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The German Enigma is surely the best known of the WW2 cipher machines used by either side in the conflict. Invented in 1918, it was developed as both a commercial and military encipherment system before and during the war. Enigma is an electro-mechanical device that utilizes a stepping wheel system to 'scramble' a plaintext message to produce ciphertext via polyalphabetic substitution. Potentially, the number of ciphertext alphabets is astronomically large - a fact that led the German military authorities to believe, wrongly as it turned out, in the absolute security of this cipher system.
Enigma's output is a very complex polyalphabetic substitution ciphertext. The 3-wheel Service Enigma consists of a number of components. A message to be enciphered is input from a keyboard - QWERTZUIO layout. The signal leaves the keyboard and passes through a plugboard where, if the plugboard socket contains a connector, its identity is switched in a monoalphabetic substitution. If the particular socket does not contain a plug, the identity of the input character is unchanged. The plugboard substitution is reciprocal - i.e. if A is switched to Z, then Z is switched to A, a weakness that was to be exploited by Allied cryptanalysts.
From the plugboard the signal then passes to the entry stator which passes it to the first of a series of three wheels. Each of these has twenty-six contacts on each of its faces, cross-wired in a random fashion so that the identity of an incoming character is changed three times as it passes through the three wheels, which are in electrical contact, each with its adjacent companion. With each keyboard input the extreme right-hand wheel moves one position - before encipherment takes place. Additionally, once during a complete revolution of each wheel, the wheel to its left steps once.
After passing through all three
wheels the signal reaches the reflector which performs two functions - it changes the
signal's identity once again and also sends it back, in the reverse direction, through the
three wheels to the entry stator. From here it passes back to the plugboard and then to
the lampboard where a lamp corresponding to the now enciphered character is illuminated.
Because of the reflector's function in the encipherment process, no plaintext character can ever encipher to itself - another weakness in the system that was exploited to great effect by the Allied cryptanalysts.
Enigma was set up according to whatever procedural instructions prevailed at the time by adjusting the following parameters.
Walzenlage: Three wheels were selected from a set of five in the case of the Army and Air Force machines - from a set of eight in the case of the Naval machines. The daily [or other periodic] instructions would also specify the reflector [Umkehrwalze] and, in the case of the Kriegmarine's M4, the selection of the fourth, 'Greek' , wheel and its 'thin' reflector.
Ringstellung: After setting the index ring on each, the three wheels were arranged on the machine's spindle in the order prescribed in the daily [or other periodic] instructions for machine initialization.
Steckerbrett: The plugboard was set up according to the same instructions. Normally, ten sets of plugs were used leaving six letters 'self-steckered'.
The internal lid of the Enigma was closed and the wheels set to the initial position.
Enigma was then ready for use.
Mathematical note: NSA's Dr. A. Ray Miller is the author of a thin booklet entitled: "The Cryptographic Mathematics of Enigma" in which he shows that the total number of possible set-up states - the so-called cryptovariable space - for a standard three-wheel German army Enigma is approximately 1023 or 1 followed by twenty-three zeros: about one hundred thousand billion billion! The figure for the four-wheel naval Enigma M4 was even greater. German cryptologists believed the Enigma cipher to be unbreakable.
Enigma - a German & English glossary
Enigma - download internal wiring information
Further reading - a bibliography
Enigma machines - known locations
Enigma and NEMA - selling prices
Infography on Enigma machine