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{{short description|German cipher machine}}
{{About|the Enigma machine itself|the Allied cracking of the machine|Cryptanalysis of the Enigma}}
{{Use dmy dates|date=January 2021}}
[[File:Enigma (crittografia) - Museo scienza e tecnologia Milano.jpg|thumb|Military Model Enigma I, in use from 1930]]
{{EnigmaSeries}}

The '''Enigma machine''' is a [[cipher]] device developed and used in the early- to mid-20th century to protect [[Commerce|commercial]], diplomatic, and military communication. It was employed extensively by [[Nazi Germany]] during [[World War II]], in all branches of the [[Wehrmacht|German military]]. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages.<ref>{{Cite web|title=EnigmaHistory|url=https://www.cryptomuseum.com/crypto/enigma/hist.htm|access-date=2020-12-16|website=cryptomuseum.com}}</ref>

The Enigma has an electromechanical [[Rotor machine|rotor mechanism]] that scrambles the 26 letters of the alphabet. In typical use, one person enters text on the Enigma's keyboard and another person writes down which of the 26 lights above the keyboard illuminated at each key press. If [[plaintext]] is entered, the illuminated letters are the [[ciphertext]]. Entering ciphertext transforms it back into readable plaintext. The rotor mechanism changes the electrical connections between the keys and the lights with each keypress.

The security of the system depends on machine settings that were generally changed daily, based on secret key lists distributed in advance, and on other settings that were changed for each message. The receiving station would have to know and use the exact settings employed by the transmitting station to decrypt a message.

Although Nazi Germany introduced a series of improvements to the Enigma over the years that hampered decryption efforts, they did not prevent [[Second Polish Republic|Poland]] from cracking the machine as early as December 1932 and reading messages prior to and into the war. Poland's sharing of their achievements enabled the [[Allies of World War II|Allies]] to exploit Enigma-enciphered messages as a major source of intelligence.{{sfn|Comer|2021}} Many commentators say the flow of [[Ultra (cryptography)|Ultra]] [[communications intelligence]] from the decrypting of Enigma, [[Lorenz cipher|Lorenz]], and other ciphers shortened the war substantially and may even have altered its outcome.<ref>{{Cite book|title=Intelligence in War|last=Keegan|first=John, Sir|publisher=Alfred A. Knopf|year=2003|location=New York}}</ref>
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==History==
The Enigma machine was invented by German engineer [[Arthur Scherbius]] at the end of [[World War I]].<ref name="Singh2011">{{cite book|first=Simon |last=Singh|title=The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography|url={{google books | plainurl=y | id=fbp9V9dkaNkC}}|date=26 January 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78784-2}}</ref> The German firm Scherbius & Ritter, co-founded by Scherbius, patented ideas for a cipher machine in 1918 and began marketing the finished product under the brand name ''Enigma'' in 1923, initially targeted at commercial markets.<ref>{{cite web | url=http://www.cryptomuseum.com/crypto/enigma/hist.htm | title=History of the Enigma | publisher=Crypto Museum | access-date=1 December 2017}}</ref> Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably [[Nazi Germany]] before and during [[World War II]].<ref>{{cite web|last=Lord|first= Bob|title=Enigma Manual|year=1998–2010|url=http://www.ilord.com/enigma-manuals|access-date=31 May 2011}}</ref>

Several Enigma models were produced,<ref>{{Cite journal |last1=Hamer |first1=David H. |last2=Sullivan |first2=Geoff |last3=Weierud |first3=Frode |date=July 1998 |title=Enigma Variations: An Extended Family of Machines |journal=Cryptologia |volume=XXII |issue=3 |pages=211–229 |doi=10.1080/0161-119891886885 |url=http://www.math.utoledo.edu/~codenth/Cryptanalysis/crypt_machs/ESIM/enigvar2.PDF |access-date=18 February 2016 |issn=0161-1194}}</ref> but the [[Wehrmacht|German military]] models, having a [[plugboard]], were the most complex. Japanese and Italian models were also in use.<ref>{{Cite web |title=Four Rotor Enigma Machine |url=https://www.spymuseum.org/exhibition-experiences/about-the-collection/collection-highlights/four-rotor-enigma-machine/ |access-date=2023-02-21 |website=International Spy Museum |language=en}}</ref> With its adoption (in slightly modified form) by the German Navy in 1926 and the German Army and Air Force soon after, the name ''Enigma'' became widely known in military circles. Pre-war German military planning emphasized fast, mobile forces and tactics, later known as [[blitzkrieg]], which depended on radio communication for command and coordination. Since adversaries would likely intercept radio signals, messages had to be protected with secure encipherment. Compact and easily portable, the Enigma machine filled that need.

=== Breaking Enigma ===
{{Main|Cryptanalysis of the Enigma}}

[[Image:Poland Bydgoszcz Rejewski monument.jpg|thumb|upright=1.3|A memorial in [[Bydgoszcz]], Poland, to [[Marian Rejewski]], the mathematician who, in 1932, first broke Enigma and, in July 1939, helped educate the French and British about Polish methods of Enigma decryption]]

[[Hans-Thilo Schmidt]] was a [[Nazi Germany|German]] who spied for the [[French Third Republic|French]], obtaining access to German cipher materials that included the daily keys used in September and October 1932. Those keys included the plugboard settings. The French passed the material to [[Second Polish Republic|Poland]]. Around December 1932, [[Marian Rejewski]], a Polish mathematician and [[Cryptanalysis|cryptologist]] at the [[Biuro Szyfrów|Polish Cipher Bureau]], used the theory of permutations,{{sfn|Rejewski|1980}} and flaws in the German military-message encipherment procedures, to break message keys of the plugboard Enigma machine.{{sfn|Vázquez|Jiménez–Seral|2018}} Rejewski used the French supplied material and the message traffic that took place in September and October to solve for the unknown rotor wiring. Consequently, the Polish mathematicians were able to build their own Enigma machines, dubbed "[[Polish Enigma double|Enigma doubles]]". Rejewski was aided by fellow mathematician-cryptologists [[Jerzy Różycki]] and [[Henryk Zygalski]], both of whom had been recruited with Rejewski from [[Adam Mickiewicz University in Poznań|Poznań University]], which had been selected for its students' knowledge of the German language, since that area was held by [[German Empire|Germany]] prior to World War I. The Polish Cipher Bureau developed techniques to defeat the plugboard and find all components of the daily key, which enabled the Cipher Bureau to read German Enigma messages starting from January 1933.<ref>Władysław Kozaczuk, ''Enigma: How the German Machine Cipher was Broken, and how it was Read by the Allies in World War Two'', edited and translated by Christopher Kasparek, Frederick, Maryland, University Publications of America, 1984, ISBN 978-0-89093-547-7, p. 21.</ref>

Over time, the German cryptographic procedures improved, and the Cipher Bureau developed techniques and designed mechanical devices to continue reading Enigma traffic. As part of that effort, the Poles exploited quirks of the rotors, compiled catalogues, built a [[cyclometer]] (invented by Rejewski) to help make a catalogue with 100,000 entries, invented and produced [[Zygalski sheets]], and built the electromechanical cryptologic [[Bomba (cryptography)|''bomba'']] (invented by Rejewski) to search for rotor settings. In 1938 the Poles had six ''bomby'' (plural of ''bomba''), but when that year the Germans added two more rotors, ten times as many ''bomby'' would have been needed to read the traffic.{{sfn|Kozaczuk|1984|p=63}}

On 26 and 27 July 1939,{{sfn|Erskine|2006|pp=294–305}} in [[Pyry, Warsaw|Pyry]], just south of [[Warsaw]], the Poles initiated French and British [[military intelligence]] representatives into the Polish [[Cryptanalysis of the Enigma|Enigma-decryption techniques]] and equipment, including Zygalski sheets and the cryptologic bomb, and promised each delegation a Polish-reconstructed Enigma (the devices were soon delivered).{{sfn|Kozaczuk|1984|pp=59–60, 236}}

In September 1939, British Military Mission 4, which included [[Colin Gubbins]] and [[Vera Atkins]], went to Poland, intending to evacuate cipher-breakers [[Marian Rejewski]], [[Jerzy Różycki]], and [[Henryk Zygalski]] from the country. The cryptologists, however, had been evacuated by their own superiors into Romania, at the time a Polish-allied country. On the way, for security reasons, the Polish Cipher Bureau personnel had deliberately destroyed their records and equipment. From Romania they traveled on to France, where they resumed their cryptological work, collaborating by teletype with the [[UK|British]], who began work on decrypting German Enigma messages, using the Polish equipment and techniques.{{sfn|Kozaczuk|1984|pp=69–94}}

[[Gordon Welchman]], who became head of [[Hut 6]] at Bletchley Park, wrote: "Hut 6 [[Ultra (cryptography)|Ultra]] would never have got 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." The Polish transfer of theory and technology at Pyry formed the crucial basis for the subsequent World War II British Enigma-decryption effort at [[Bletchley Park]], where Welchman worked.{{sfn|Welchman|1982|p=289}}

