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Enigma machine

2007 Schools Wikipedia Selection. Related subjects: Cryptography; Engineering

   The plugboard, keyboard, lamps and finger-wheels of the rotors emerging
   from the inner lid of a three-rotor German military Enigma machine
   (version with labels)
   Enlarge
   The plugboard, keyboard, lamps and finger-wheels of the rotors emerging
   from the inner lid of a three-rotor German military Enigma machine
   (version with labels)

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

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

   The German military model, the Wehrmacht Enigma, is the version most
   commonly discussed. The machine has gained notoriety because Allied
   cryptologists were able to decrypt a large number of messages that had
   been enciphered on the machine. The intelligence gained through this
   source — codenamed ULTRA — was a significant aid to the Allied war
   effort. The exact influence of ULTRA is debated, but a typical
   assessment is that the end of the European war was hastened by two
   years because of the decryption of German ciphers.

   Although the Enigma cipher has cryptographic weaknesses, it was, in
   practice, only their combination with other significant factors which
   allowed codebreakers to read messages: mistakes by operators,
   procedural flaws, and the occasional captured machine or codebook.

   This article discusses the Enigma machine itself: its components and
   its procedures. For the history and techniques of how Enigma was
   broken, see Cryptanalysis of the Enigma. For a discussion of how
   Enigma-derived intelligence was put to use, see ULTRA.
   The Enigma cipher machine
     * Enigma machine
          + Enigma rotor details
     * Cryptanalysis of the Enigma
          + Cyclometer
          + Perforated sheets
          + Bomba
          + Bombe
     * Ultra

Description

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

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

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

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

Rotors

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

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

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

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

   The rotors each contain a notch (sometimes multiple notches), used to
   control the stepping of the rotors. In the military versions, the
   notches are located on the alphabet ring.
     Exploded view of an Enigma rotor      Three rotors in sequence
    1. notched ring
    2. marking dot for "A" contact
    3. alphabet ring
    4. plate contacts
    5. wire connections
    6. pin contacts
    7. spring-loaded ring adjusting lever
    8. hub
    9. finger wheel
   10. ratchet wheel

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

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

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

Stepping motion

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

   To avoid merely implementing a simple substitution cipher, some rotors
   turn with consecutive presses of a key. This ensures that the
   cryptographic transformation is different at each position, producing a
   formidable polyalphabetic substitution cipher.

   The most common arrangement utilises a ratchet and pawl mechanism. Each
   rotor is affixed with a ratchet with 26 teeth; a group of pawls engage
   the teeth of the ratchet. The pawls are pushed forward in unison with
   each keypress on the machine. If a pawl engages the teeth of a ratchet,
   that rotor advances by one step.

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

   This double stepping causes the rotors to deviate from a normal
   odometer. A double step occurs as follows: the first rotor steps, and
   takes the second rotor one step further. If the second rotor has moved
   by this step into its own notch-position, the third pawl can drop down.
   On the next step this pawl pushes the ratchet of the third rotor and
   advances it, but will also push into the second rotor's notch,
   advancing the second rotor a second time in a row.

   With three wheels and only single notches in the first and second
   wheels, the machine has a period of 26 × 25 × 26 = 16,900 (NOT 26 X 26
   X 26 because of the double stepping of the second rotor. see bottom of
   page in the references section, for a link to a PDF file on this
   'double stepping'). Historically, messages were limited to a couple of
   hundred letters, and so there was no risk of repeating any position
   within a single message.

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

   When pressing a key, the rotors step before the electrical circuit is
   connected.
   The Enigma rotor assembly. The three movable rotors are sandwiched
   between two fixed wheels: the entry wheel on the right and the
   reflector (here marked "B") on the left.
   Enlarge
   The Enigma rotor assembly. The three movable rotors are sandwiched
   between two fixed wheels: the entry wheel on the right and the
   reflector (here marked "B") on the left.

Entry wheel

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

Reflector

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

   In the commercial Enigma model C, the reflector can be inserted in one
   of two different positions. In Model D the reflector can be set in 26
   possible positions, although it does not move during encipherment. In
   the Abwehr Enigma, the reflector is stepped during encryption in a
   similar way to the other wheels.

