TheEnigma machine is acipher device developed and used in the early- to mid-20th century to protectcommercial, diplomatic, and military communication. It was employed extensively byNazi Germany duringWorld War II, in all branches of theGerman military. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages.[1]
The Enigma has an electromechanicalrotor 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. Ifplaintext is entered, the illuminated letters are theciphertext. 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,cryptanalysis of the Enigma enabledPoland to first crack the machine as early as December 1932 and to read messages prior to and into the war. Poland's sharing of their achievements enabled theAllies to exploit Enigma-enciphered messages as a major source of intelligence.[2] Many commentators say the flow ofUltracommunications intelligence from the decrypting of Enigma,Lorenz, and other ciphers shortened the war substantially and may even have altered its outcome.[3]
The Enigma machine was invented by German engineerArthur Scherbius at the end ofWorld War I.[4] 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 nameEnigma in 1923, initially targeted at commercial markets.[5] Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notablyNazi Germany before and duringWorld War II.[6]
Several Enigma models were produced,[7] but theGerman military models, having aplugboard, were the most complex. Japanese and Italian models were also in use.[8] With its adoption (in slightly modified form) by the German Navy in 1926 and the German Army and Air Force soon after, the nameEnigma became widely known in military circles. Pre-war German military planning emphasised fast, mobile forces and tactics, later known asblitzkrieg, 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.
A memorial inBydgoszcz, Poland, toMarian 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 aGerman who spied for theFrench, 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 toPoland. Around December 1932,Marian Rejewski, a Polish mathematician andcryptologist at thePolish Cipher Bureau, used the theory of permutations,[9] and flaws in the German military-message encipherment procedures, to break message keys of the plugboard Enigma machine.[10] 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 "Enigma doubles". Rejewski was aided by fellow mathematician-cryptologistsJerzy Różycki andHenryk Zygalski, both of whom had been recruited with Rejewski fromPoznań University, which had been selected for its students' knowledge of the German language, since that area was held byGermany 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.[11]
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 acyclometer (invented by Rejewski) to help make a catalogue with 100,000 entries, invented and producedZygalski sheets, and built the electromechanical cryptologicbomba (invented by Rejewski) to search for rotor settings. In 1938 the Poles had sixbomby (plural ofbomba), but when that year the Germans added two more rotors, ten times as manybomby would have been needed to read the traffic.[12]
On 26 and 27 July 1939,[13] inPyry, just south ofWarsaw, the Poles initiated French and Britishmilitary intelligence representatives into the PolishEnigma-decryption techniques and equipment, including Zygalski sheets and the cryptologic bomb, and promised each delegation a Polish-reconstructed Enigma (the devices were soon delivered).[14]
In September 1939, British Military Mission 4, which includedColin Gubbins andVera Atkins, went to Poland, intending to evacuate cipher-breakersMarian Rejewski,Jerzy Różycki, andHenryk 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 travelled on to France, where they resumed their cryptological work, collaborating with theBritish, who began work on decrypting German Enigma messages, using the Polish equipment and techniques.[15]
Among those who joined the cryptanalytic effort in France was a team of seven Spanish cryptographers, known as "Equipo D" (Team D), led byAntonio Camazón, former head of the cipher service (Servicio de Información Militar) of theSpanish Republican Army during theSpanish Civil War. After the fall of the Republic in 1939, Camazón and his colleagues sought refuge in France and were recruited by French intelligence officerGustave Bertrand. They were assigned to thePC Bruno centre near Paris, where they worked alongside Polish cryptanalysts analysing Enigma-encrypted traffic and contributing to the adaptation of Polish decryption methods.
