM • 23 Comments |url=http://www.schneier.com/blog/archives/2012/03/rare_spanish_en.html |title=Schneier on Security: Rare Spanish Enigma Machine |publisher=Schneier.com |date=2012-03-26 |accessdate=2013-09-08}}</ref>
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| The [[Bulgaria]]n military used Enigma machines with a [[Cyrillic script|Cyrillic]] keyboard; one is on display in the [[National Museum of Military History (Bulgaria)|National Museum of Military History]] in [[Sofia]].{{citation needed|date=February 2012}}
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| ==Derivatives==
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| {{Original research|date=April 2013}}
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| The Enigma was influential in the field of cipher machine design, spinning off other rotor machines. 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. The British paid no royalties for the use of the patents, to protect secrecy. The Typex implementation is not the same as that found in German or other Axis versions.
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| A Japanese Enigma clone was codenamed GREEN by American cryptographers. Little used, it contained four rotors mounted vertically. In the U.S., cryptologist [[William F. Friedman|William Friedman]] designed the [[M-325]], a machine logically similar, although not in construction.
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| A unique rotor machine was constructed in 2002 by [[Netherlands]]-based Tatjana van Vark. This device makes use of 40-point rotors, allowing letters, numbers and some punctuation to be used; each rotor contains 509 parts.<ref>van Vark, Tatjana ''[http://www.tatjavanvark.nl/tvv1/pht10.html The coding machine]''</ref>
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| Machines like the [[SIGABA]], [[NEMA (machine)|NEMA]], [[Typex]] and so forth, are deliberately not considered to be Enigma derivatives as their internal ciphering functions are not mathematically identical to the Enigma transform.
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| Several software implementations exist, but not all exactly match Enigma behavior. The most commonly used software derivative (that is not compliant with any hardware implementation of the Enigma) is at EnigmaCo.de. Many Java applet Enigmas only accept single letter entry, complicating use even if the applet is Enigma compliant. Technically, Enigma@home is the largest scale deployment of a software Enigma, but the decoding software does not implement encipherment making it a derivative (as all original machines could cipher and decipher).
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| A user-friendly 3-rotor simulator, where users can select rotors, use the plugboard and define new settings for the rotors and reflectors is available.<ref>[http://w1tp.com/enigma/enigma_w.zip 3 rotor download]</ref> The output appears in separate windows which can be independently made "invisible" to hide decryption.<ref>[http://membres.multimania.fr/pc1/enigma/ Enigma at Multimania]</ref> Another includes an "autotyping" function which takes plaintext from a clipboard and converts it to cyphertext (or vice-versa) at one of four speeds. The "very fast" option produces 26 characters in less than one second.<ref>[http://w1tp.com/enigma/EnigmaSim.zip Autotype download]</ref>
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| <gallery mode=packed heights=148px>
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| Image:Japanese secure teletype 2.jpg|A Japanese Enigma clone, codenamed GREEN by American cryptographers.
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| Image:Tatjavanavark-machine.jpg|Tatjana van Vark's Enigma-inspired rotor machine.
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| File:Enigma simulator-IMG 0515-black.jpg|Electronic implementation of an Enigma machine, sold at the Bletchley Park souvenir shop
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| </gallery>
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| {{-}}
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| ==In popular culture==
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| *The play ''[[Breaking the Code]]'' by [[Hugh Whitemore]] focuses on the life and death of [[Alan Turing]], who was the central force in continuing to break the Enigma in the [[United Kingdom]] during [[World War II]]. Turing was played by [[Derek Jacobi]], who also played Turing in a 1996 television adaptation of the play.
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| *[[Robert Harris (novelist)|Robert Harris]]'s 1995 novel ''[[Enigma (novel)|Enigma]]'' is set against the backdrop of World War II [[Bletchley Park]] and cryptologists working to read Naval Enigma in [[Hut 8]]. The book, with substantial changes in plot, was made into the 2001 film ''[[Enigma (2001 film)|Enigma]],'' directed by [[Michael Apted]] and starring [[Kate Winslet]] and [[Dougray Scott]]. The film was criticized for historical inaccuracies, including neglect of the role of [[Poland]]'s ''[[Biuro Szyfrów]]''. The film – like the book – makes a Pole the villain, who seeks to betray the secret of Enigma decryption.<ref>Laurence Peter, [http://news.bbc.co.uk/2/hi/europe/8158782.stm How Poles cracked Nazi Enigma secret], BBC News, 20 July 2009</ref>
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| *An earlier Polish film dealing with Polish aspects of the subject was the 1979 ''[[Sekret Enigmy]]'', whose title translates as ''The Enigma Secret''.<ref>{{IMDb title|tt0079878}}</ref>
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| *[[Wolfgang Petersen]]'s 1981 film ''[[Das Boot]]'' includes an Enigma machine which is evidently a four-rotor Kriegsmarine variant. It appears in many scenes. The plot of ''[[U-571 (film)|U-571]]'', released in 2000, revolves around an attempt by American, rather than British, forces to seize an Enigma machine from a German U-boat.
