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The Enigma A and Enigma B

The very first cipher machines sold under the Enigma trademark were rotor machines, but they did not have the reflecting rotor that made the Enigma so unique.

Also, they both looked like very large typewriters, and printed their output rather than merely indicating letters with glowlamps. The Enigma B used the normal 26-letter alphabet, while the Enigma A had a 28-letter alphabet, including three accented letters for the German language, but omitting one letter of the alphabet not often used in German.

Instead, they had four rotors, used once in normal fashion, controlled by four cams, with 11, 15, 17, and 19 positions. These cams all moved one position with every letter enciphered, and a raised tooth on any one cam caused the rotor corresponding to that cam to advance one step.

Occasionally, none of the four rotors would advance between letters, and this probably made the machine appear weak. However, this kind of irregular rotor movement does eliminate the isomorph method of attack, and therefore this kind of design appears to be quite promising. Since, however, it was cams and not user-settable pinwheels that were used, an adversary knowing the sequence of raised teeth on each cam would no doubt have been able to develop alternative methods of attack on this system.

Had the machine had five rotors instead of four, then the thirty-two possible rotor motions would have exceeded the number of letters in the alphabet. With four rotors, there were at most only sixteen possible alphabets the machine could present at each step, and this could also be exploited.

A machine with ten pinwheels, all of different sizes, with the XOR from two pinwheels controlling each of five rotors? Such a machine might well have been very strong. However, the search for the ultimate in irregular rotor movements was pursued in a different direction by the Americans, resulting in an even stronger machine, the SIGABA, which we will meet later.

A late version of the Enigma, the Enigma H, was very similar to the Enigma B. A surviving specimen of the Enigma H-29, found in Hungary, has allowed a description of that machine to appear on the web, on which the outline of its design below is based.

The pinwheels were positioned in line with the rotors, giving the appearance of additional rotors on both sides of the actual rotors. On that machine, the pinwheels had 26, 27, 29, and 31 positions.

As well, only the pinwheels with 26 and 31 positions stepped for every letter; in addition to controlling the first and fourth rotors respectively, they also controlled the motion of the pinwheels with 27 and 29 positions. This was done through sensing the pins on those pinwheels at a different position from that to control the associated rotor. As well, the pinwheel drove a gear which itself had some teeth omitted on the driving end, so that the pinwheel advance would have a different sequence from the rotor advance; this means that the position of that gear would be an additional variable to control in the initial setup.

Another variation of the Enigma was the one used by the Abwehr. It was an Enigma without a plugboard, but the rotors had a large number of notches, so that the slower rotors still moved fairly often.

In the chapter of Codebreakers (not David Kahn's book, but a collection of contributions by former cryptanalysts at Bletchley Park, published by Oxford University Press) entitled "The Abwehr Enigma", it was observed that multinotched rotors created a serious difficulty for the cryptanalyst, but not quite as serious as that created by the plugboard. It was seen as peculiar - but fortunate - that the Germans did not get the idea of putting both improvements on the same Enigma. As at that time, thanks to the book Machine Cryptography and Modern Cryptanalysis by Cipher A. Deavours and Louis Kruh, it was already public knowledge that the British were doing exactly that: the Typex, which we will meet in the next section, used extra entrance rotors as a non-reciprocal plugboard (thus also gaining the advantages of the Uhr box) and highly multinotched rotors, this comment was worth a raised eyebrow when I first encountered it.

It may also be noted that the Abwehr Enigma's reflecting rotor moved as the slowest rotor during encipherment. Also, like the commercial pre-war Enigma C and D, in addition to not having a plugboard, the keyboard and lamps were connected to the rotors following the layout of the typewriter keyboard rather than in alphabetical order; thus, an Abwehr Enigma had the rotating reflecting rotor, and the multiple notches on the rotors, as its only changes from the commercial model Enigma. With one other minor, but interesting, addition: this version of the Enigma also had digits and punctuation marks printed with the letters on both the keyboard and the lampboard.

The keyboard arrangement was:

 1  2  3  4  5  6  7  8  9
 Q  W  E  R  T  Z  U  I  O

  %  ,  :  §  /  ?  &  m
  A  S  D  F  G  H  J  K

0  -  +  !  (  )  =  .  '
P  Y  X  C  V  B  N  M  L

with the punctuation marks shown here above the letters, following the usual convention, although the actual location, on both the keys and lamps of the Abwehr Enigma was below the letters. The lowercase m indicates a script capital M, presumably used as a currency symbol for the German Mark.

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