During theNorwegian campaign (8 April – 10 June 1940), three intact Enigma cipher machines belonging to the German Army and Air Force (Luftwaffe) were captured. Starting on 17 May 1940, and were put into operation at the British intelligence centre atBletchley Park.[16]
Following theGerman invasion of France in June 1940, the Spanish team relocated first to theCadix centre in theVichy-controlled zone and later toAlgiers, continuing their work with the Western Allies. Their tasks included manual decryption, rotor setting reconstruction, and message traffic analysis. Though their contribution remained largely unknown for decades, recent historical research and documentaries have highlighted their role in the broader Allied effort to break Enigma.[17][18][19]
Gordon Welchman, who became head ofHut 6 at Bletchley Park, wrote: "Hut 6Ultra 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 atBletchley Park, where Welchman worked.[20]
During the war, British cryptologists decrypted a vast number of messages enciphered on Enigma. The intelligence gleaned from this source, codenamed "Ultra" by the British, was a substantial aid to theAllied war effort.[a]
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.[21][22]
TheAbwehr used different versions of Enigma machines. In November 1942, duringOperation 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.[23]
The Abwehr code had been broken on 8 December 1941 byDilly 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 theDouble-Cross System to operate.[23] From October 1944, the German Abwehr used theSchlüsselgerät 41 in limited quantities.[24]
Like other rotor machines, the Enigma machine is a combination of mechanical and electrical subsystems. The mechanical subsystem consists of akeyboard; a set of rotating disks calledrotors arranged adjacently along aspindle; 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.[25]
Enigma wiring diagram with arrows and the numbers 1 to 9 showing how current flows from key depression to a lamp being lit. TheA key is encoded to theD 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.[25] The mechanical parts act by forming a varyingelectrical 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 displaylamp, which shows the output letter. For example, when encrypting a message startingANX..., the operator would first press theA key, and theZ lamp might light, soZ would be the first letter of theciphertext. The operator would next pressN, and thenX in the same fashion, and so on.
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 andAbwehr 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.[26]
The repeated changes of electrical path through an Enigma scrambler implement apolyalphabetic 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 letterA encrypts differently with consecutive key presses, first toG, and then toC. 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.
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.
The rotors (alternativelywheels ordrums,Walzen in German) form the heart of an Enigma machine. Each rotor is a disc approximately 10 cm (3.9 in) in diameter made fromEbonite orBakelite with 26brass, 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 thealphabet — 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 theM4 naval variant.
Three Enigma rotors and the shaft, on which they are placed when in use
By itself, a rotor performs only a very simple type ofencryption, a simplesubstitution cipher. For example, the pin corresponding to the letterE might be wired to the contact for letterT 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 analphabet 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 theRingstellung ("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 theinitialisation vector.
Two Enigma rotors showing electrical contacts, stepping ratchet (on the left) and notch (on the right-hand rotor oppositeD)
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 withRoman 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 PolishClock Method and BritishBanburismus attacks.
The Naval version of theWehrmacht 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 orGamma, 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.
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.
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 aturnover by the British. This was achieved by aratchet 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.[27] 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.[28]
Position of turnover notches
Rotor
Turnover position(s)
BP mnemonic
I
R
Royal
II
F
Flags
III
W
Wave
IV
K
Kings
V
A
Above
VI, VII and VIII
A and N
The design also included a feature known asdouble-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.[27] This double-stepping caused the rotors to deviate fromodometer-style regular motion.
With three wheels and only single notches in the first and second wheels, the machine had a period of 26×25×26 = 16,900 (not 26×26×26, because of double-stepping).[27] 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 theLückenfüllerwalze (gap-fill wheel) that implemented irregular stepping. It allowed field configuration of notches in all 26 positions. If the number of notches was arelative 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.[29]
The current entry wheel (Eintrittswalze in German), or entrystator, connects theplugboard 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 aQWERTZ keyboard:Q→A,W→B,E→C and so on. The military Enigma connects them in straight alphabetical order:A→A,B→B,C→C, and so on. It took inspired guesswork for Rejewski to penetrate the modification.