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| *A re-imagined version of an Enigma Machine is used heavily in the 'Enigma Conundrum' side-mission in the 2011 video game, [[Batman: Arkham City]].
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| *[[Neal Stephenson]]'s novel ''[[Cryptonomicon]]'' prominently features the Enigma machine and efforts to break it, and portrays the German [[U-boat]] command under [[Karl Dönitz]] using it in apparently deliberate ignorance of its penetration.
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| *In the comedy war film ''[[All the Queen's Men]]'', released in 2001, starring [[Matt LeBlanc]] alongside [[Eddie Izzard]], four World War II Allied soldiers parachute into Germany, where, dressed as women, they attempt to steal an Enigma machine. They eventually learn that the Allies already had the machine and that the mission was a ruse intended to mislead the Germans into thinking that Enigma was a closed book to the Allies.
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| *''EnigmaWarsaw'' is an outdoor city game in [[Warsaw]] organised by StayPoland travel agency. This [[treasure hunt]] game is devised to help the players envision pre-war Warsaw. EnigmaWarsaw is named to commemorate the pioneering work of the Polish cryptologists in decrypting the machine.
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| *''[[To Say Nothing of the Dog]]'' is a science fiction novel about time-traveling historians that stresses the importance of the Allies obtaining Enigma.
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| *In the TV show ''[[Sanctuary (TV Series)|Sanctuary]]'', the breaking of the Enigma cipher is credited to [[Nikola Tesla (Sanctuary)|Nikola Tesla]] in the episode "Into the Black", released on 20 June 2011.
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| *In Ian Fleming's ''[[From Russia, with Love (novel)|From Russia, with Love]]'', the fictitious Lektor cipher machine, based on Enigma, is used as a plot device. This device would supposedly intercept Russian enciphered traffic and decrypt it, allowing MI6's cryptologists to access confidential information.
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| *In the [[Fox Network]] series ''[[Bones (TV series)|Bones]]'', two Enigma machines with attached printers are used as a means of concealing the exchange of information about a murder case from the Killer in the episode "The Corpse on the Canopy". The depiction is highly unrealistic, as Enigma did not feature all characters shown on print-out (e. g. space, dot...) and could not be used to type at speed shown.
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| *Progressive metal band [[Dream Theater]]'s [[Dream Theater (album)|eponymous 2013 album]] includes an instrumental song titled "Enigma Machine." The album's liner notes feature a picture of an Enigma on the page listing the song's credits.
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| *In Season 7, Episode 28 of the [[History Channel]] [[reality show]] "[[Pawn Stars]]", a patron offered to sell the store an Enigma machine for $149,300. After an inspection by an expert, [[Rick Harrison]] counteroffered $50,000. The customer lowered his asking price to $115,000. Harrison declined to buy the machine.
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| *In February 2013, a pair of students created a [[Weblog]] titled Operation Turing, a Fictional Role-Play Narrative of [[Office of Strategic Services]], [[Secret Intelligence Service]], and [[Deuxième Bureau]] Agents using stolen or captured Enigma machines to communicate with each other, creating a Counter-Espionage Plotline using the encoded messages among and other mediums.<ref>http://operationturing.tumblr.com</ref>
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| ==References==
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| ===Notes===
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| {{Reflist|30em}}
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| ===Bibliography===
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| {{Refbegin|30em}}
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| * {{cite book|last=Bauer |first=F. L. |year=2000 |title=Decrypted Secrets |publisher=Springer |edition=2 |isbn=3-540-66871-3 |ref=harv}}
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| * Hamer, David H.; Sullivan, Geoff; Weierud, Frode (July 1998). "Enigma Variations: an Extended Family of Machines", ''Cryptologia'', 22(3). [http://www.eclipse.net/~dhamer/downloads/enigvar1.zip Online version (zipped PDF)].
