ENIGMA [|========|] WWII German Cryptograph Enigma, Ultra, cyclometer, bombas, bombes, Bletchley, Banbury, Turing. The list of names associated with the solution of the code is endless. There is certainly no intent here to slight the effort of any nation(s) or individual(s) by omitting them from this list. Indeed, there is equally no intention of extending this paper into the area, where angels fear to tread, of the several controversies which have arisen, as they always do around legends. Rather, the intent of this paper, and indeed this library of files, will be to present, on a very small scale, the Enigma as a device, and the technical factors involved in interceptions. A few of those points will be simply mentioned now, to put the entire issue in perspective, by associating the legends. 1) The question of which nation took what part, at which stage, and under what constraints, in the monumental effort. 2) The relative impact of the project on the conduct or outcome of World War II, from winning the war to incidental. 3) The often repeated, but unsubstantiated, questions surrounding the bombing of Coventry in 1940. Actually, one controversy may be of interest in computer terms. It has been reported that Great Britain, which in 1943 developed the "world's first electronic computer" (referring, of course, to COLOSSUS, though even that title is disputable), did so as an outgrowth of the earlier (electromechanical) bombas and bombes, and applied it to the solution of Enigma traffic. This report has been questioned, on the grounds that the COLOSSUS systems were used to attack the German Geheimschreibers (secret writers), more complex than the Enigma. The origin during the 1920s of the Enigma as we know it was as a commercial device, sold to German industrial and business users and in the 1930s to other nationalities as well. Poland first became aware of the device about 1927, through a weekend incident in Polish Customs involving a shipment made in error to a German firm in Poland. Later, Poland openly purchased one from the German manufacturer. The effort more often attributed to the Poles was the capturing of a military version by the underground early in the war. In any event, several European nations, including Great Britain, Poland, and France were involved during the 1930s in deciphering messages using the Enigma, with little cooperation, yet with considerable success. An early, non-plugboard version was used in the Spanish Civil War. Of course, the military version differed in some respects, notably that the reflecting drum was immovable in it, but the point here is that the Enigma concept had been studied by the Allies long before the opening of the was in 1939. The external case of the original device physically resembled a portable typewriter, though the ratio of the length of its sides differed, being long and narrow. It contained a 26-letter keyboard with flashlight-like lamps in place of the typebars, a plug-type switchboard which actually exchanged letter pairs, a battery for power, and its most important part, a shaft holding three drums (rotors), together with a fourth reflecting drum. On each drum was a ring, on which were engraved the 26 letters of the alphabet, and which could be rotated with respect to the rest of the drum. The center of each drum was an insulating disk with 26 stationary contacts on one side connected irregularly to 26 spring contacts on the other side. The drums had toothed gears to allow relative turning of one by the next one. When a key was pressed, the rightmost drum rotated 1/26th of its circumference, and current flowed through the key, through the three drums to the reflecting drum, then back again through the three drums, through the plugboard, to light the proper lamp for the enciphered letter. As encipherment continued, each successive drum in turn rotated according to a plan much like an odometer. In certain positions the second drum might rotate two positions for one complete rotation of the previous one, unlike an odometer. As this description indicates, a number of factors influenced encipherment : 1) The connections of the drums, which were a factor of manufacture. 2) The daily key, including the setting of the rings, the order of the drums on the shaft, the plugboard settings, and others. 3) The message key. This was the name applied to the initial setting of the drums, with which the current message began. It should be noted that, in early usage, the daily key was changed on a somewhat extended schedule, perhaps once each month for some. As the war progressed the daily keys were changed with increasing frequency, until it became finally apparent that the Germans suspected their traffic was being handled with some degree of success. As the war ended a new cipher machine was being introduced on the line. Clearly, the intent of such a device relies less on the device itself than on the management of its several factors. The Germans decided that each military message originator would randomly set his own message key, transmitting it in three enciphered characters at the beginning of each message. Because of the unreliability of military communications at that stage, they were transmitted twice in succession. Thus, the first six characters of each message were the message key. This gave the receiving operator the initial settings of the drums. To illustrate the complexity of the problem, the number of possible unique interconnection sets of enciphering drums is 26! (called 26 factor), or 403,291,461,126,605,635,584,000,000 , and the number of unique reflecting drum connections is 7,905,853,580,025. However, from a practical point of view, all military machines would have the same set of connections to insure universal military communications. This was the importance of capturing a military unit without the enemy's certain knowledge. Clearly, the replacement of all military units (estimated at 100,000 to 200,000) during the war would be a monumental logistic task, to be avoided unless totally necessary. Yet even the keys presented no small problem. Each enciphering drum can be set 26 different ways. With only three drums this means 17,576 possibilities and, since their order on the shaft can be changed, the combination of the two yields 105,456 possibilities. Add to this the plugboard variations (the original 6 pairs of letters was later increased to 10 pairs, leaving only 6 self-stickers of the 26 letters), and the problem increases. Note that as early as 1939 some parts of the German military used a selection of eight drums from which to draw their three and the U-boats later used a 4-drum device. Each of these geometrically increased complexity. The task at hand was statistically a gigantic one, but one which could be solved with sufficient resources, both mechanical and human. These were applied during the war in a number of locations, mostly in England from Alan Turing's organization, with its statisticians and other specialists to "the girls of Banbury," as they were known. These were the scores of young women who daily prepared the "Banbury sheets." The Banbury sheets were laboriously punched forms of daily message traffic, from which repeat patterns were derived, using weights of evidence. As history knows, it was solved, to the great benefit of the Allied war effort. I sincerely hope that this writing, though perhaps too simple for those with an interest in cryptoanalysis, has provided you with some knowledge of the nature of the Enigma and the project which the British called Ultra. The program included in this library illustrates the techniques described here. There are a number of papers and books on the subject for those who wish to pursue it, including the one from which part of this material was drawn. That article, which itself contains some bibliography, appeared in the Annals of the History of Computing, Vol 3, # 3, copyright July 1981, AFIPS (American Federation of Information Processing Societies). Permission to excerpt was granted on condition that it not be used for direct commercial advantage, and notice of copyright be included, as it is here. Therefore, the several files of this library must not be separated, and this notice must be left intact. -------------------------------------------------------------------------- This document file was originally written on July 30, 1988 by J. E. Eller, 536 Caren Drive Virginia Beach, VA 23452, (804) 340-3848. -------------------------------------------------------------------------- This version was edited, spelling corrected and grammar corrected on December 31, 1988 by Richard Bash of Combat Arms, 2869 Grove Way, Castro Valley, CA 94546, (415) 538-6544. --------------------------------------------------------------------------