indicators. Hence there was probably only one motor key, controlling all five PSI
The five partial motor keys, obtained from the five impulses, were therefore
compared, and it was found that the assumptions that they were all partial
descriptions of the same fundamental motor sequence led to no inconsistencies ( or
at any rate to no more inconsistencies than could be explained by rare corruptions
in the text). The five motor keys were accordingly combined to give the true
motor key. Even this was not free from ambiguities, but most of its signs were
The Research Section now tried out a number of hypotheses on the motor key,
without success, until it was noticed that the key was nearly periodic. It was
then found that it was derived from a truly periodic sequence, of period 37, by a
system of extensions just as the PSI' keys were derived from periodic sequences.
The pattern of the 37 wheel was readily determined, as was the law governing
its extension. For the "motor-key" governing the movement of the 37 wheel was
simply a sequence of dots and crosses of period 61.
41E TWO MORE DEPTHS
The cryptographic problem presented by the depth H Q I B P E X E Z M U G
had now been completely solved. The next problem was to find what changes were
made in the machine between the encipherment of different messages. For example,
could the wheel patterns be changed, if so how often were they changed? Again,
could the actual order of the wheels be changed, so that say, the 41 wheel became
the X wheel of the 3rd. impulse?
The first attack on this problem was made by attempting to set messages of
30th August 1941 and other dates close to this, on the set of wheels found for H Q
I B P E X E Z M U G, taken in the same order. In this way it was hoped that the
period of time over which these wheel patterns, with this wheel order were
valid could be determined. But these attempts at message setting all failed. An
attempt was then made to set a depth of July 3rd, the indicator letters of which
were D K T N F Q G W A O S H. This depth was usually referred to as "Waosh". Now
that a good knowledge of the type of plain language used in the traffic had
been obtained from H Q I B E E X E Z M U G, and now that it was known that keys
could be broken, depth breaking became a much more rapid and successful process
than it had been in July and August, 1941. Two passages of the depth were read,
one about 500 letters long, and the other about 300 letters long, and two possible
subtractor keys were obtained from each passage.
These possible keys were submitted to the analysis that had succeeded in the
case of H Q I B E E X E Z M U G , but the columns were now counted in three,
rather than fives. The alternative which seemed to give the most significant
results in the fifth impulse, on a width of 23, was retained in the case of each
of the passages that had been read. The information given by both passages was
now combined, and the fifth impulse was successfully broken up into a X key of
period 23, and an extended PSI key of period 59. The ambiguity in the key was
now eliminated for all five impulses. The analysis was now applied to the other
four impulses on the assumption that the wheel order was the same as in H Q I B E
E X E Z M U G, and successful results were obtained in each case. No difficulty
was then found in the determination of the motor key.
It was found that the patterns of the PSI wheels in W A O S H were
identical with the PSI wheel patterns of H Q I B P E X E Z M U G, but the
patterns of all the other wheels were different in the two depths.