Talk:Enigma machine

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Introduction of Reflector isn't consistent

In the section about Design> Reflector: "With the exception of models A and B, the last rotor came before a 'reflector' "

That's inconsistent with the section about Models > Die Glühlampenmaschine, Enigma A (1924):

"The reflector, suggested by Scherbius' colleague Willi Korn, was introduced with the glow lamp version."

And just after that in the description for Enigma B:

"... 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.

I suspect there's a mistake in one or the other but I'm not sure which. EchelonForce (talk) 13:32, 22 April 2023 (UTC)[reply]

Your objection is justified. All incandescent lamp machines (Enigma A, B and C) had a reversing roller or reflector ("Umkehrwalze" in German). It was installed in the Enigma A as early as 1923, but not patented until 1926 by Willi Korn. Only three machines produced by Scherbius did not have a reflector, but a complicated switchover from encryption to decryption and vice versa of 26 or 28 rotor contacts instead, so that the current ran through the machine once in one direction and once in the opposite direction (All three machines had four encoding rotors. The "Schreibende (writing) Enigma" and the "Enigma H or Enigma II" had four additional advancing rotors). The third machine was the "Handelsmaschine ("Trading Enigma") its cipher rotors moved with irregularly indexed gap gears. "Schreibende Enigma" and Enigma H used a build in typewriter, "Handelsmaschine" a printing typewheel.

The Enigma A ("small military machine") had 26 rotor contacts, TWO adjustable rotors and an ADJUSTABLE, settable reflector (keyboard with 13 + 13 keys in two rows). On the Enigma B, the rotors had 28 contacts (keyboard with 10 + 9 + 9 keys in three rows), including the German letters Ä, Ö ("Umlaute"). A swedish version came without a key for letter W, but offered one for the scandinavian letter Å. There were two versions of the machine: the earlier one ("Mark I") had TWO rotors and an adjustable reflector, the later one ("Mark II") had three adjustable rotors, but with a fixed build in reflector. The Enigma C again had 26 rotor contacts (keyboard with 9 + 8 + 9 keys in three rows), this time there were again three adjustable rotors, the reflector could not be adjusted but could be installed in two different positions. An alternative of the Enigma C with 28 rotor contacts and 29 letter keys (Ä, Ö, Ü) was sold to the German "Kriegsmarine" (X was directly connected with its glow lamp, keyboard 10 + 9 + 10 keys in three rows, five choosable rotors !). A special version with 28 letter keys was sold to Sweden, without keys for Ü and W, but offering keys for Ä, Ö and Å. (Keyboard 10 + 9 + 9 keys in three rows). Permissiveactionlink (talk) 20:48, 6 July 2025 (UTC)[reply]

Serbian Enigma

There is Enigma exhibited in the military museum in Belgrade Serbia as well. 87.212.165.3 (talk) 13:53, 5 September 2024 (UTC)[reply]

Cycle length and number of effective rotor settings

If, as you correctly write, the period length of the Enigma with single-notch rotors was 16,900 (this also applies to 120 rotor combinations of the Enigma M4, if the right and centre moving rotors are single-notch rotors), the number of rotor settings relevant for the key space ("groundsetting") is just as high, although you can select 17,576 different ground settings, but the machine ignores 676 of them: in the first ciphering process, it switches the right OR the right and centre OR all three moving rotors one step further (to a three-rotor position belonging to the key period for sure !), and only then executes the first ciphering step. The home position is not used for ciphering unless it belongs to the key period itself: in this case its key alphabet is only used for the first time after a further 16,899 ciphering steps ! If two-notch rotors are used in the two right-hand rotor positions of the Enigma M4, the period length is reduced to 4,056 cipher steps. It can be assumed that the number of effective rotor settings is then also reduced to 4,056. Although the remaining 13,520 rotor settings are possible, they are not part of the key space: for each of these settings, the corresponding key alphabet is never used, as the machine in the first ciphering step immediately switches to a three-rotor position that itself belongs to the very short key period. Permissiveactionlink (talk) 17:06, 6 July 2025 (UTC)[reply]

Mathematical Analysis ?

Unfortunately, this is not correct. Although you can select 17,576 rotor settings, only 16,900 of these contribute to the key space. It has also been forgotten that each of the 5*4*3 = 60 rotor combinations provides 676 different key periods, as 26 different effective ring positions ("ringsettings") can be selected for each of the two rotors on the right and in the centre (the ring position on the left rotor can be selected, but does not contribute to the key space). The Enigma I therefore has the key space :

5*4*3 * 16.900 * 676 * 150.738.274.937.250 = 103.325.660.891.587.134.000.000 = 1.03*10^23 ("103 Trilliarden" in German, "103 sextillion" in the US)

And that corresponds to 76.45 bits. Permissiveactionlink (talk) 09:52, 8 July 2025 (UTC)[reply]

Reflector

"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."

