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 war 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.

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This document file was originally written on July 30, 1988 by J. E. Eller,
536 Caren Drive Virginia Beach, VA 23452, (804) 340-3848.
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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.
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