During the war, British cryptologists decrypted a vast number of messages enciphered on Enigma. The intelligence gleaned from this source, codenamed "[[Ultra (cryptography)|Ultra]]" by the British, was a substantial aid to the [[Allies of World War II|Allied]] war effort.{{efn|Much of the German cipher traffic was encrypted on the Enigma machine, and the term "Ultra" has often been used almost synonymously with "[[Cryptanalysis of the Enigma|Enigma decrypts]]". 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 other Italian ciphers and codes, as well as of Japanese ciphers and codes such as [[Type B Cipher Machine|Purple]] and [[Japanese naval codes#JN-25|JN-25]].}}

Though Enigma had some cryptographic weaknesses, in practice it was German procedural flaws, operator mistakes, 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}}

The [[Abwehr]] used different versions of Enigma machines. In November 1942, during [[Operation Torch]], a machine was captured which had no plugboard and the three rotors had been changed to rotate 11, 15, and 19 times rather than once every 26 letters, plus a plate on the left acted as a fourth rotor.<ref name="Flem11">{{cite book |title=Ian Fleming's Commandos: The Story of 30 Assault Unit in WWII |last=Rankin |first=Nicholas |publisher=Oxford University Press |isbn=978-0199782826 |date=2011}}</ref> 

The Abwehr code had been broken on 8 December 1941 by [[Dilly Knox]]. Agents sent messages to the Abwehr in a simple code which was then sent on using an Enigma machine. The simple codes were broken and helped break the daily Enigma cipher. This breaking of the code enabled the [[Double-Cross System]] to operate.<ref name="Flem11"/> From October 1944, the German Abwehr used the [[Schlüsselgerät 41]] in limited quantities.<ref name="NSA-German">{{cite web |url=https://www.nsa.gov/Portals/70/documents/about/cryptologic-heritage/historical-figures-publications/publications/wwii/german_cipher.pdf |title=German Cipher Machines of World War II |pages=22–25 |work=Center for Cryptologic History |publisher=[[National Security Agency]]|archive-url=https://web.archive.org/web/20230514055454/https://www.nsa.gov/portals/75/documents/about/cryptologic-heritage/historical-figures-publications/publications/wwii/german_cipher.pdf|archive-date=14 May 2023  |access-date=21 January 2024 |year=2014 }}</ref>

== Design ==
[[File:Bundesarchiv Bild 183-2007-0705-502, Chiffriermaschine "Enigma".jpg|thumb|upright|Enigma in use, 1943]]
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]]; one of various stepping components to turn at least one rotor with each key press, and a series of lamps, one for each letter. These design features are the reason that the Enigma machine was originally referred to as the rotor-based cipher machine during its intellectual inception in 1915.<ref name="Enigma History">{{Cite web|title=Enigma History|url=https://www.cryptomuseum.com/crypto/enigma/hist.htm|access-date=2020-12-16|website=cryptomuseum.com}}</ref>

=== Electrical pathway ===
[[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.]]
An electrical pathway is a route for current to travel. By manipulating this phenomenon the Enigma machine was able to scramble messages.<ref name="Enigma History"/> The mechanical parts act by forming a varying [[electrical network|electrical circuit]]. When a key is pressed, one or more rotors rotate on the spindle. On the sides of the rotors are a series of electrical contacts that, after rotation, line up with contacts on the other rotors or fixed wiring on either end of the spindle. When the rotors are properly aligned, each key on the keyboard is connected to a unique electrical pathway through the series of contacts and internal wiring. Current, typically from a battery, flows through the pressed key, into the newly configured set of circuits and back out again, ultimately lighting one display [[Electric light|lamp]], which shows 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, 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.

[[File: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.]]
Current flows from the battery (1) through a depressed bi-directional keyboard switch (2) to the plugboard (3). Next, it passes 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 enters the reflector (6). The reflector returns 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; [https://www.ciphermachinesandcryptology.com/en/enigmatech.htm Technical details of the Enigma machine] Cipher Machines & Cryptology</ref>

The repeated changes of electrical path through an Enigma scrambler implement a [[polyalphabetic cipher|polyalphabetic substitution cipher]] that provides Enigma's security. The diagram on the right shows how the electrical pathway changes with each key depression, which causes rotation of at least the right-hand rotor. Current passes 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 steps (rotates one position) on each key press, sending the signal on a completely different route. Eventually other rotors step with a key press.

=== Rotors ===
[[File:Enigma rotors with alphabet rings.jpg|thumb|Enigma rotor assembly. In the Enigma I, three movable rotors are sandwiched between two fixed wheels: the entry wheel, on the right, and the reflector on the left.]]
{{Main|Enigma rotor details}}
The rotors (alternatively ''wheels'' or ''drums'', ''Walzen'' in German) form the heart of an Enigma machine. Each rotor is a disc approximately {{convert|10|cm|in|abbr=on}} in diameter made from [[Ebonite]] or [[Bakelite]] with 26 [[brass]], spring-loaded, [[electrical contact]] pins arranged in a circle on one face, with the other face housing 26 corresponding electrical contacts in the form of circular plates. The pins and contacts represent the [[alphabet]]&nbsp;— typically the 26 letters A–Z, as will be assumed for the rest of this description. When the rotors are mounted side by side on the spindle, the pins of one rotor rest against the plate contacts of the neighbouring rotor, forming an electrical connection. Inside the body of the rotor, 26 wires connect each pin on one side to a contact on the other in a complex pattern. Most of the rotors are identified by Roman numerals, and each issued copy of rotor I, for instance, is wired identically to all others. The same is true for the special thin beta and gamma rotors used in the [[Enigma-M4|M4]] naval variant.

[[File:enigma-rotors.jpg|thumb|left|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, and so on. Enigma's security comes from using several rotors in series (usually three or four) and the regular stepping movement of the rotors, thus implementing a polyalphabetic substitution cipher.

Each rotor can be set to one of 26 starting positions when placed in an Enigma machine. After insertion, a rotor can be turned to the correct position by hand, using the grooved finger-wheel which protrudes from the internal Enigma cover when closed. In order for the operator to know the rotor's position, each has an ''alphabet tyre'' (or letter ring) attached to the outside of the rotor disc, with 26 characters (typically letters); one of these is visible through the window for that slot in the cover, thus indicating the rotational position of the rotor. In early models, the alphabet ring was fixed to the rotor disc. A later improvement was the ability to adjust the alphabet ring relative to the rotor disc. The position of the ring was known as the ''Ringstellung'' ("ring setting"), and that setting was a part of the initial setup needed prior to an operating session. In modern terms it was a part of the [[initialization vector]].

[[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''')]]
Each rotor contains one or more notches that control rotor stepping. In the military variants, the notches are located on the alphabet ring.

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 turnover 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.

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.

=== Stepping ===
To avoid merely implementing a simple (solvable) 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.

=== Turnover ===
[[File: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.]]
The advancement of a rotor other than the left-hand one was called a ''turnover'' by the British. This was achieved by a [[Ratchet (device)|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.

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|author-link=Tony Sale|title=Technical specifications of the Enigma rotors| work=Technical Specification of the Enigma|url=http://www.codesandciphers.org.uk/enigma/rotorspec.htm|access-date=15 November 2009}}</ref>

{|class="wikitable" style="margin: 1em auto 1em auto"
|+Position of turnover notches
|-
! style="width:130pt;"| Rotor
! style="width:130pt;"| Turnover position(s)
! style="width:130pt;"| BP mnemonic
|- style="text-align:center;"
| |I|| style="text-align:center;"|R|| style="text-align:center;"|Royal
|- style="text-align:center;"
| |II|| style="text-align:center;"|F|| style="text-align:center;"|Flags
|- style="text-align:center;"
| |III|| style="text-align:center;"|W|| style="text-align:center;"|Wave
|- style="text-align:center;"
| |IV|| style="text-align:center;"|K|| style="text-align:center;"|Kings
|- style="text-align:center;"
| |V|| style="text-align:center;"|A|| style="text-align:center;"|Above
|-
| style="text-align:center;"|VI, VII and VIII|| style="text-align:center;"|A and N|||
|}

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">{{cite journal |first=David |last=Hamer |title=Enigma: Actions Involved in the 'Double-Stepping' of the Middle Rotor |journal=Cryptologia |volume=21 |issue=1 |date=January 1997 |pages=47–50 |url=http://www.eclipse.net/~dhamer/downloads/rotorpdf.zip |archive-date=19 July 2011 |archive-url=https://web.archive.org/web/20110719081659/http://www.eclipse.net/~dhamer/downloads/rotorpdf.zip |format=zip |doi=10.1080/0161-119791885779}}</ref> This double-stepping caused the rotors to deviate from [[odometer]]-style regular motion.

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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&nbsp;= 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.

To make room for the Naval fourth rotors, the reflector was made much thinner. The fourth rotor fitted 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.

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 [[Coprime integers|relative 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 |access-date=17 July 2012}}</ref>{{Clear}}

=== Entry wheel ===
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 a [[QWERTZ]] keyboard: ''Q''&rarr;''A'', ''W''&rarr;''B'', ''E''&rarr;''C'' and so on. The military Enigma connects them in straight alphabetical order: ''A''&rarr;''A'', ''B''&rarr;''B'', ''C''&rarr;''C'', and so on. It took inspired guesswork for Rejewski to penetrate the modification.