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

Plugboard

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

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

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

   Current flows from the keyboard through the plugboard, and proceeds to
   the entry-rotor or Eintrittswalze. Each letter on the plugboard has two
   jacks. Inserting a plug will disconnect 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 is inserted into another
   letter's jacks, switching the connections of the two letters.
   The "Schreibmax" was a printing unit which could be attached to the
   Enigma, removing the need for laboriously writing down the letters
   indicated on the light panel.
   Enlarge
   The "Schreibmax" was a printing unit which could be attached to the
   Enigma, removing the need for laboriously writing down the letters
   indicated on the light panel.

Accessories

   The Enigma Uhr attachment
   Enlarge
   The Enigma Uhr attachment

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

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

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

Mathematical description

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

          E = PRMLUL ^− 1M ^− 1R ^− 1P ^− 1

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

          E = P(ρ^iRρ ^− i)(ρ^jMρ ^− j)(ρ^kLρ ^− k)U(ρ^kL ^− 1ρ ^− k)(ρ^jM
          ^− 1ρ ^− j)(ρ^iR ^− 1ρ ^− i)P ^− 1

Procedures for using the Enigma

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

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

   An Enigma machine's initial state, the cryptographic key, has several
   aspects:
     * Wheel order (Walzenlage) — the choice of rotors and the order in
       which they are fitted.
     * Initial position of the rotors: — chosen by the operator, different
       for each message.
     * Ring settings (Ringstellung) — the position of the alphabet ring
       relative to the rotor wiring.
     * Plug settings (Steckerverbindungen) — the connections of the plugs
       in the plugboard.
     * In very late versions, the wiring of the reconfigurable reflector.

   Enigma was designed to be secure even if the rotor wiring was known to
   an eavesdropper, although in practice the wiring was kept secret. With
   secret wiring, the total number of possible configurations has been
   calculated to be around 10^114 (approximately 380 bits); with known
   wiring and other operational constraints, this is reduced to around
   10^23 (76 bits). Users of Enigma were assured of its security by the
   large number of possibilities; it was not feasible for an adversary to
   even begin to try every possible configuration in a brute force attack.

Indicators

   Most of the keys were kept constant for a set time period, typically a
   day. However, a different initial rotor position was chosen for each
   message, because if a number of messages are sent encrypted with
   identical or near-identical settings, a cryptanalyst has several
   messages "in depth", and might be able to attack the messages using
   frequency analysis. To counter this, a different starting position for
   the rotors was chosen for each message; a similar concept to an
   initialisation vector in modern cryptography. The starting position was
   transmitted just before the ciphertext. The exact method used is termed
   the "indicator procedure" — weak indicator procedures allowed the
   initial breaks into Enigma.
   Figure 2. With the inner lid placed down, the Enigma is ready for use.
   The finger wheels of the rotors protrude through the lid, allowing the
   operator to set the rotors, and the current position — here RDKP — is
   visible to the operator through a set of windows.
   Enlarge
   Figure 2. With the inner lid placed down, the Enigma is ready for use.
   The finger wheels of the rotors protrude through the lid, allowing the
   operator to set the rotors, and the current position — here RDKP — is
   visible to the operator through a set of windows.

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

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

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

   During the War the codebooks were used only to set up the rotors and
   ringsettings. For each message, the operator selected a random start
   position, let's say WZA, and random message key, let's say SXT. He
   moved the rotors to the WZA start position and encoded the message key
   SXT. Let us assume that the result was UHL. He then set up the message
   key SXT as the start position and encoded the message. Next, he
   transmitted the start position WZA, the encoded message key UHL and
   then the message. The receiver set up the start position according the
   first trigram, WZA and decoded the second trigram, UHL, to obtain the
   SXT message key. Next, he used this SXT message key as start position
   to decode the message. This way, each ground setting was different and
   the new procedure avoided the security flaw of double encoded message
   keys.

   This procedure was used by Wehrmacht and Luftwaffe only. The
   Kriegsmarine procedures on sending messages with the Enigma were far
   more complex and elaborate. Prior to encryption with the Enigma, the
   message was encoded with the Kurzsignalheft code book. The
   Kurzsignalheft contained tables that converted sentences into
   four-letter groups. All kinds of expressions in many different topics
   were listed, e.g. logistic matters such as refueling and rendezvous
   with supply ships, positions and grid lists, names of harbors,
   countries, weapons, weather conditions, enemy positions and ships, date
   and time tables. All possible situations and topics were listed.
   Another codebook contained the Kenngruppen and Spruchschlüssel: the key
   identification and message key. More details on Kurzsignale on German
   U-Boats