Internal mechanism of an Enigma machine showing the type B reflector and rotor stack
With the exception of modelsA andB, the last rotor came before a 'reflector' (German:Umkehrwalze, meaning 'reversal rotor'), a patented feature[30] 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 beself-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 theAbwehr 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',[31] and was replaced byUmkehrwalze B on 1 November 1937. A third version,Umkehrwalze C was used briefly in 1940, possibly by mistake, and was solved byHut 6.[32] The fourth version, first observed on 2 January 1944, had a rewireable reflector, calledUmkehrwalze D, nick-named Uncle Dick by the British, allowing the Enigma operator to alter the connections as part of the key settings.
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,[33] and was soon adopted by theReichsmarine (German Navy). The plugboard contributed more cryptographic strength than an extra rotor, as it had 150 trillion possible settings (see below).[34] Enigma without a plugboard (known asunsteckered 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 andQ 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 pressedE, the signal was diverted toQ 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 orEintrittswalze. 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.
TheSchreibmax 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.[35]
Some M4 Enigmas used theSchreibmax, a smallprinter 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. TheSchreibmax 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 decryptedplaintext.
Another accessory was the remote lamp panelFernlesegerät. 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 theSchreibmax, that the lamp panel and light bulbs be removed.[26] The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it.
In 1944, theLuftwaffe introduced a plugboard switch, called theUhr (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.[26] In one switch position, theUhr did not swap letters, but simply emulated the 13 stecker wires with plugs.
The Enigma transformation for each letter can be specified mathematically as a product ofpermutations.[9] Assuming a three-rotor German Army/Air Force Enigma, letP denote the plugboard transformation,U denote that of the reflector (), andL,M,R denote those of the left, middle and right rotors respectively. Then the encryptionE can be expressed as
After each key press, the rotors turn, changing the transformation. For example, if the right-hand rotorR is rotatedn positions, the transformation becomes
whereρ is thecyclic permutation mapping A to B, B to C, and so forth. Similarly, the middle and left-hand rotors can be represented asj andk rotations ofM andL. The encryption transformation can then be described as
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 159quintillion or about 67bits).[34]
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
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 apseudo-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 thecyphertext 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 differentsubstitution 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 inMorse code, to an operator of another Enigma machine. This operator would type in the cyphertext and — as long as all the settings of the deciphering machine were identical to those of the enciphering machine — for every key press the reverse substitution would occur and the plaintext message would emerge.
German Kenngruppenheft (a U-boatcodebook with grouped key codes)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 termedkeys atBletchley Park, and were assignedcode names, such asRed,Chaffinch, andShark. 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 auxiliarycodebooks. 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 (itscryptographic 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 around3×10114 (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around1023 (76 bits).[36] 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 abrute-force attack.
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 aninitialisation vector in modern cryptography. The reason is that encrypting many messages with identical or near-identical settings (termed in cryptanalysis as beingindepth), would enable an attack using a statistical procedure such asFriedman'sIndex of coincidence.[37] The starting position for the rotors was transmitted just before the ciphertext, usually after having been enciphered. The exact method used was termed theindicator procedure. Design weakness and operator sloppiness in these indicator procedures were two of the main weaknesses that made cracking Enigma possible.
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, hereRDKP, was visible to the operator through a set of windows.
One of the earliestindicator 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 (theGrundstellung), say,AOH. The operator turned his rotors untilAOH 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 selectEIN, and that became themessage setting for that encryption session. The operator then typedEIN into the machine twice, this producing the encrypted indicator, for exampleXHTLOA. 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 themessage setting that the sender used to encrypt this message. The receiving operator would set his rotors toEIN, 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".[38]
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 sayWZA, and a random message key, perhapsSXT. He moved the rotors to theWZA start position and encoded the message keySXT. Assume the result wasUHL. 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 theSXT message setting. Next, he used thisSXT 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.[39]
This procedure was used byHeer andLuftwaffe only. TheKriegsmarine procedures for sending messages with the Enigma were far more complex and elaborate. Prior to encryption the message was encoded using theKurzsignalheft code book. TheKurzsignalheft 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 theKenngruppen andSpruchschlüssel: the key identification and message key.[40]
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. TheWehrmacht replaced a comma with ZZ and the question mark with FRAGE or FRAQ.
TheKriegsmarine 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.