=== Reflector ===
[[File:Enigma insides.agr.jpg|thumb|left|Internal mechanism of an Enigma machine showing the type B reflector and rotor stack]]
With the exception of models ''A'' and ''B'', the last rotor came before a 'reflector' (German: ''Umkehrwalze'', meaning 'reversal rotor'), a patented feature<ref name="Korn"/> 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 would be [[Involution (mathematics)|self-reciprocal]]; thus, with two identically configured machines, a message could be encrypted on one and decrypted on the other, without the need for a bulky mechanism to switch between encryption and decryption modes. The reflector allowed a more compact design, but it also gave Enigma the property that no letter ever encrypted to itself. This was a severe cryptological flaw that was subsequently exploited by codebreakers.

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 similar to 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',{{sfn|Marks|Weierud|2000}} 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]].{{sfn|Marks|2001|pp=101–141}} The fourth version, first observed on 2 January 1944, had a rewireable reflector, called ''Umkehrwalze D'', nick-named Uncle Dick by the British, allowing the Enigma operator to alter the connections as part of the key settings.{{Clear}}

=== Plugboard ===
[[File:Enigma-plugboard.jpg|right|thumb|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).]]
The plugboard (''Steckerbrett'' in German) permitted variable wiring that could be reconfigured by the operator. It was introduced on German Army versions in 1928,<ref>Craig P. Bauer: ''Secret History&nbsp;– The Story of Cryptology''. CRC Press, Boca Raton 2013, p.&nbsp;248. ISBN 978-1-4665-6186-1.</ref> and was soon adopted by the ''[[Reichsmarine]]'' (German Navy). The plugboard contributed more cryptographic strength than an extra rotor, as it had 150 trillion possible settings (see below).<ref name="158,962,555,217,826,360,000">{{Cite news|last1=Van Manen|first1=Dirk-Jan|last2=Johan O. A.|first2=Robertsson|date=2016|title=Codes and Ciphers|work=Geo ExPro|url=https://geoexpro.com/codes-and-ciphers-part-i/|access-date=October 13, 2023}}</ref> Enigma without a plugboard (known as ''unsteckered Enigma'') could be solved relatively straightforwardly using hand methods; these techniques were generally defeated by the plugboard, driving Allied cryptanalysts to develop special machines to solve it.

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 pressed ''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.

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.

=== Accessories ===
[[File:Enigma-printer-2.jpg|thumb|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.]]
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 |access-date=22 July 2010}}</ref>

==== ''Schreibmax'' ====
Some M4 Enigmas used the ''Schreibmax'', a small [[Printer (computing)|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]].

==== ''Fernlesegerät'' ====
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 light bulbs be removed.<ref name="Rijmenants" /> The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it.

==== ''Uhr'' ====
[[File:Enigma-uhr-box.jpg|right|thumb|upright|The Enigma Uhr attachment]]
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.

=== Mathematical analysis ===
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 {{mvar|P}} denote the plugboard transformation, {{mvar|U}} denote that of the reflector (<math>U=U^{-1}</math>), and {{mvar|L}}, {{mvar|M}}, {{mvar|R}} denote those of the left, middle and right rotors respectively. Then the encryption {{mvar|E}} can be expressed as

:<math>E=PRMLUL^{-1}M^{-1}R^{-1}P^{-1}.</math>

After each key press, the rotors turn, changing the transformation. For example, if the right-hand rotor {{mvar|R}} is rotated {{mvar|n}} positions, the transformation becomes

:<math>\rho^nR\rho^{-n},</math>

where {{mvar|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 {{mvar|j}} and {{mvar|k}} rotations of {{mvar|M}} and {{mvar|L}}. The encryption transformation can then be described as

:<math>E=P\left(\rho^n R\rho^{-n}\right)\left(\rho^j M\rho^{-j}\right)\left(\rho^{k}L\rho^{-k}\right)U\left(\rho^kL^{-1}\rho^{-k}\right)\left(\rho^j M^{-1}\rho^{-j}\right)\left(\rho^n R^{-1}\rho^{-n}\right)P^{-1}.</math>

Combining three rotors from a set of five, each of the 3 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 different settings (nearly 159 [[Names of large numbers|quintillion]] or about 67 [[bit]]s).<ref name="158,962,555,217,826,360,000"/>

* Choose 3 rotors from a set of 5 rotors = 5 x 4 x 3 = 60
* 26 positions per rotor = 26 x 26 x 26 = 17,576
* Plugboard = 26! / ( 6! x 10! x 2^10) = 150,738,274,937,250
* Multiply each of the above = 158,962,555,217,826,360,000

== Operation ==
=== Basic operation ===
[[File:Encrypting and decrypting using an enigma machine.webm|thumb|Enciphering and deciphering using an Enigma machine]]
A German Enigma operator would be given a plaintext message to encrypt. After setting up his machine, he would type the message on the Enigma keyboard. For each letter pressed, one lamp lit indicating a different letter according to a [[Pseudorandomness|pseudo-random]] substitution determined by the electrical pathways inside the machine. The letter indicated by the lamp would be recorded, typically by a second operator, as the [[cyphertext]] letter. The action of pressing a key also moved one or more rotors so that the next key press used a different electrical pathway, and thus a different substitution would occur even if the same plaintext letter were entered again. For each key press there was rotation of at least the right hand rotor and less often the other two, resulting in a different [[Pseudorandomness|substitution alphabet]] being used for every letter in the message. This process continued until the message was completed. The cyphertext recorded by the second operator would then be transmitted, usually by radio in [[Morse code]], to an operator of another Enigma machine. This operator would type in the cyphertext and&nbsp;— as long as all the settings of the deciphering machine were identical to those of the enciphering machine&nbsp;— for every key press the reverse substitution would occur and the plaintext message would emerge.

=== Details ===
[[File:Kenngruppenheft.jpg|thumb|German Kenngruppenheft (a U-boat [[codebook]] with grouped key codes)]]
[[File:Enigma keylist 3 rotor.jpg|thumb|Monthly key list number 649 for the German Air Force Enigma, including settings for the reconfigurable reflector (which only change once every eight days)]]
In use, the Enigma required a list of daily key settings and auxiliary documents. 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 given the same settings list for its Enigma, valid for a period of time. The procedures for German Naval Enigma were more elaborate and more secure than those in other services and employed auxiliary [[codebook]]s. Navy codebooks were printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were endangered or if the vessel was sunk.

An Enigma machine's setting (its [[Key (cryptography)|cryptographic key]] in modern terms; ''Schlüssel'' in German) specified each operator-adjustable aspect of the machine:
* Wheel order (''Walzenlage'') – the choice of rotors and the order in which they are fitted.
* Ring settings (''Ringstellung'') – the position of each alphabet ring relative to its rotor wiring.
* Plug connections (''Steckerverbindungen'') – the pairs of letters in the plugboard that are connected together.
* In very late versions, the wiring of the reconfigurable reflector.
* Starting position of the rotors (''Grundstellung'') – chosen by the operator, should be different for each message.

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, ring positions, plugboard connections and starting rotor positions must be identical. Except for the starting positions, these settings were established beforehand, distributed in key lists and changed daily. For example, the settings for the 18th day of the month in the German Luftwaffe Enigma key list number 649 (see image) were as follows:
* Wheel order: IV, II, V
* Ring settings: 15, 23, 26
* Plugboard connections: EJ OY IV AQ KW FX MT PS LU BD
* Reconfigurable reflector wiring: IU AS DV GL FT OX EZ CH MR KN BQ PW
* Indicator groups: lsa zbw vcj rxn

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 {{val|3e114}} (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around {{val|e=23}} (76 bits).<ref name="engima_cryptographic_mathematics">{{cite journal |last1=Miller |first1=A. Ray |title=The cryptographic mathematics of Enigma |journal=Cryptologia |date=January 1995 |volume=19 |issue=1 |pages=65–80 |doi=10.1080/0161-119591883773 |url=https://www.tandfonline.com/doi/abs/10.1080/0161-119591883773}}</ref> Because of the large number of possibilities, users of Enigma were confident of its security; it was not then feasible for an adversary to even begin to try a [[brute-force attack]].

=== Indicator ===
{{See also|Cryptanalysis#Indicator}}
Most of the key was kept constant for a set time period, typically a day. 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 [[Cryptanalysis#Depth|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.|author-link=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 weaknesses that made cracking Enigma possible.

[[File:Enigma-rotor-windows.jpg|left|thumb|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'' for the Enigma was cryptographically flawed and allowed Polish cryptanalysts to make the initial breaks into the plugboard Enigma. The procedure had the operator set his machine in accordance with the secret settings that all operators on the net shared. The settings included an initial position for the rotors (the ''Grundstellung''), 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 the message he would send. An operator might select ''EIN'', and that became the ''message setting'' for that encryption session. The operator then typed ''EIN'' into the machine twice, this producing the encrypted indicator, for example ''XHTLOA''. This was then transmitted, at which point the operator would turn the rotors to his message settings, ''EIN'' in this example, and then type the plaintext of the message.

At the receiving end, the operator set the machine to the initial settings (''AOH'') and typed in the first six letters of the message (''XHTLOA''). In this example, ''EINEIN'' emerged on the lamps, so the operator would learn the ''message setting'' that the sender used to encrypt this message. The receiving operator would set his rotors to ''EIN'', type in the rest of the ciphertext, and get the deciphered message.

