Talk:Enigma machine

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)

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)

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)

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. Programmable notches in odd numbers (deutsch: "Lückenfüllerwalzen", produced in 1945, but were not introduced in service), but not 13, with all rotors having notches at the same letter positions, and which can ALSO be placed directly next to one another without any problems (if double stepping is prevented !), increase the key space even further by a factor of: (sum of i = 1 to 13 (C(26, (2i - 1))) - C(26,13) = 23,153,832. This corresponds to a further increase in the key space of 24.5 bits. A 199 bit keyspace !

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. And that doesn’t even take into account the key space for the programmable notches! Permissiveactionlink (talk) 08:30, 22 July 2025 (UTC)

Issue in lead

I have an issue with a statement in the lead, saying that Enigma was considered so secure it was used to transmit top-secret messages. This may have been true before the war and into the first year or two, but the top-level strategy that was transmitted from Hitler to his generals was completely done by Lorenz cipher starting in 1941 and completely in 1942. I'm not going to change it without consensus here, but I propose modifying it to "It was considered so secure that top-secret messages were sent via Enigma during the first half of the war." MrAureliusR_{Yell at me!} 03:38, 18 January 2026 (UTC)

As far as I am aware, that is correct. The ENIGMA was used primarily for tactical information that did not need to remain secret for long.

For information relating to strategic military planning, teletype encryption devices such as the Lorenz SZ 40 or 42, or those manufactured by Siemens – including the T43, which was theoretically unbreakable (one-time pad encryption!) – were used almost exclusively. Information regarding the orders and ‘results’ of the genocide (including that of Russian prisoners of war who were starved or murdered) was apparently NOT encrypted at all when communicated by radio, but was instead relayed by motorbike couriers.

The German leadership was ruthless, criminal and, as far as cryptography was concerned, astonishingly negligent. The experts on the German side, however, were not. They knew or suspected the problems with ENIGMA, including the naval specialists (M4 development). Yet they were largely ignored, even though new developments such as ‘gap-filling rotors’ or SG 41 show that trust in the Enigma was by then only limited.

Towards the end of the war, even experts such as Dr Erich Hüttenhain recommended that ENIGMA-encrypted messages should, for security’s sake, be subjected to a subsequent column transposition. Fortunately for Germany, of course, this all came too late; otherwise, the madness of this war would have dragged on for much longer, with even more casualties. Permissiveactionlink (talk) 16:53, 8 October 2026 (UTC)

Cycle length II

Provided that the ENIGMA MACHINE has three rotors in place, the reflector is NOT rotated, and the numbers of notches on the right-hand and middle rotors are relatively prime to 26 AND less than 13 (1, 3, 5, 7, 9, 11), that these notches are NEVER placed directly next to one another on the letter ring, and that the middle rotor always exhibits a double-stepping anomaly, the period length of the Enigma is always calculated as 26*(k - 1)*26, where k is the number of notches on the middle rotor. The number of notches on the centre and right rotors need not be identical nor appear at the same letter positions, but it enhances cryptographic security if this is the case. The ENIGMA T (5 notches per rotor) thus had a period length of 26 × 21 × 26 = 14,196, whilst the ENIGMA KD used by the German ‘Sicherheitsdienst’ (9 notches per rotor) had a period length of only 26 × 17 × 26 = 11,492. Higher numbers of notches, and particularly even notch numbers, shorten the period lengths even further and generate multiple key periods per machine key. Due to the Double Stepping Anomaly, directly adjacent notches result in +/- longer ‘pre-periods’ of rotor positions which do NOT belong to a key period, but which are nevertheless used (once per cipher) to encrypt with their key alphabets. The Double Stepping Anomaly was a serious design flaw in the ENIGMA, which only the ENIGMA G was free from, as its rotors were shifted differently. The three German naval rotors, each with two notches (!), had these notches at identical letter positions, but these were situated exactly opposite one another on the rotor ring, 13 characters apart. Hardly anyone has ever investigated this: this symmetrical arrangement of notches allows for only 13 effective ring positions relative to the rotor’s internal wiring. If two of these rotors are used for the right and middle rotor positions, the total key space of the M3 and M4 naval Enigma machines is reduced by 75% in each case! Permissiveactionlink (talk) 17:22, 8 October 2026 (UTC)