Abbreviations and guidelines

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

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

History and development of the machine

   Far from being a single design, there are numerous models and variants
   of the Enigma family. The earliest Enigma machines were commercial
   models dating from the early 1920s. Starting in the mid-1920s, the
   various branches of the German military began to use Enigma, making a
   number of changes in order to increase its security. In addition, a
   number of other nations either adopted or adapted the Enigma design for
   their own cipher machines.
   A selection of seven Enigma machines and paraphernalia exhibited at the
   USA's National Cryptologic Museum. From left to right, the models are:
   1) Commercial Enigma; 2) Enigma T; 3) Enigma G; 4) Unidentified; 5)
   Luftwaffe (Air Force) Enigma; 6) Heer (Army) Enigma; 7) Kriegsmarine
   (Naval) Enigma — M4.
   Enlarge
   A selection of seven Enigma machines and paraphernalia exhibited at the
   USA's National Cryptologic Museum. From left to right, the models are:
   1) Commercial Enigma; 2) Enigma T; 3) Enigma G; 4) Unidentified; 5)
   Luftwaffe (Air Force) Enigma; 6) Heer (Army) Enigma; 7) Kriegsmarine
   (Naval) Enigma — M4.

Commercial Enigma

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

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

   The reflector — an idea suggested by Scherbius' colleague Willi Korn —
   was first introduced in the Enigma C (1926) model. The reflector is a
   key feature of the Enigma machines.
   A rare 8-rotor printing Enigma.
   Enlarge
   A rare 8-rotor printing Enigma.

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

Military Enigma

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

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

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

   There was also a large, eight-rotor printing model, the Enigma II.
   During 1933, Polish codebreakers detected that it was in use for
   high-level military communications, but that it was soon withdrawn from
   use after it was found to be unreliable and jam frequently.
   Enigma G, used by the Abwehr, had four rotors, no plugboard, and
   multiple notches on the rotors.
   Enlarge
   Enigma G, used by the Abwehr, had four rotors, no plugboard, and
   multiple notches on the rotors.

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

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

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

Surviving Enigmas

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

   The effort to break the Enigma was not disclosed until the 1970s. Since
   then, interest in the Enigma machine has grown considerably and a
   number of Enigmas are on public display in museums in the US and
   Europe. The Deutsches Museum in Munich has both the three and
   four-wheel German military variants, as well as several older civilian
   versions. A functional Enigma is on display in the NSA's National
   Cryptologic Museum at Fort Meade, MD, where visitors can try their hand
   at encrypting messages and deciphering code. There are also examples at
   the Computer History Museum in the United States, at Bletchley Park in
   the United Kingdom, and the Australian War Memorial at Canberra in
   Australia, as well as a number of other locations in Germany, the US,
   the UK and elsewhere. A number are also in private hands.

   Occasionally, Enigma machines are sold at auction; prices of US$20,000
   are not unusual.

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

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

Enigma derivatives

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

   A unique rotor machine was constructed in 2002 by Netherlands-based
   Tatjana van Vark. This unusual device was inspired by Enigma but makes
   use of 40-point rotors, allowing letters, numbers and some punctuation
   to be used; each rotor contains 509 parts.
   The Japanese developed an Enigma clone, codenamed GREEN by American
   cryptographers, although it was little used.
   Enlarge
   The Japanese developed an Enigma clone, codenamed GREEN by American
   cryptographers, although it was little used.
   Tatjana van Vark's Enigma-inspired rotor machine, constructed in 2002.
   The rotors of this machine contain 40 contacts, compared to the
   original Enigma's 26.
   Enlarge
   Tatjana van Vark's Enigma-inspired rotor machine, constructed in 2002.
   The rotors of this machine contain 40 contacts, compared to the
   original Enigma's 26.

Fiction

   Robert Harris' 1996 novel Enigma is set against the backdrop of World
   War II Bletchley Park and cryptologists working to read Enigma. The
   book was made into the 2001 film, Enigma, starring Kate Winslet and
   Dougray Scott; the film has been criticized for many historical
   inaccuracies. An earlier film dealing (somewhat superficially) with the
   Polish aspects of the subject was the 1979 Sekret Enigmy (The Enigma
   Secret).

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

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

   Jonathan Mostow's 2000 film U-571 describes a fictional voyage of
   American submariners who have hijacked a German submarine to obtain an
   Enigma machine. The machine used in the film was an authentic Enigma
   obtained from a collector. The real-life capture of an enigma machine
   (by the British Royal Navy) happened a long time before the Americans
   joined the war.

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

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

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