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| * {{cite book|last=Stripp |first=Alan |title=The Enigma Machine: Its Mechanism and Use |editors=Hinsley, F. H.; and Stripp, Alan (editors), |work=Codebreakers: The Inside Story of Bletchley Park |year=1993 |ref=harv}}
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| * {{Cite book |last=Kahn |first=David |authorlink=David Kahn (writer) |year=1991 |title=Seizing the Enigma: The Race to Break the German U-Boats Codes, 1939-1943 |publisher= |isbn=0-395-42739-8 |ref=harv |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}
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| * {{cite book|last=Kozaczuk |first=Władysław |authorlink=Władysław Kozaczuk |title=Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two |editor1-first=Christopher |editor1-last=Kasparek |editor1-link=Christopher Kasparek |location=Frederick, MD |publisher=University Publications of America |year=1984 |isbn=0-89093-547-5 |ref=harv}}
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| * {{cite web|last=Kozaczuk |first=Władysław |authorlink=Władysław Kozaczuk |url=http://www.enigmahistory.org/text.html |title=The origins of the Enigma/ULTRA }}
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| * {{cite doi|10.1080/0161-110291890731 }}
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| * Marks, Philip; Weierud, Frode (January 2000). "Recovering the Wiring of Enigma's Umkehrwalze A", ''Cryptologia'' 24(1), pp55–66.
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| * {{Cite journal | last = Rejewski | first = Marian | author-link = Marian Rejewski | title = An Application of the Theory of Permutations in Breaking the Enigma Cipher | journal = Applicationes mathematicae | volume = 16 | issue = 4 | year = 1980 | url = http://cryptocellar.org/ | issn = 1730-6280 | ref = harv | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}
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| * Smith, Michael (1998). ''Station X'' (Macmillan) ISBN 0-7522-7148-2
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| * {{Cite book | last = Smith | first = Michael | authorlink = Michael Smith (newspaper reporter) | year = 2006 | contribution = How it began: Bletchley Park Goes to War | editor-last = Copeland | editor-first = B Jack | editor-link = Jack Copeland | title = Colossus: The Secrets of Bletchley Park's Codebreaking Computers | publication-place = Oxford | publisher = Oxford University Press | isbn = 978-0-19-284055-4 | ref = harv | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}
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| * {{Cite web |last=Ulbricht |first=Heinz |title=Die Chiffriermaschine Enigma — Trügerische Sicherheit: Ein Beitrag zur Geschichte der Nachrichtendienste |language=German |trans_title=The Enigma Cipher Machine — Deceptive Security: A contribution to the history of intelligence services |series=PhD Thesis |year=2005 |url=http://opus.tu-bs.de/opus/volltexte/2005/705/pdf/enigmadiss.pdf |ref=harv |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}
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| {{Refend}}
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| ==Further reading==
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| {{Refbegin|30em}}
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| * Aldrich, Richard J. ''GCHQ: The Uncensored Story of Britain's Most Secret Intelligence Agency'', HarperCollins, July 2010.
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| * Bertrand, Gustave. ''Enigma ou la plus grande énigme de la guerre 1939–1945'', Plon, 1973.
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| * [[Peter Calvocoressi|Calvocoressi, Peter]]. ''Top Secret Ultra''. Baldwin, new edn 2001. 978-0-947712-36-5
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| * [[Anthony Cave Brown|Cave Brown, Anthony]]. ''Bodyguard of Lies'', 1975. A journalist's sensationalist best-seller that purported to give a history of Enigma decryption and its effect on the outcome of World War II. Worse than worthless on the seminal Polish work that made "[[Ultra]]" possible. See [[Richard Woytak]], prefatory note (pp. 75–76) to [[Marian Rejewski]], "Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by [[Harry Hinsley|F.H. Hinsley]]", ''[[Cryptologia]]'', vol. 6, no. 1 (January 1982), pp. 76–83.
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| * [[Józef Garliński|Garliński, Józef]] ''Intercept'', Dent, 1979. A superficial, sometimes misleading account of Enigma decryption before and during World War II, of equally slight value as to both the Polish and British phases. See [[Richard Woytak]] and [[Christopher Kasparek]], "The Top Secret of World War II", ''[[The Polish Review]]'', vol. XXVIII, no. 2, 1983, pp. 98–103 (specifically, about Garliński, pp. 101–3).