This indicator scheme had two weaknesses. First, the use of a global initial position (''Grundstellung'') meant all message keys used the same polyalphabetic substitution. In later indicator procedures, the operator selected his initial position for encrypting the indicator and sent that 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. These security flaws enabled the Polish Cipher Bureau to break into the pre-war Enigma system as early as 1932. The early indicator procedure was subsequently described by German cryptanalysts as the "faulty indicator technique".{{sfn|Huttenhain|Fricke|1945|pp=4,5}}

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; [https://www.ciphermachinesandcryptology.com/en/enigmaproc.htm Enigma message procedures] Cipher Machines & Cryptology</ref>

This procedure was used by ''Heer'' and ''Luftwaffe'' only. The ''Kriegsmarine'' procedures for sending messages with the Enigma were far more complex and elaborate. Prior to encryption the message was encoded using the ''[[Kurzsignale|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 refuelling and rendezvous with supply ships, positions and grid lists, harbour names, countries, weapons, weather conditions, enemy positions and ships, date and time tables. Another codebook contained the ''[[Discriminant Book|Kenngruppen]]'' and ''Spruchschlüssel'': the key identification and message key.<ref>Rijmenants, Dirk; [https://www.ciphermachinesandcryptology.com/en/kurzsignale.htm Kurzsignalen on German U-boats] Cipher Machines & Cryptology</ref>

=== Additional details ===
The Army Enigma machine used only the 26 alphabet characters. Punctuation was replaced with rare character combinations. A space was omitted or replaced with an X. The X was generally used as full-stop.

Some punctuation marks were different in other parts of the armed forces. The ''Wehrmacht'' replaced a comma with ZZ and the question mark with FRAGE or FRAQ.

The ''Kriegsmarine'' replaced the comma with Y and the question mark 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.

The ''Wehrmacht'' and the ''Luftwaffe'' transmitted messages in groups of five characters and counted the letters.

The ''Kriegsmarine'' used four-character groups and counted those groups. 
Frequently used names or words were varied as much as possible. Words like ''Minensuchboot'' (minesweeper) could be written as MINENSUCHBOOT, MINBOOT or MMMBOOT. 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|access-date=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|access-date=16 October 2006}}</ref>{{Clear}}

=== Example enciphering process ===
The character substitutions by the Enigma machine as a whole can be expressed as a string of letters with each position occupied by the character that will replace the character at the corresponding position in the alphabet. For example, a given machine configuration that enciphered A to L, B to U, C to S, ..., and Z to J could be represented compactly as

 LUSHQOXDMZNAIKFREPCYBWVGTJ

and the enciphering of a particular character by that configuration could be represented by highlighting the enciphered character as in

 D > LUS(H)QOXDMZNAIKFREPCYBWVGTJ

Since the operation of an Enigma machine enciphering a message is a series of such configurations, each associated with a single character being enciphered, a sequence of such representations can be used to represent the operation of the machine as it enciphers a message. For example, the process of enciphering the first sentence of the main body of the famous "Dönitz message"<ref>{{cite web|url=https://www.cryptomuseum.com/crypto/enigma/msg/p1030681.htm|title=Message from Dönitz&nbsp;— 1 May 1945|access-date=27 November 2018}}</ref> to

 RBBF PMHP HGCZ XTDY GAHG UFXG EWKB LKGJ

can be represented as

 0001 F > KGWNT(R)BLQPAHYDVJIFXEZOCSMU CDTK 25 15 16 26
 0002 O > UORYTQSLWXZHNM(B)VFCGEAPIJDK CDTL 25 15 16 01
 0003 L > HLNRSKJAMGF(B)ICUQPDEYOZXWTV CDTM 25 15 16 02
 0004 G > KPTXIG(F)MESAUHYQBOVJCLRZDNW CDUN 25 15 17 03
 0005 E > XDYB(P)WOSMUZRIQGENLHVJTFACK CDUO 25 15 17 04
 0006 N > DLIAJUOVCEXBN(M)GQPWZYFHRKTS CDUP 25 15 17 05
 0007 D > LUS(H)QOXDMZNAIKFREPCYBWVGTJ CDUQ 25 15 17 06
 0008 E > JKGO(P)TCIHABRNMDEYLZFXWVUQS CDUR 25 15 17 07
 0009 S > GCBUZRASYXVMLPQNOF(H)WDKTJIE CDUS 25 15 17 08
 0010 I > XPJUOWIY(G)CVRTQEBNLZMDKFAHS CDUT 25 15 17 09
 0011 S > DISAUYOMBPNTHKGJRQ(C)LEZXWFV CDUU 25 15 17 10
 0012 T > FJLVQAKXNBGCPIRMEOY(Z)WDUHST CDUV 25 15 17 11
 0013 S > KTJUQONPZCAMLGFHEW(X)BDYRSVI CDUW 25 15 17 12
 0014 O > ZQXUVGFNWRLKPH(T)MBJYODEICSA CDUX 25 15 17 13
 0015 F > XJWFR(D)ZSQBLKTVPOIEHMYNCAUG CDUY 25 15 17 14
 0016 O > FSKTJARXPECNUL(Y)IZGBDMWVHOQ CDUZ 25 15 17 15
 0017 R > CEAKBMRYUVDNFLTXW(G)ZOIJQPHS CDVA 25 15 18 16
 0018 T > TLJRVQHGUCXBZYSWFDO(A)IEPKNM CDVB 25 15 18 17
 0019 B > Y(H)LPGTEBKWICSVUDRQMFONJZAX CDVC 25 15 18 18
 0020 E > KRUL(G)JEWNFADVIPOYBXZCMHSQT CDVD 25 15 18 19
 0021 K > RCBPQMVZXY(U)OFSLDEANWKGTIJH CDVE 25 15 18 20
 0022 A > (F)CBJQAWTVDYNXLUSEZPHOIGMKR CDVF 25 15 18 21
 0023 N > VFTQSBPORUZWY(X)HGDIECJALNMK CDVG 25 15 18 22
 0024 N > JSRHFENDUAZYQ(G)XTMCBPIWVOLK CDVH 25 15 18 23
 0025 T > RCBUTXVZJINQPKWMLAY(E)DGOFSH CDVI 25 15 18 24
 0026 Z > URFXNCMYLVPIGESKTBOQAJZDH(W) CDVJ 25 15 18 25
 0027 U > JIOZFEWMBAUSHPCNRQLV(K)TGYXD CDVK 25 15 18 26
 0028 G > ZGVRKO(B)XLNEIWJFUSDQYPCMHTA CDVL 25 15 18 01
 0029 E > RMJV(L)YQZKCIEBONUGAWXPDSTFH CDVM 25 15 18 02
 0030 B > G(K)QRFEANZPBMLHVJCDUXSOYTWI CDWN 25 15 19 03
 0031 E > YMZT(G)VEKQOHPBSJLIUNDRFXWAC CDWO 25 15 19 04
 0032 N > PDSBTIUQFNOVW(J)KAHZCEGLMYXR CDWP 25 15 19 05

where the letters following each mapping are the letters that appear at the windows at that stage (the only state changes visible to the operator) and the numbers show the underlying physical position of each rotor.

The character mappings for a given configuration of the machine are in turn the result of a series of such mappings applied by each pass through a component of the machine: the enciphering of a character resulting from the application of a given component's mapping serves as the input to the mapping of the subsequent component.  For example, the 4th step in the enciphering above can be expanded to show each of these stages using the same representation of mappings and highlighting for the enciphered character:
 
 <nowiki> G > ABCDEF(G)HIJKLMNOPQRSTUVWXYZ
&nbsp;  P EFMQAB(G)UINKXCJORDPZTHWVLYS &nbsp; &nbsp; &nbsp; &nbsp; AE.BF.CM.DQ.HU.JN.LX.PR.SZ.VW
&nbsp;  1 OFRJVM(A)ZHQNBXPYKCULGSWETDI&nbsp; N&nbsp; 03&nbsp; VIII
&nbsp;  2 (N)UKCHVSMDGTZQFYEWPIALOXRJB&nbsp; U&nbsp; 17&nbsp; VI
&nbsp;  3 XJMIYVCARQOWH(L)NDSUFKGBEPZT&nbsp; D&nbsp; 15&nbsp; V
&nbsp;  4 QUNGALXEPKZ(Y)RDSOFTVCMBIHWJ&nbsp; C&nbsp; 25&nbsp; β
&nbsp;  R RDOBJNTKVEHMLFCWZAXGYIPS(U)Q &nbsp; &nbsp; &nbsp; &nbsp; c
&nbsp;  4 EVTNHQDXWZJFUCPIAMOR(B)SYGLK &nbsp; &nbsp; &nbsp; &nbsp; β
&nbsp;  3 H(V)GPWSUMDBTNCOKXJIQZRFLAEY &nbsp; &nbsp; &nbsp; &nbsp; V
&nbsp;  2 TZDIPNJESYCUHAVRMXGKB(F)QWOL &nbsp; &nbsp; &nbsp; &nbsp; VI
&nbsp;  1 GLQYW(B)TIZDPSFKANJCUXREVMOH &nbsp; &nbsp; &nbsp; &nbsp; VIII
&nbsp;  P E(F)MQABGUINKXCJORDPZTHWVLYS &nbsp; &nbsp; &nbsp; &nbsp; AE.BF.CM.DQ.HU.JN.LX.PR.SZ.VW
 F < KPTXIG(F)MESAUHYQBOVJCLRZDNW</nowiki>

Here the enciphering begins trivially with the first "mapping" representing the keyboard (which has no effect), followed by the plugboard, configured as AE.BF.CM.DQ.HU.JN.LX.PR.SZ.VW which has no effect on 'G', followed by the VIII rotor in the 03 position, which maps G to A, then the VI rotor in the 17 position, which maps A to N, ..., and finally the plugboard again, which maps B to F, producing the overall mapping indicated at the final step: G to F.