With a further increase in the number of rotors above three, it became increasingly difficult to continue switching with the help of a letter key to be pressed: the force required to enter the plain text (or cipher text) became so great that it was hardly possible to operate the machine properly. For this reason, the German employee of the Enigma manufacturer H&R (Heimsoeth & Rinke, successor to ChMaAG (Chiffriermaschinen Aktiengesellschaft)), senior engineer Willi Korn, invented the reflector ("Umkehrwalze" in German), as the signal then passes through not just three but six rotors, with comparable effort. Machines with more than three rotors either have additional rotors (stators, e.g. in the Typex machine) that can only be adjusted but are not moved along, or they are electromagnetically indexed by stepper motors (SIGABA !).

The reflector facilitated cryptanalysis. However, the reflector was NOT the decisive reason for the decryption of the Enigma machine. It merely ensured that it was not necessary to check numerous start settings of the bombs for numerous positions of a "crib" inside the suspected plaintext, which considerably reduced the time required for decryption. This can be shown very simply by the fact that the British Typex machine (an unlicensed Enigma replica with numerous useful additions, but still with three moving rotors, double stepping anomaly of the centre moving rotor and REFLECTOR (!)) was never cracked at the time. One such Typex machine was captured and analysed by the Germans in Dunkirk. But apparently without consequences. However, these machines were very large and heavy, and therefore completely unsuitable for tactical and, above all, mobile use.

The reasons for the failure of the Enigma were : a) too few rotors, from which three were selected b) much too regular rotor indexing, too few notches per rotor c) rotor notches at different letter positions d) involutory plugboard e) double stepping anomaly of the centre rotor f) reflector does not move with the rotors, and cannot be plugged (pluggable reflector D : 1944 !) g) internal rotor wiring unchanged for more than a decade (!) until the end of the war i) unnecessary abandonment of fixed points in combination with a reflector (see below)

A hypothetical Enigma machine with 3 of 12 rotors, without double-stepping-anomaly of the centre rotor, with non-involutory plug board, pluggable, co-rotated (!) reflector, interchangeable notch rings with 11, 15 or 17 notches on each of the rotorrings used and always in the same letter positions, would have increased the key space to: 12*11*10 * 26^4 * 26^3 * 26! * 25!! = 33,802,993,397,904,090,986,291,777,145,317,755,138,867,200,000,000,000,000 (12*11*10 : rotorcombinations, 26^4 : rotor(and reflector)settings, 26^3 : ringsettings (only rotors), 26! : plugboardsettings, 25!! : pluggable reflector settings) And that corresponds to 174.5 bits. This machine could not have been cracked with the electro-mechanical resources available at the time.

Even fixed points would have been possible in the simplest way if the number of contacts of the rotors (and the reflector) had been chosen odd from the outset (preferably prime : p = 29 or 31, including the German letters Ä, Ö and Ü, or the additional five characters Ä, Ö, Ü, ẞ and ?). In this case, a single contact would have been routed out of the reflector without reflection, ensuring that the lamp of the letter whose key is currently being pressed lights up (Statistical frequency of occurrence of fixed points : (1/p)*100%). Another advantage: if the number of contacts Z of the rotors is prime, then any number of notches from 1 to (Z - 1) can be used: the period length always remains at Z^4 (without double stepping anomaly of the middle rotor). In these cases, the key space would have increased by a further 25 bits (Z = 29) or 40 bits (Z = 31) to 200 or 215 bits respectively.

It may be annoying that the fixed-point signal only passes through the rotors in one direction. But there is also a remedy for this: with a character set of Z = 31, you now use rotors with 32 contacts (2^5 ---> each odd number of notches gives the maximum period length, 1,048,576, 62 times longer that in Enigma I), a (pluggable, moving) reflector with 16 connecting bridges, and a plug board with 31 sockets on the letter-key side and 32 sockets on the rotor side. An additional socket marked in red is provided for the fixed point. According to the daily key, one of the 32 sockets on the rotor side is connected to the fixed point socket with a (red) cable. Use a further 31 (black) cables to connect free sockets on the letter-key side to free sockets on the rotor side according to the daily key. Number of connection options of the plugboard : 32 * 31! = 32!. Key space now: 12*11*10 * 32^8 * 31! * 31!! = 2,290,170,146,898,600,033,522,691,491,062,613,900,749,260,535,409,672,192,000,000,000,000,000, and that corresponds to 220.5 bits. Permissiveactionlink (talk) 08:30, 22 July 2025 (UTC)[reply]