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| * [[John Herivel|Herivel, John]]. ''Herivelismus and the German military Enigma''. Baldwin, 2008. 978-0-947712-46-4
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| * [[John Keen|Keen, John]]. ''Harold 'Doc' Keen and the Bletchley Park Bombe''. Baldwin, 2003. 978-0-947712-42-6
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| * Large, Christine. ''Hijacking Enigma'', 2003, ISBN 0-470-86347-1.<!--Large is mentioned in the text so this may be a source but it is not cited-->
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| * Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector—Part I", ''Cryptologia'' 25(2), April 2001, pp. 101–141.
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| * Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector—Part II", ''Cryptologia'' 25(3), July 2001, pp. 177–212.
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| * Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector—Part III", ''Cryptologia'' 25(4), October 2001, pp. 296–310.
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| * Paillole, Paul. ''Notre espion chez Hitler'', Robert Laffont, 1985
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| * {{cite book |title=Inside ENIGMA |author=Perera, Tom |year=2010 |isbn=978-1-905086-64-1 | publisher=[[Radio Society of Great Britain]] |location=Bedford, UK}}
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| * Perera, Tom. ''The Story of the ENIGMA: History, Technology and Deciphering'', 2nd Edition, CD-ROM, 2004, Artifax Books, ISBN 1-890024-06-6 [http://w1tp.com/enigma/ecds.htm sample pages]
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| * [[Marian Rejewski|Rejewski, Marian]]. "[http://chc60.fgcu.edu/images/articles/rejewski.pdf How Polish Mathematicians Deciphered the Enigma]", ''Annals of the History of Computing 3'', 1981. This article is regarded by Andrew Hodges, Alan Turing's biographer, as "the definitive account" (see Hodges' ''Alan Turing: The Enigma'', Walker and Company, 2000 paperback edition, p. 548, footnote 4.5).
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| * Quirantes, Arturo. "Model Z: A Numbers-Only Enigma Version", ''Cryptologia'' 28(2), April 2004.
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| * [[Hugh Sebag-Montefiore|Sebag-Montefiore, Hugh]]. ''Enigma: the battle for the code''. Cassell Military Paperbacks, London, 2004. 978-1-407-22129-8
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| * Ulbricht, Heinz. Enigma Uhr, ''Cryptologia'', 23(3), April 1999, pp. 194–205.
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| * [[Gordon Welchman|Welchman, Gordon]]. ''The Hut Six Story: breaking the Enigma codes''. Baldwin, new edition, 1997. 978-0-947712-34-1
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| * Winterbotham, F.W, ''The Ultra Secret'', Harper and Row, New York, 1974; Spanish edition ''Ultrasecreto'', Ediciones Grijalbo, Madrid, 1975
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| {{Refend}}
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| ==External links==
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| <!-- PLEASE BE CAUTIOUS IN ADDING MORE LINKS TO THIS ARTICLE.-->
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| {{Commons category|Enigma machine}}
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| * [http://www.bletchleypark.org.uk/ Bletchley Park National Code Center] Home of the British codebreakers during the Second World War
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| * [http://cnm.open.ac.uk/projects/stationx/enigma/index.html Pictures of a four-rotor naval enigma, including Flash (SWF) views of the machine]
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| * [http://www.cgisecurity.net/2008/04/getting-to-see-an-enigma-machine-at-rsa-2008-.html Enigma Pictures and Demonstration by NSA Employee at RSA]
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| * {{dmoz|Science/Math/Applications/Communication_Theory/Cryptography/Historical/}}
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| * [http://russells.freeshell.org/enigma/ An online Enigma Machine simulator]
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| * [http://pc1cipher.pagesperso-orange.fr/enigma-en/ A three rotor Enigma Machine simulator]
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| * [http://www.students.oamk.fi/~k0khro00/Enigma.html Online Enigma simulator]
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| * [http://www.wwiiarchives.net/servlet/action/document/index/97/0 Kenngruppenheft]
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| * [http://www.enigma-maschine.de/en/ Process of building an Enigma M4 replica]
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| * [http://www.enigma.hoerenberg.com Breaking German Navy Ciphers]
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| * {{cite web|last=Grime|first=James|title=Enigma – 158,962,555,217,826,360,000|url=http://www.numberphile.com/videos/enigma.html|work=Numberphile|publisher=[[Brady Haran]]}}
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| * {{cite web|last=Grime|first=James|title=The Enigma Flaw |url=http://www.numberphile.com/videos/enigma_flaw.html|work=Numberphile|publisher=[[Brady Haran]]}}
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