This model has 4 rotors (lines 1 through 4) and the reflector (line R) also permutes (garbles) letters.

== Models ==
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.

{|style="margin: 1em auto 0 auto;"
|-
| [[File:Enigmas.jpg|upright=2.0|thumb|A selection of seven Enigma machines and paraphernalia exhibited at the U.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&nbsp;— M4.]]
|}

An estimated 40,000 Enigma machines were constructed.{{sfn|Bauer|2000|p=123}}<ref>[https://cryptocellar.org/enigma/e-history/enigma-reichswehr-wehrmacht-orders.pdf ''Reichswehr and Wehrmacht Enigma Orders''] {{Webarchive|url=https://web.archive.org/web/20210629133408/https://cryptocellar.org/enigma/e-history/enigma-reichswehr-wehrmacht-orders.pdf |date=29 June 2021 }} in Frode Weierud’s CryptoCellar, accessed 29&nbsp;June 2021.</ref> After the end of World War II, the Allies sold captured Enigma machines, still widely considered secure, to developing countries.{{sfn|Bauer|2000|p=112}}

=== Commercial Enigma ===
[[File:Scherbius-1928-patent.png|thumb|right|upright=1.45|Scherbius Enigma patent, {{US patent|1657411}}, granted in 1928]]
On 23 February 1918,<ref>{{cite web| url = https://www.cdvandt.org/Enigma%20DE416219C1.pdf| title = German patent No. 416219 from 23 February 1918}}</ref> [[Arthur Scherbius]] applied for a [[patent]] for a ciphering machine that used [[rotor machine|rotors]].<ref>{{cite patent |inventor-last=Scherbius |inventor-first=Arthur |title=Ciphering Machine |country-code=US |patent-number=1657411 |gdate=24 January 1928 |pridate=11 February 1922 |fdate=6 February 1923 |assign1=Chiffriermaschinen AG}}</ref> Scherbius and [[E. Richard Ritter]] founded the firm of Scherbius & Ritter. They approached the [[Reichsmarine|German Navy]] and Foreign Office with their design, but neither agency was interested. Scherbius & Ritter 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.

==== Enigma Handelsmaschine (1923) ====
Chiffriermaschinen AG began advertising a rotor machine, ''Enigma Handelsmaschine'', which was exhibited at the Congress of the [[Universal Postal Union|International Postal Union]] in 1924. The machine was heavy and bulky, incorporating a [[typewriter]]. It measured 65×45×38&nbsp;cm and weighed about {{convert|50|kg|lb}}.

==== Schreibende Enigma (1924) ====
This was also a model with a type writer. There were a number of problems associated with the printer and the construction was not stable until 1926. Both early versions of Enigma lacked the reflector and had to be switched between enciphering and deciphering.

==== Glühlampenmaschine, Enigma A (1924) ====
The reflector, suggested by Scherbius' colleague Willi Korn,<ref name="Korn">{{cite book |last1=De Leeuw |first1=Karl Maria Michael |last2=Bergstra |first2=J A |title=The history of information security : a comprehensive handbook |date=2007 |publisher=Elsevier |location=Amsterdam |isbn=9780080550589 |page=393}}</ref> was introduced with the glow lamp version.

The machine was also known as the military Enigma. It had two rotors and a manually rotatable reflector. The typewriter was omitted and glow lamps were used for output. The operation was somewhat different from later models. Before the next key pressure, the operator had to press a button to advance the right rotor one step.

==== Enigma B (1924) ====
[[File:Enigma-Glühlämpchen.jpg|thumb|upright|Typical glowlamps (with flat tops), as used for Enigma]]
Enigma ''model B'' was introduced late in 1924, 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|url-status=dead|archive-url=https://web.archive.org/web/20051021083422/http://www.armyradio.com/publish/Articles/The_Enigma_Code_Breach/Pictures/enigma_type_b.jpg|archive-date=21 October 2005}}</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. This model of Enigma machine was referred to as the Glowlamp Enigma or ''Glühlampenmaschine'' since it produced its output on a lamp panel rather than paper. This method of output was much more reliable and cost effective. Hence this machine was 1/8th the price of its predecessor.<ref name="Enigma History"/>

==== Enigma C (1926) ====
''Model C'' was the third model of the so-called ″glowlamp Enigmas″ (after A and B) and it again lacked a typewriter.<ref name="Enigma History"/>

==== Enigma D (1927) ====
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. In 1927 [[Hugh Foss]] at the British [[Government Communications Headquarters|Government Code and Cypher School]] was able to show that commercial Enigma machines could be broken, provided suitable cribs were available.<ref>Bletchley Park Trust Museum display</ref> Soon, the Enigma D would pioneer the use of a standard keyboard layout to be used in German computing.  This "QWERTZ" layout is very similar to the American [[QWERTY]] keyboard format used in many languages.

===== "Navy Cipher D" =====
Other countries used Enigma machines. The [[Italian Navy]] adopted the commercial Enigma as "Navy Cipher D". The Spanish also used commercial Enigma machines during their [[Spanish Civil War|Civil War]]. British codebreakers succeeded in breaking these machines, which lacked a plugboard.{{sfn|Smith|2006|p=23}} Enigma machines were also used by diplomatic services.

==== Enigma H (1929) ====
[[File:Enigma-8-rotor.jpg|right|thumb|upright|A rare 8-rotor printing Enigma model H (1929)]]
There was also a large, eight-rotor printing model, the ''Enigma H'', called ''Enigma II'' by the ''[[Reichswehr]]''. In 1933 the Polish Cipher Bureau detected that it was in use for high-level military communication, but it was soon withdrawn, as it was unreliable and jammed frequently.{{sfn|Kozaczuk|1984|p=28}}

==== Enigma K ====
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 (1927)|Enigma D]]. The machine's code was cracked by Poland, France, the United Kingdom and the United States; the latter code-named it INDIGO. An ''Enigma T'' model, code-named ''Tirpitz'', was used by Japan.

=== Military Enigma ===
The various services of the [[Wehrmacht]] used various Enigma versions, and replaced them frequently, sometimes with ones adapted from other services. Enigma seldom carried high-level strategic messages, which when not urgent went by courier, and when urgent went by other cryptographic systems including the [[Geheimschreiber]].

==== Funkschlüssel C ====
The Reichsmarine 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}}

The keyboard and lampboard contained 29 letters&nbsp;— A-Z, Ä, Ö and Ü&nbsp;— that were arranged alphabetically, as opposed to the QWERTZUI ordering.{{sfn|Ulbricht|2005|p=4}} The rotors had 28 contacts, with the letter ''X'' wired to bypass the rotors unencrypted.{{sfn|Stripp|1993}} 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}}

==== Enigma G (1928–1930) ====
By 15 July 1928,{{sfn|Kahn|1991|pp=41, 299}} the German Army (''[[Reichswehr]]'') had introduced their own exclusive version of the Enigma machine, the ''Enigma G''.

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

==== Wehrmacht Enigma I (1930–1938) ====
Enigma machine G was modified 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#Deutsche Reichsbahn-Gesellschaft (1924-1937)|railways]]{{sfn|Smith|2000|p= 73}}) before and during [[World War II]].

[[File:Bundesarchiv Bild 101I-769-0229-10A, Frankreich, Guderian, "Enigma" cropped.jpg|thumb|upright|[[Heinz Guderian]] in the [[Battle of France]], with an Enigma machine. Note one soldier is keying in text while another writes down the results.]]
The major difference between ''Enigma I'' (German Army version from 1930), 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 {{convert|28|x|34|x|15|cm|in|abbr=on}} and weighed around {{convert|12|kg|lb|abbr=on}}.{{sfn|Stripp|1993|p=83}}

In August 1935, the Air Force introduced the Wehrmacht Enigma for their communications.{{sfn|Kruh|Deavours|2002|p=97}}

==== M3 (1934) ====
By 1930, the Reichswehr 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 Reichsmarine 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}}
[[File:Bundesarchiv Bild 101I-241-2173-09, Russland, Verschlüsselungsgerät Enigma.jpg|thumb|left|Enigma in use on the Russian front]]

==== Two extra rotors (1938) ====
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}}

==== M4 (1942) ====
{{See also|Cryptanalysis of the Enigma#M4 (German Navy 4-rotor Enigma)}}
A four-rotor Enigma was introduced by the Navy for U-boat traffic on 1 February 1942, called ''[[Cryptanalysis of the Enigma#M4 (German Navy 4-rotor Enigma)|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.