TheWehrmacht and theLuftwaffe transmitted messages in groups of five characters and counted the letters.
TheKriegsmarine used four-character groups and counted those groups.
Frequently used names or words were varied as much as possible. Words likeMinensuchboot (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.[41][42]
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"[43] to
RBBF PMHP HGCZ XTDY GAHG UFXG EWKB LKGJ
can be represented as
0001 F > KGWNT(R)BLQPAHYDVJIFXEZOCSMU CDTK 25 15 16 260002 O > UORYTQSLWXZHNM(B)VFCGEAPIJDK CDTL 25 15 16 010003 L > HLNRSKJAMGF(B)ICUQPDEYOZXWTV CDTM 25 15 16 020004 G > KPTXIG(F)MESAUHYQBOVJCLRZDNW CDUN 25 15 17 030005 E > XDYB(P)WOSMUZRIQGENLHVJTFACK CDUO 25 15 17 040006 N > DLIAJUOVCEXBN(M)GQPWZYFHRKTS CDUP 25 15 17 050007 D > LUS(H)QOXDMZNAIKFREPCYBWVGTJ CDUQ 25 15 17 060008 E > JKGO(P)TCIHABRNMDEYLZFXWVUQS CDUR 25 15 17 070009 S > GCBUZRASYXVMLPQNOF(H)WDKTJIE CDUS 25 15 17 080010 I > XPJUOWIY(G)CVRTQEBNLZMDKFAHS CDUT 25 15 17 090011 S > DISAUYOMBPNTHKGJRQ(C)LEZXWFV CDUU 25 15 17 100012 T > FJLVQAKXNBGCPIRMEOY(Z)WDUHST CDUV 25 15 17 110013 S > KTJUQONPZCAMLGFHEW(X)BDYRSVI CDUW 25 15 17 120014 O > ZQXUVGFNWRLKPH(T)MBJYODEICSA CDUX 25 15 17 130015 F > XJWFR(D)ZSQBLKTVPOIEHMYNCAUG CDUY 25 15 17 140016 O > FSKTJARXPECNUL(Y)IZGBDMWVHOQ CDUZ 25 15 17 150017 R > CEAKBMRYUVDNFLTXW(G)ZOIJQPHS CDVA 25 15 18 160018 T > TLJRVQHGUCXBZYSWFDO(A)IEPKNM CDVB 25 15 18 170019 B > Y(H)LPGTEBKWICSVUDRQMFONJZAX CDVC 25 15 18 180020 E > KRUL(G)JEWNFADVIPOYBXZCMHSQT CDVD 25 15 18 190021 K > RCBPQMVZXY(U)OFSLDEANWKGTIJH CDVE 25 15 18 200022 A > (F)CBJQAWTVDYNXLUSEZPHOIGMKR CDVF 25 15 18 210023 N > VFTQSBPORUZWY(X)HGDIECJALNMK CDVG 25 15 18 220024 N > JSRHFENDUAZYQ(G)XTMCBPIWVOLK CDVH 25 15 18 230025 T > RCBUTXVZJINQPKWMLAY(E)DGOFSH CDVI 25 15 18 240026 Z > URFXNCMYLVPIGESKTBOQAJZDH(W) CDVJ 25 15 18 250027 U > JIOZFEWMBAUSHPCNRQLV(K)TGYXD CDVK 25 15 18 260028 G > ZGVRKO(B)XLNEIWJFUSDQYPCMHTA CDVL 25 15 18 010029 E > RMJV(L)YQZKCIEBONUGAWXPDSTFH CDVM 25 15 18 020030 B > G(K)QRFEANZPBMLHVJCDUXSOYTWI CDWN 25 15 19 030031 E > YMZT(G)VEKQOHPBSJLIUNDRFXWAC CDWO 25 15 19 040032 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:
G > ABCDEF(G)HIJKLMNOPQRSTUVWXYZ P EFMQAB(G)UINKXCJORDPZTHWVLYS AE.BF.CM.DQ.HU.JN.LX.PR.SZ.VW 1 OFRJVM(A)ZHQNBXPYKCULGSWETDI N 03 VIII 2 (N)UKCHVSMDGTZQFYEWPIALOXRJB U 17 VI 3 XJMIYVCARQOWH(L)NDSUFKGBEPZT D 15 V 4 QUNGALXEPKZ(Y)RDSOFTVCMBIHWJ C 25 β R RDOBJNTKVEHMLFCWZAXGYIPS(U)Q c 4 EVTNHQDXWZJFUCPIAMOR(B)SYGLK β 3 H(V)GPWSUMDBTNCOKXJIQZRFLAEY V 2 TZDIPNJESYCUHAVRMXGKB(F)QWOL VI 1 GLQYW(B)TIZDPSFKANJCUXREVMOH VIII P E(F)MQABGUINKXCJORDPZTHWVLYS AE.BF.CM.DQ.HU.JN.LX.PR.SZ.VW F < KPTXIG(F)MESAUHYQBOVJCLRZDNW
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.
