HAM Radio 1/HamRadio.cdr/tech/enigma/enigma_2.doc

Text File | 1979-12-31 | 9.4 KB | 152 lines

                                    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 to slight here
     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  surround-
     ing 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 COLOSSI were used to attack the
     German  Geheimschreibers  (secret writers),  more complex  than the
     Enigma.

        The origin during the 1920's, of the Engima as we know it was as
     a commercial device, sold to  German industrial and business users,
     and indeed  in the 1930's  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 1930's
     in deciphering messages using the Engima,  with little cooperation,
     yet  with  considerable success.   Indeed, 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 1939, the war's opening.

        Physically, the external case of the original device 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, finally, 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.
     Actually,  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, 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, 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, they were changed with increasing frequency,
     until finally, it became 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, i.e. 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!,
     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, then, is 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.   Even  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-steckers of the 26 letters), and the problem increases.  Then,
     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 organisation, with its
     statisticians  and other specialists  to "the girls" of Banbury, as
     they were known,  the scores of young women  who daily prepared the
     "Banbury sheets".   These were  laboriously punched forms  of daily
     message  traffic,  from which  repeat patterns were derived,  using
     "weights of evidence".  And,  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  Engima,  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.

     J. E. Eller    536 Caren Dr    Va.Beach,VA 23452    [phone]