<gallery mode="packed" heights="160">
File:Enigma-G.jpg|Enigma G, used by the ''[[Abwehr]]'', had four rotors, no plugboard, and multiple notches on the rotors.
File:Enigma-IMG 0484-black.jpg|The German-made Enigma-K used by the Swiss Army had three rotors and a reflector, but no plugboard. It had locally re-wired rotors and an additional lamp panel.
File:Four-rotor-enigma.jpg|An Enigma model T (Tirpitz), a modified commercial Enigma K manufactured for use by the Japanese
File:Enigma Decoder Machine.jpg|An Enigma machine in the UK's Imperial War Museum
File:Bundesarchiv Bild 101I-241-2173-06, Russland, Verschlüsselungsgerät Enigma.jpg|Enigma in use in Russia
File:Bundesarchiv Bild 146-2006-0188, Verschlüsselungsgerät "Enigma".jpg|Enigma in radio car of the 7th Panzer Div. staff, August 1941
</gallery>

[[File:CMoA Enigma Machine Exhibit in Georgia.JPG|thumb|A three-rotor Enigma machine on display at [[Computer Museum of America]] and its two additional rotors]]

== Surviving machines ==
[[File:Enigma and Decoder (from above) at Discovery Park of America.jpg|alt=|left|thumb|Surviving three-rotor Enigma on display at [[Discovery Park of America]] in [[Union City, Tennessee|Union City, Tennessee, U.S.]]]]
The effort to break the Enigma was not disclosed until 1973. Since then, interest in the Enigma machine has grown. Enigmas are on public display in museums around the world, and several are in the hands of private collectors and computer history enthusiasts.<ref name=ng>Ng, David. [http://www.latimes.com/entertainment/arts/culture/la-et-cm-imitation-game-enigma-machine-david-bohnett-20150122-story.html "Enigma machine from World War II finds unlikely home in Beverly Hills"]. ''[[Los Angeles Times]]''. 22 January 2015.</ref>

The ''[[Deutsches Museum]]'' in [[Munich]] has both the three- and four-rotor German military variants, as well as several civilian versions. The ''[[Deutsches Spionagemuseum]]'' in [[Berlin]] also showcases two military variants.<ref>{{Cite web |title=Enigma-Maschine: Die Entschlüsselung der Chiffriermaschine |url=https://www.deutsches-spionagemuseum.de/sammlung/enigma |access-date=2024-02-03 |website=Deutsches Spionagemuseum |language=de-DE}}</ref> Enigma machines are also exhibited at the National Codes Centre in [[Bletchley Park]], the [[Government Communications Headquarters]], the [[Science Museum, London|Science Museum]] in [[London]], [[Discovery Park of America]] in Tennessee, the [[Polish Army Museum]] in Warsaw, the [[Swedish Army Museum]] (''Armémuseum'') in [[Stockholm]], the Military Museum of [[A Coruña]] in Spain, the Nordland Red Cross War Memorial Museum in [[Narvik]],<ref>{{cite web|url=http://www.warmuseum.no/no/English/|title=War Museum}}</ref> Norway, [[The Artillery, Engineers and Signals Museum]] in [[Hämeenlinna]], Finland<ref>{{cite web|url=http://www.viestikiltojenliitto.fi/viestimuseo/_eng/index.html |title=The National Signals Museum}}</ref> the [[Technical University of Denmark]] in Lyngby, Denmark, in [[Skanderborg Bunkerne]] at Skanderborg, Denmark, and at the [[Australian War Memorial]] and in the foyer of the [[Australian Signals Directorate]], both in [[Canberra]], Australia. The Jozef Pilsudski Institute in London exhibited a rare [[Polish Enigma double]] assembled in France in 1940.<ref>{{Cite web|url=http://www.thenews.pl/1/10/Artykul/244703,Enigma-exhibition-in-London-pays-tribute-to-Poles |title=Enigma exhibition in London pays tribute to Poles|website=Polskie Radio dla Zagranicy|access-date=2016-04-05|archive-url= https://web.archive.org/web/20160423092753/http://thenews.pl/1/10/Artykul/244703,Enigma-exhibition-in-London-pays-tribute-to-Poles |archive-date=23 April 2016|url-status=dead}}</ref><ref>{{Cite web|url= http://pilsudski.org.uk/en/aktualnosci.php?news=205&wid=13&wai=&year=&back=%252Fen%252F |archive-url= https://web.archive.org/web/20160422230532/http://pilsudski.org.uk/en/aktualnosci.php?news=205&wid=13&wai=&year=&back=%252Fen%252F |url-status=dead|archive-date=2016-04-22|title=13 March 2016, 'Enigma Relay'– how Poles passed the baton to Brits in the run for WWII victory|website=J. Piłsudski Institute in London|access-date=2016-04-05}}</ref> In 2020, thanks to the support of the Ministry of Culture and National Heritage, it became the property of the Polish History Museum.<ref>{{Cite web|url=http://muzhp.pl/pl/c/1887/enigma-w-kolekcji-mhp|title=Enigma w kolekcji MHP - Muzeum Historii Polski|website=|access-date=11 November 2021|archive-date=11 November 2021|archive-url=https://web.archive.org/web/20211111122950/http://muzhp.pl/pl/c/1887/enigma-w-kolekcji-mhp|url-status=dead}}</ref>

[[File:Kriegsmarine Enigma.png|thumb|upright|A four-rotor ''[[Kriegsmarine]]'' (German Navy, 1. February 1942 to 1945) Enigma machine on display at the U.S. National Cryptologic Museum]]
In the United States, Enigma machines can be seen at the [[Computer History Museum]] in [[Mountain View, California]], and at the [[National Security Agency]]'s [[National Cryptologic Museum]] in [[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 alongside the submarine at the [[Museum of Science and Industry (Chicago)|Museum of Science and Industry]] in [[Chicago]], Illinois. A three-rotor Enigma is on display at [[Discovery Park of America]] in [[Union City, Tennessee]]. A four-rotor device is on display in the ANZUS Corridor of the [[The Pentagon|Pentagon]] on the second floor, A ring, between corridors 8 and 9. This machine is on loan from Australia. The United States Air Force Academy in Colorado Springs has a machine on display in the Computer Science Department. There is also a machine located at [[The National WWII Museum]] in New Orleans. [[The International Museum of World War II]] near Boston has seven Enigma machines on display, including a U-boat four-rotor model, one of three surviving examples of an Enigma machine with a printer, one of fewer than ten surviving ten-rotor code machines, an example blown up by a retreating German Army unit, and two three-rotor Enigmas that visitors can operate to encode and decode messages. [[Computer Museum of America]] in [[Roswell, Georgia]] has a three-rotor model with two additional rotors. The machine is fully restored and CMoA has the original paperwork for the purchase on 7 March 1936 by the German Army. The [[National Museum of Computing]] also contains surviving Enigma machines in Bletchley, England.<ref>{{Cite web|title=The National Museum of Computing|url=https://www.tnmoc.org/ |access-date=2020-12-16|website=The National Museum of Computing|language=en-GB}}</ref>

[[File:Muzeum 2 Wojny Swiatowej Gdansk Enigma cipher machine.jpg|thumb|left|A four-rotor ''[[Kriegsmarine]]'' Enigma machine on display at the [[Museum of the Second World War]], [[Gdańsk]], Poland]]
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 four-rotor Enigma machine is on display at the [[Military Communications and Electronics Museum]] at [[CFB Kingston|Canadian Forces Base (CFB) Kingston]] in [[Kingston, Ontario]].

Occasionally, Enigma machines are sold at auction; prices have in recent years ranged from US$40,000<ref>Hamer, David; ''[http://www.eclipse.net/~dhamer/location.htm Enigma machines – known locations*]'' {{webarchive |url=https://web.archive.org/web/20111104151545/http://www.eclipse.net/~dhamer/location.htm |date=4 November 2011}}</ref><ref>Hamer, David; ''[http://www.eclipse.net/~dhamer/enigma_p.htm Selling prices of Enigma and NEMA – all prices converted to US$]'' {{webarchive |url= https://web.archive.org/web/20110927033657/http://www.eclipse.net/~dhamer/enigma_p.htm |date=27 September 2011}}</ref> to US$547,500<ref>Christi's; ''[https://web.archive.org/web/20170617050627/http://artdaily.com/news/96771/Christie-s-sets-world-auction-record-for-an-Enigma-Machine-sold-to-online-bidder#.WZ80cZN94RF 4 Rotor enigma auction]''</ref> in 2017. 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.