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.
A selection of seven Enigma machines and paraphernalia exhibited at the USNational Cryptologic Museum. From left to right, the models are: 1) Commercial Enigma; 2) Enigma T; 3) Enigma G; 4) Unidentified; 5)Luftwaffe (Air Force) Enigma; 6)Heer (Army) Enigma; 7)Kriegsmarine (Naval) Enigma — M4.
An estimated 40,000 Enigma machines were constructed.[44][45] After the end of World War II, the Allies sold captured Enigma machines, still widely considered secure, to developing countries.[46]
On 23 February 1918,[47]Arthur Scherbius applied for apatent for a ciphering machine that usedrotors.[48] Scherbius andE. Richard Ritter founded the firm of Scherbius & Ritter. They approached theGerman Navy and Foreign Office with their design, but neither agency was interested. Scherbius & Ritter then assigned the patent rights to Gewerkschaft Securitas, who founded theChiffriermaschinen Aktien-Gesellschaft (Cipher Machines Stock Corporation) on 9 July 1923; Scherbius and Ritter were on the board of directors.
Chiffriermaschinen AG began advertising a rotor machine,Enigma Handelsmaschine, which was exhibited at the Congress of theInternational Postal Union in 1924. The machine was heavy and bulky, incorporating atypewriter. It measured 65×45×38 cm and weighed about 50 kilograms (110 lb).
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.
The reflector, suggested by Scherbius' colleague Willi Korn,[30] 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.
Typical glowlamps (with flat tops), as used for Enigma
Enigmamodel B was introduced late in 1924, and was of a similar construction.[49] While bearing the Enigma name, both modelsA andB 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 orGlühlampenmaschine 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.[25]
TheEnigma C quickly gave way toEnigma D (1927). This version was widely used, with shipments to Sweden, the Netherlands, United Kingdom, Japan, Italy, Spain, United States and Poland. In 1927Hugh Foss at the BritishGovernment Code and Cypher School was able to show that commercial Enigma machines could be broken, provided suitable cribs were available.[50] 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 AmericanQWERTY keyboard format used in many languages.
Other countries used Enigma machines. TheItalian Navy adopted the commercial Enigma as "Navy Cipher D". The Spanish also used commercial Enigma machines during theirCivil War. British codebreakers succeeded in breaking these machines, which lacked a plugboard.[51] Enigma machines were also used by diplomatic services.
There was also a large, eight-rotor printing model, theEnigma H, calledEnigma II by theReichswehr. 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.[52]
The Swiss used a version of Enigma calledModel K orSwiss K for military and diplomatic use, which was very similar to commercialEnigma D. The machine's code was cracked by Poland, France, the United Kingdom and the United States; the latter code-named it INDIGO. AnEnigma T model, code-namedTirpitz, was used by Japan.
The various services of theWehrmacht 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 theGeheimschreiber.
