known, and the only independent information that would suffice seemed to be a
knowledge of one of the X patterns, or of a number of alternatives for such a
pattern. The only way of getting a length of key with this additional
information, seemed to be by the study of a near depth, for which the two
indicators concerned differed only in the last five letters. The Germans could not
be relied upon to send such near depths at the rate of one a month.
It seemed possible that a pair of messages whose indicators differed
only in one of the first five letters, so that only one PSI wheel was differently
set in the two messages, might also be breakable. However there was never any
occasion for the Research Section to attempt the feat of breaking such a pair.
One possible line of research would have been the search for a new method of
breaking into a length of key, so that wheel patterns might again be derived from
true depths. It was not until July, 1942 that such a method was discovered,(by
Even such a method would have been useless in the case of a month in which
no depth had been sent, and there had been several much months.
(b) Idea of using indicators for breaking the wheels, May, 1942
The Research Section sought therefore for a method of machine breaking
independent of depths. It seemed possible that such a method could be developed
from a study of the indicators and first few cipher letters of a sufficiently
large number of messages. Even if the process was not carried on to completion it
might give the pattern of a single X wheel and thus permit the breaking of a
machine when a depth was available.
A study of the May messages was therefore began as soon as about 10 days
traffic had accumulated. The workings have not been preserved, but similar
workings for June still exist.
(c) The first experiment
In the first experiment which was made, the fifth impulse of the second
letter of each cipher message was tabulated against the fifth and twelfth
indicator letters, corresponding to the fifth PSI, and X wheels respectively. The
row, and also the columns, were lettered in order from A to Z, excluding J, which
had never been used is an indicator letter. The fifth impulse of the second
letter of a cipher message was entered in the row whose letter was the PSI
indicator, and the column whose letter was the X indicator. Several hundreds of
messages were used.
Many of the 625 squares contained more than one entry, but it was very rare
to find two different signs in the same square. This confirmed the assumption
that almost all the messages began in the same way, and also showed that the
setting of the PSI wheel for the second letter was fixed uniquely by the PSI
indicator. A very similar effect was found when the fifth impulse of the third
cipher letter was tabulated in the same way, but when the fifth impulse of the
fourth letter was tabulated, very many cases of different signs appearing in the
same square were found. It was deduced that the movement of the PSI wheel
was the same for all messages up to the third letter, but that between the third
and the fourth letters the wheel could either advance one place or else stay