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 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 afterward, the machine was sent anonymously to BBC journalist [[Jeremy Paxman]], missing three rotors.
[[File:LGD 8293-2.jpg|thumb|Enigma machine - model K 470 on display at the [[Enigma Cipher Centre]], [[Poznań]], Poland]]
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 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|access-date=2 May 2010}}</ref>

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 four-rotor commercial machines had helped Franco's Nationalists win the [[Spanish Civil War]], because, though the British cryptologist [[Dilly Knox|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. ''[https://archive.today/20100201144500/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 |access-date=8 September 2013 |archive-url=https://web.archive.org/web/20130611204718/http://www.cripto.es/museo/enigma-esp-fotos.htm |archive-date=11 June 2013 |url-status=dead }}</ref> including one at the National Museum of Science and Technology (MUNCYT) in La Coruña and one at the [[Museum of the Army (Toledo)|Spanish Army Museum]]. Two have been given to Britain's GCHQ.<ref>{{cite web|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=26 March 2012 |access-date=8 September 2013}}</ref>

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]].<ref>{{cite web|url=http://www.znam.bg/com/action/showAppArticle?appID=3&encID=2&article=3514226659&sectionID=1 |title=Communication equipment|publisher=znam.bg|date=29 November 2003|access-date=13 January 2015|archive-url= https://web.archive.org/web/20150113062919/http://www.znam.bg/com/action/showAppArticle?appID=3&encID=2&article=3514226659&sectionID=1 |archive-date=13 January 2015|url-status=dead}}</ref>

On 3 December 2020, German divers working on behalf of the [[World Wide Fund for Nature]] discovered a destroyed Enigma machine in [[Flensburg Firth]] (part of the [[Baltic Sea]]) which is believed to be from a scuttled U-boat.<ref>{{Cite news|date=3 December 2020|title=Divers discover Nazi WW2 enigma machine in Baltic Sea|work=[[Reuters]]|url=https://www.reuters.com/article/us-germany-war-enigma-idUSKBN28D25F |url-status=live|access-date=3 December 2020|archive-url= https://web.archive.org/web/20201203171005/https://www.reuters.com/article/us-germany-war-enigma-idUSKBN28D25F |archive-date=3 December 2020}}</ref> This Enigma machine will be restored by and be the property of the Archaeology Museum of [[Schleswig Holstein]].<ref>{{cite web |last1=Welle (www.dw.com) |first1=Deutsche |title=German divers hand over Enigma encryption machine in Baltic {{!}} DW {{!}} 04.12.2020 |url=https://www.dw.com/en/german-divers-hand-over-enigma-encryption-machine-in-baltic/a-55829171 |website=DW.COM}}</ref>

An M4 Enigma was salvaged in the 1980s from the German minesweeper R15, which was sunk off the [[Istria]]n coast in 1945. The machine was put on display in the [[Pivka Park of Military History]] in [[Slovenia]] on 13 April 2023.<ref>{{cite web| url = https://www.parkvojaskezgodovine.si/en/23851/| title = Revealing of Enigma in the Park of Military History Pivka| date = 13 April 2023}}</ref>

== Derivatives ==
The Enigma was influential in the field of cipher machine design, spinning off other [[rotor machine]]s. Once the British discovered Enigma's principle of operation, they created the [[Typex]] rotor cipher, which the Germans believed to be unsolvable.<ref>{{cite book |last1=Ferris |first1=John Robert |title=Intelligence and strategy : selected essays |date=2005 |publisher=F. Cass |location=New York, NY |isbn=978-0415361958 |page=165|series=Cass series - Studies in intelligence|oclc=243558411}}</ref> Typex was originally derived from the Enigma patents;<ref name="royal">{{cite book |last1=Greenberg |first1=Joel |title=Gordon Welchman: Bletchley Park's architect of ultra intelligence |date=2014 |publisher=Pen & Sword Books Ltd |location=London |isbn=9781473885257 |page=85|oclc=1023312315}}</ref> 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.<ref name="royal"/>  In the United States, cryptologist [[William F. Friedman|William Friedman]] designed the [[M-325]] machine,<ref name="LeeuwBergstra2007">{{cite book|author1=Karl Maria Michael de Leeuw|author2=Jan Bergstra|title=The History of Information Security: A Comprehensive Handbook|url=https://books.google.com/books?id=pQBrsonDp6cC&pg=PA407|date=28 August 2007|publisher=Elsevier Science |isbn=978-0-08-055058-9|pages=407–}}</ref> starting in 1936,<ref>{{cite book |last1=Mucklow |first1=Timothy |title=The SIGABA / ECM II Cipher Machine: "A Beautiful Idea |date=2015 |publisher=Center for Cryptologic History, NSA |location=Fort George G. Meade, MD|page=16 |url=https://www.nsa.gov/Portals/70/documents/about/cryptologic-heritage/historical-figures-publications/publications/technology/The_SIGABA_ECM_Cipher_Machine_A_Beautiful_Idea3.pdf}}</ref> that is logically similar.<ref>{{cite book |last1=Bauer |first1=Friedrich Ludwig |title=Decrypted secrets: methods and maxims of cryptology |date=2007 |publisher=Springer |location=Berlin |isbn=9783540245025 |page=133 |edition=4th revision and extended|oclc=255507974}}</ref>

Machines like the [[SIGABA]], [[NEMA (machine)|NEMA]], Typex, and so forth, are not considered to be Enigma derivatives as their internal ciphering functions are not mathematically identical to the Enigma transform.

A unique rotor machine called Cryptograph 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>

<gallery mode="packed" heights="148px">
File:Japanese secure teletype 2.jpg|A Japanese Enigma clone, codenamed GREEN by American cryptographers
File:Tatjavanavark-machine.jpg|Tatjana van Vark's Enigma-inspired rotor machine
File:Enigma simulator-IMG 0515-black.jpg|Electronic implementation of an Enigma machine, sold at the Bletchley Park souvenir shop
</gallery>

== Simulators ==
{{Main|List of Enigma machine simulators}}

== See also ==
* [[Alastair Denniston]]
* [[Arlington Hall]]
* [[Arne Beurling]]
* [[Beaumanor Hall]], a stately home used during the Second World War for military intelligence
* [[Cryptanalysis of the Enigma]] 
* [[Erhard Maertens]]—investigated Enigma security 
* [[Erich Fellgiebel]]
* [[SIGABA|ECM Mark II]]—cipher machine used by the Americans in the Second World War
* [[Fritz Thiele]]
* [[Gisbert Hasenjaeger]]—responsible for Enigma security
* [[United States Naval Computing Machine Laboratory]]
* [[Typex]]—cipher machine used by the British in the Second World War, based on the principles of the commercial Enigma machine

== Explanatory notes ==
{{Notelist}}

== References ==
=== Citations ===
{{Reflist}}

=== General and cited references ===
{{Refbegin|30em}}
* {{Cite book |last=Bauer |first=F. L. |year=2000 |title=Decrypted Secrets |publisher=Springer |edition=2nd |isbn=978-3-540-66871-8 |url={{google books |plainurl=y |id=E-epCAAAQBAJ}}}}
* {{Cite web |last=Comer |first=Tony |title=Poland's Decisive Role in Cracking Enigma and Transforming the UK's SIGINT Operations |publisher=[[RUSI]] |series=Commentary |date=27 January 2021 |url=https://rusi.org/commentary/poland-decisive-role-cracking-enigma-and-transforming-uk-sigint-operations |access-date=20 April 2022}}
*{{cite journal |last1=Erskine |first1=Ralph |title=The Poles Reveal their Secrets: Alastair Denniston's Account of the July 1939 Meeting at Pyry |journal=Cryptologia |date=December 2006 |volume=30 |issue=4 |pages=294–305 |doi=10.1080/01611190600920944|location=Philadelphia, Pennsylvania |s2cid=13410460 }}
* {{Cite web |last1=Huttenhain |first1=Orr |last2=Fricke |title=OKW/Chi Cryptanalytic Research on Enigma, Hagelin and Cipher Teleprinter Messages |publisher=TICOM |year=1945 |url=https://drive.google.com/file/d/0B7sNVKDp-yiJOWYxZWFmNDgtODUyMS00Y2FiLThkNWItYmQ5N2JmMzEyMzIz/view}}
* {{Cite book |last=Kahn |first=David |author-link=David Kahn (writer) |year=1991 |title=Seizing the Enigma: The Race to Break the German U-Boats Codes, 1939–1943 |publisher=Houghton Mifflin Company |isbn=978-0-395-42739-2 |url={{google books |plainurl=y |id=j1MC2d2LPAcC}}}}
* {{Cite book |last=Kozaczuk |first=Władysław |author-link=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=978-0-89093-547-7 |url={{google books |plainurl=y |id=5hJnAAAAMAAJ}}}}
* {{Cite web |last=Kozaczuk |first=Władysław |author-link=Władysław Kozaczuk |url=http://www.enigmahistory.org/text.html |title=The origins of the Enigma/ULTRA |url-status=dead |archive-url=https://web.archive.org/web/20030717071218/http://www.enigmahistory.org/text.html |archive-date=17 July 2003}}
* {{Cite journal |last1=Kruh |first1=L. |last2=Deavours |first2=C. |doi=10.1080/0161-110291890731 |title=The Commercial Enigma: Beginnings of Machine Cryptography |journal=Cryptologia |volume=26 |pages=1–16 |year=2002 |s2cid=41446859}}
* {{cite journal |last1=Marks |first1=Philip |title=Umkehrwalze D: Enigma's Rewirable Reflector - Part I |journal=Cryptologia |date=April 2001 |volume=25 |issue=2 |pages=101–141 |doi=10.1080/0161-110191889842|s2cid=11111300 |language=en |issn=0161-1194}}
* {{Cite journal |last1=Marks |first1=Philip |last2=Weierud |first2=Frode |year=2000 |title=Recovering the Wiring of Enigma's Umkehrwalze A |url=http://cryptocellar.web.cern.ch/cryptocellar/pubs/ukwa.pdf |journal=Cryptologia |volume=24 |issue=1 |pages=55–66 |doi=10.1080/0161-110091888781 |url-status=dead |archive-url=https://web.archive.org/web/20120213152736/http://cryptocellar.web.cern.ch/cryptocellar/pubs/ukwa.pdf |archive-date=13 February 2012 |citeseerx=10.1.1.622.1584 |s2cid=4473786}}
* {{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 |pages=543–559 |year=1980 |url=https://cryptocellar.org/enigma/files/rew80.pdf |issn=1730-6280 |doi=10.4064/am-16-4-543-559 |doi-access=free}}
* {{Cite book |first=Michael |last=Smith |author-link=Michael Smith (newspaper reporter) |title=Station X: The Codebreakers of Bletchley Park |url={{google books |plainurl=y |id=Wv4mSVDtA-wC}} |year=2000 |publisher=Pan |isbn=978-0-7522-7148-4}}
* {{Cite book |last=Smith |first=Michael |author-link=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 |location=Oxford |url={{google books |plainurl=y |id=e6ocfloTkJ4C}} |publisher=Oxford University Press |isbn=978-0-19-284055-4}}
* {{Cite book |last=Stripp |first=Alan |title=The Enigma Machine: Its Mechanism and Use |editor-last1=Hinsley |editor-first1=F. H. |editor-last2=Stripp |editor-first2=Alan |work=Codebreakers: The Inside Story of Bletchley Park |year=1993 |url={{google books |plainurl=y |id=j1MC2d2LPAcC}}}}
* {{Cite thesis |last=Ulbricht |first=Heinz |title=Die Chiffriermaschine Enigma&nbsp;— Trügerische Sicherheit: Ein Beitrag zur Geschichte der Nachrichtendienste |language=de |trans-title=The Enigma Cipher Machine&nbsp;— Deceptive Security: A contribution to the history of intelligence services |series=PhD Thesis |year=2005 |publisher=Universitätsbibliothek Braunschweig |doi=10.24355/dbbs.084-200511080100-324 |url=http://opus.tu-bs.de/opus/volltexte/2005/705/pdf/enigmadiss.pdf}}
* {{cite journal |last1=Vázquez |first1=Manuel |last2=Jiménez–Seral |first2=Paz |title=Recovering the military Enigma using permutations—filling in the details of Rejewski's solution |journal=Cryptologia |date=4 March 2018 |volume=42 |issue=2 |pages=106–134 |doi=10.1080/01611194.2016.1257522|s2cid=4451333 }}
* {{Cite book  |last=Welchman |first=Gordon |author-link=Gordon Welchman |title=The Hut Six Story: Breaking the Enigma Codes |year=1982 |publisher=McGraw-Hill |isbn=978-0-07-069180-3}}
{{Refend}}