The Reichsmarine was the first military branch to adopt Enigma. This version, namedFunkschlüssel C ("Radio cipher C"), had been put into production by 1925 and was introduced into service in 1926.[53]
The keyboard and lampboard contained 29 letters — A-Z, Ä, Ö and Ü — that were arranged alphabetically, as opposed to the QWERTZUI ordering.[54] The rotors had 28 contacts, with the letterX wired to bypass the rotors unencrypted.[22] Three rotors were chosen from a set of five[55] and the reflector could be inserted in one of four different positions, denoted α, β, γ and δ.[56] The machine was revised slightly in July 1933.[57]
By 15 July 1928,[58] the German Army (Reichswehr) had introduced their own exclusive version of the Enigma machine, theEnigma G.
TheAbwehr used theEnigma 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 theZählwerk Enigma.
Enigma machine G was modified to theEnigma I by June 1930.[59] Enigma I is also known as theWehrmacht, or "Services" Enigma, and was used extensively by German military services and other government organisations (such as therailways[60]) before and duringWorld War II.
Heinz Guderian in theBattle of France, with an Enigma machine. Note one soldier is keying in text while another writes down the results.
The major difference betweenEnigma 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 28 cm × 34 cm × 15 cm (11.0 in × 13.4 in × 5.9 in) and weighed around 12 kg (26 lb).[61]
In August 1935, the Air Force introduced the Wehrmacht Enigma for their communications.[59]
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.[62] The Reichsmarine eventually agreed and in 1934[63] brought into service the Navy version of the Army Enigma, designatedFunkschlüssel ' orM3. While the Army used only three rotors at that time, the Navy specified a choice of three from a possible five.[64]
In December 1938, the Army issued two extra rotors so that the three rotors were chosen from a set of five.[59] 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.[64]
A four-rotor Enigma was introduced by the Navy for U-boat traffic on 1 February 1942, calledM4 (the network was known asTriton, orShark 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.
Enigma G, used by theAbwehr, had four rotors, no plugboard, and multiple notches on the rotors.
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.
An Enigma model T (Tirpitz), a modified commercial Enigma K manufactured for use by the Japanese
An Enigma machine in the UK's Imperial War Museum
Enigma in use in Russia
Enigma in radio car of the 7th Panzer Div. staff, August 1941
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.[65]
A four-rotorKriegsmarine (German Navy, 1. February 1942 to 1945) Enigma machine on display at the US National Cryptologic Museum
In the United States, Enigma machines can be seen at theComputer History Museum inMountain View, California, and at theNational Security Agency'sNational Cryptologic Museum inFort Meade, Maryland, where visitors can try their hand at enciphering and deciphering messages. Two machines that were acquired after the capture ofU-505 during World War II are on display alongside the submarine at theMuseum of Science and Industry inChicago, Illinois. A three-rotor Enigma is on display atDiscovery Park of America inUnion City, Tennessee. A four-rotor device is on display in the ANZUS Corridor of thePentagon 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 atThe 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.Mimms Museum of Technology and Art inRoswell, 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. TheNational Museum of Computing also contains surviving Enigma machines in Bletchley, England.[72]Carnegie Mellon University Libraries also has two enigma machines, stored within its Special Collections.[73] These models are a three-rotor A5005 and a four-rotor M16681.[74]
Occasionally, Enigma machines are sold at auction; prices have in recent years ranged from US$40,000[75][76] to US$547,500[77] 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 rareAbwehr Enigma machine, designated G312, was stolen from theBletchley 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 journalistJeremy Paxman, missing three rotors.
