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7. In all, the plain texts for parts
of some 15 fairly lengthy messages were obtained by the methods
indicated above, and these were subjected to most intensive and
exhaustive cryptanalytic studies. To the consternation of the
cryptanalysts, it was found that not only was there a complete and
absolute absence of any causal repetitions within any single message,
no matter how long, or between two messages with different indicators
on the same day, but also that when repetitions of three, or
occasionally four, cipher letters were found, these never represented the same plain text. In
fact, a statistical calculation gave the astonishing result that the
number of repetitions actually present in these cryptograms was less
than the number to be expected had the letters comprising them been
drawn randomly out of a hat! Apparently, the machine had
with malicious intent -- but brilliantly -- been constructed to
suppress all plain text repetition. Nevertheless, the
cryptanalysts had a feeling that this very circumstance would, in the
final analysis, prove to be the "undoing" of the system and mechanism.
And so it turned out! 8. In all the foregoing studies, several factors stood out. First, the basic law underlying the B-machine was of such character that the ciphering mechanisms seemed to start from certain initial settings and to progress absolutely methodically without cyclic repetition of any sort, straight through to the end of the messages, the longest of which for which plain text had been recovered comprised 1,500 letters. Secondly, two identical plain-text letters in sequence could never be represented by two identical cipher-text letters; nor could two identical plain text letters 26 letters apart be identically enciphered. This phenomenon which was termed "suppression of duplicate encipherments at the 1st and 26th intervals" formed the subject of long and arduous study, fruitless experimentation and much discussion. [...] Fifthly, two messages with different indicators on the same day (same plugboard arrangement) were absolutely different and showed no cryptographic similarities whatsoever. Sixthly, in each line of 26 letters, two identical letters could be identically enciphered except at the 1st interval, that is, identical encipherments could, and often did, occur within a line of 26 letters at all intervals, except at the 1st intervals, although this phenomenon was rare at the 2d, 3d, 4th and 5th intervals. 9. [...] In this long, exhaustive and tedious search for repeated sequences or partially repeated sequences must labor and energy was expended but it was realized that the difficulty was probably due to the paucity of the text, despite the number and length of the individual messages available for study and for which the plain text had been reconstructed. It became apparent that what would be necessary was to obtain, by some manner or other, several messages in the same indicator and on the same day, or else to convert several messages with the same indicator but on different days to the same base, before even the existence of such cyclic sequences could be detected. |