== Further reading ==
{{Refbegin|30em}}
* {{Cite book |first=Richard James |last=Aldrich |title=GCHQ: The Uncensored Story of Britain's Most Secret Intelligence Agency |url={{google books |plainurl=y |id=4I2PmCtrHOgC}} |year=2010 |publisher=HarperPress |isbn=978-0-00-727847-3 }}
* {{Cite book |first=Gustave |last=Bertrand |title=Enigma: ou, La plus grande énigme de la guerre 1939–1945 |url={{google books |plainurl=y |id=o2UNAAAAIAAJ}} |year=1973 |publisher=Plon }}
* {{Cite book |first=Peter |last=Calvocoressi |author-link=Peter Calvocoressi |title=Top Secret Ultra |url={{google books |plainurl=y |id=qxiHPwAACAAJ |page=98}} |pages=98–103 |year=2001 |publisher=M & M Baldwin |isbn=978-0-947712-41-9 }}
* {{Cite web |last=Grime |first=James |title=The Enigma Flaw |url=http://www.numberphile.com/videos/enigma_flaw.html |work=Numberphile |publisher=[[Brady Haran]] |access-date=7 April 2013 |archive-url=https://web.archive.org/web/20130330065120/http://www.numberphile.com/videos/enigma_flaw.html |archive-date=30 March 2013 |url-status=dead }}
* Heath, Nick, [http://www.techrepublic.com/article/the-women-who-helped-crack-nazi-codes-at-bletchley-park Hacking the Nazis: The secret story of the women who broke Hitler's codes] TechRepublic, 27 March 2015
* {{Cite book |first=John |last=Herivel |author-link=John Herivel |title=Herivelismus: And the German Military Enigma |url={{google books |plainurl=y |id=voM0QwAACAAJ}} |year=2008 |publisher=M & M Baldwin }}
* {{Cite book |first=John |last=Keen |title=Harold 'Doc' Keen and the Bletchley Park Bombe |url={{google books |plainurl=y |id=tfq7MQEACAAJ}} |date=1 August 2012 |publisher=M & M Baldwin |isbn=978-0-947712-48-8 }}
* {{Cite book |first=Christine |last=Large |title=Hijacking Enigma: The Insider's Tale |url={{google books |plainurl=y |id=jAkiAQAAIAAJ}} |date=6 October 2003 |publisher=Wiley |isbn=978-0-470-86346-6 }}
* Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector&nbsp;— Part I", ''Cryptologia'' 25(2), April 2001, pp.&nbsp;101–141.
* Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector&nbsp;— Part II", ''Cryptologia'' 25(3), July 2001, pp.&nbsp;177–212.
* Marks, Philip. "Umkehrwalze D: Enigma's Rewirable Reflector&nbsp;— Part III", ''Cryptologia'' 25(4), October 2001, pp.&nbsp;296–310.
* {{Cite book |last=Paillole |first=Paul |title=Notre espion chez Hitler |trans-title=Our Spy with Hitler |language=fr |publisher=Robert Laffont |year=1985}}
* {{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}}
* 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]
* Rebecca Ratcliffe: Searching for Security. The German Investigations into Enigma's security. In: Intelligence and National Security 14 (1999) Issue 1 (Special Issue) S. 146–167.
* {{Cite book |first=Rebecca |last=Ratcliffe |title=How Statistics led the Germans to believe Enigma Secure and Why They Were Wrong: neglecting the practical Mathematics of Cipher machines |editor-first=Brian J. |editor-last=Winkel |work=The German Enigma Cipher Machine: Beginnings, Success, and Ultimate Failure |url={{google books |plainurl=y |id=1eVOAAAAMAAJ}} |date=1 January 2005 |publisher=Artech House |isbn=978-1-58053-996-8 }}
* [[Marian Rejewski|Rejewski, Marian]]. [http://chc60.fgcu.edu/images/articles/rejewski.pdf "How Polish Mathematicians Deciphered the Enigma"] {{Webarchive|url=https://web.archive.org/web/20111004194534/http://chc60.fgcu.edu/images/articles/rejewski.pdf |date=4 October 2011 }}, ''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.&nbsp;548, footnote 4.5).
* {{Cite journal |last=Quirantes |first=Arturo |title=Model Z: A Numbers-Only Enigma Version |journal=Cryptologia |volume=28 |issue=2 |date=April 2004 |doi=10.1080/0161-110491892845 |pages=153–156 |s2cid=44319455}}
* {{Cite book |first=Hugh |last=Sebag-Montefiore |author-link=Hugh Sebag-Montefiore |title=Enigma: The Battle for the Code |year=2011 |publisher=Orion |isbn=978-1-78022-123-6}}
* Ulbricht, Heinz. Enigma Uhr, ''Cryptologia'', 23(3), April 1999, pp.&nbsp;194–205.
* {{Cite book |last=Turing |first=Dermot |author1-link=Dermot Turing |title=[[X, Y & Z: The Real Story of How Enigma Was Broken]] |publisher=History Press |location=Gloustershire England |year=2018 |isbn=978-0-7509-8782-0 |oclc=1029570490}}
* {{Cite book |first=F. W. |last=Winterbotham |title=The Ultra Secret |year=1999 |publisher=Weidenfeld & Nicolson |isbn=978-0-297-64405-7}}
* [https://web.archive.org/web/20051118083351/http://news.mod.uk/news/press/news_headline_story.asp?newsItem_id=3339 Untold Story of Enigma Code-Breaker — The Ministry of Defence (U.K.) ]
{{Refend}}

== External links ==
<!-- PLEASE BE CAUTIOUS IN ADDING MORE LINKS TO THIS ARTICLE. -->
{{Commons category|Enigma machine}}
* [https://www.bbc.com/news/magazine-28167071 Gordon Corera, Poland's overlooked Enigma codebreakers, BBC News Magazine, 4 July 2014]
* [http://enigmadisplays.blogspot.ca/ Long-running list of places with Enigma machines on display]
* [http://www.bletchleypark.org.uk/ Bletchley Park National Code Centre Home of the British codebreakers during the Second World War] {{Webarchive|url=https://web.archive.org/web/20091209184137/http://www.bletchleypark.org.uk/ |date=9 December 2009 }}
* [http://www.cryptomuseum.com/crypto/enigma/ Enigma machines on the Crypto Museum Web site]
* [http://cnm.open.ac.uk/projects/stationx/enigma/index.html Pictures of a four-rotor naval enigma, including Flash (SWF) views of the machine] {{Webarchive|url=https://web.archive.org/web/20110724015209/http://cnm.open.ac.uk/projects/stationx/enigma/index.html |date=24 July 2011 }}
* [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]
* [https://web.archive.org/web/20130426233328/http://www.wwiiarchives.net/servlet/action/document/index/97/0 Kenngruppenheft]
* [http://www.enigma-maschine.de/en/ Process of building an Enigma M4 replica] {{Webarchive|url=https://web.archive.org/web/20130318013252/http://www.enigma-maschine.de/en/ |date=18 March 2013 }}
* [http://www.enigma.hoerenberg.com/ Breaking German Navy Ciphers]

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