In November 2000, an antiques dealer named Dennis Yates was arrested after telephoningThe 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.[78]
In October 2008, the Spanish daily newspaperEl 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 theSpanish Civil War, because, though the British cryptologistAlfred 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,[79][80] including one at the National Museum of Science and Technology (MUNCYT) in La Coruña and one at theSpanish Army Museum. Two have been given to Britain's GCHQ.[81]
On 3 December 2020, German divers working on behalf of theWorld Wide Fund for Nature discovered a destroyed Enigma machine inFlensburg Firth (part of theBaltic Sea) which is believed to be from a scuttled U-boat.[83] This Enigma machine will be restored by and be the property of the Archaeology Museum ofSchleswig Holstein.[84]
An M4 Enigma was salvaged in the 1980s from the German minesweeper R15, which was sunk off theIstrian coast in 1945. The machine was put on display in thePivka Park of Military History inSlovenia on 13 April 2023.[85]
In November 2025, the Paris branch of auction houseChristie's sold an Enigma M4 used byKarl Dönitz to an unidentified buyer for 482,600 euros.[86]
The Enigma was influential in the field of cipher machine design, spinning off otherrotor machines. Once the British discovered Enigma's principle of operation, they created theTypex rotor cipher, which the Germans believed to be unsolvable.[87] Typex was originally derived from the Enigma patents;[88] 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.[88] In the United States, cryptologistWilliam Friedman designed theM-325 machine,[89] starting in 1936,[90] that is logically similar.[91]
Machines like theSIGABA,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.[92]
A Japanese Enigma clone, codenamed GREEN by American cryptographers
Tatjana van Vark's Enigma-inspired rotor machine
Electronic implementation of an Enigma machine, sold at the Bletchley Park souvenir shop
^Much of the German cipher traffic was encrypted on the Enigma machine, and the term "Ultra" has often been used almost synonymously with "Enigma decrypts". Ultra also encompassed decrypts of the GermanLorenz SZ 40 and 42 machines that were used by theGerman High Command, and decrypts ofHagelin ciphers and other Italian ciphers and codes, as well as of Japanese ciphers and codes such asPurple andJN-25.
^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.
^Quirantes, Arturo (2021). "Faustino Camazón: El español que descifró la máquina Enigma". The Conversation España. Retrieved 1 June 2024.
^RTVE (2020).Equipo D: los códigos olvidados. Directed by Jorge Laplace. RTVE Play. Retrieved 1 June 2024.
^García Abadillo, Esteban (2019). "El olvidado matemático vallisoletano cuyo trabajo fue decisivo para derrotar a Hitler".El País. Retrieved 1 June 2024.
^abDe Leeuw, Karl Maria Michael; Bergstra, J A (2007).The history of information security : a comprehensive handbook. Amsterdam: Elsevier. p. 393.ISBN9780080550589.
^Friedman, W.F. (1922).The index of coincidence and its applications in cryptology. Department of Ciphers. Publ 22. Geneva, Illinois, USA: Riverbank Laboratories.OCLC55786052.
^Ferris, John Robert (2005).Intelligence and strategy : selected essays. Cass series - Studies in intelligence. New York, NY: F. Cass. p. 165.ISBN978-0415361958.OCLC243558411.
^abGreenberg, Joel (2014).Gordon Welchman: Bletchley Park's architect of ultra intelligence. London: Pen & Sword Books Ltd. p. 85.ISBN9781473885257.OCLC1023312315.
^Bauer, Friedrich Ludwig (2007).Decrypted secrets: methods and maxims of cryptology (4th revision and extended ed.). Berlin: Springer. p. 133.ISBN9783540245025.OCLC255507974.
Erskine, Ralph (December 2006). "The Poles Reveal their Secrets: Alastair Denniston's Account of the July 1939 Meeting at Pyry".Cryptologia.30 (4). Philadelphia, Pennsylvania:294–305.doi:10.1080/01611190600920944.S2CID13410460.
Vázquez, Manuel; Jiménez–Seral, Paz (4 March 2018). "Recovering the military Enigma using permutations—filling in the details of Rejewski's solution".Cryptologia.42 (2):106–134.doi:10.1080/01611194.2016.1257522.S2CID4451333.
Perera, Tom.The Story of the ENIGMA: History, Technology and Deciphering, 2nd Edition, CD-ROM, 2004, Artifax Books,ISBN1-890024-06-6sample pages
Rebecca Ratcliff: Searching for Security. The German Investigations into Enigma's security. In: Intelligence and National Security 14 (1999) Issue 1 (Special Issue) S. 146–167.
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