on different days (different plugboard arrangements into the machine) were absolutely different. Fifthly, two messages with different indicators on the same day (same plugboard arrangement) were absolutely different and showed no cryptograhic 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 interval, although this phenomenon was rare at the 2d, 3d, 4th and 5th intervals.
9. At the same time as the foregoing phenomena were being studied, intensive research was continued in an endeavor to establish primary or basic cipher sequences of the nature of those usually found in cryptographs with rotating commutators, rotors, and the like, such as in the Hebern and Enigma cryptographs, our M-134, etc. For it was inconceivable that the machine employed a multiplicity of non-repeating keys of lengths corresponding to the lengths of the messages and, moreover, theoretical considerations eliminated the possibility that running keys were being used. Somewhere, somehow, the existence of cyclically repeating keys or sequences must be uncovered before solution could be effected. But all efforts to disclose the presence of cyclically repeating sequences were fruitless. In one and only one case was there found even the slightest hint of such sequences as were being sought. In a certain English text message the letter E was found to be represented by Q, 26 letters away another E was found to be represented by Y, and again 26 letters away another E was found to be represented by V, making the sequence QYV; in the very same message the same trigaph Q Y V was found to represent three E's similarly spaced. Attempts to add to this Q Y V sequence were absolutely unavailing. In this long, exhaustive and tedious search for repeated sequences or partially repeated sequences much 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 sequence could be detected.
10. In all the thousand or more messages on hand there were but a mere baker's half dozen or so cases where there were two messages on the same day and in the same indicator. More than two had never been found and this was to be expected in a system with 120 different indicators available for selection each day. In one case of this rare phenomenon the plain text for one of the two messages was available but very little could be done even then as regards the solution of the other member of this pair of messages. For such a method of attack at least 20-25 messages all in the sane indicator and on the same day would be necessary and this was of course recognized as a perfectly hopeless expectation. There remained the possibility of converting several messages with the same indicator but on different days to the same base and while this method of attack looked extremely difficult it did not appear hopeless.
