The theory of message setting which was attempted in March, 1942, after the
breaking of the first three depths is simple. It had been observed from these,
and from depths that had only been decoded for a few letters, that most
messages contained the group S P R U C H 9+ + or S P R U C H N U M M E R 9++
either right at the beginning or else preceded only by such groups as 89. or + +
Z Z Z 8 8 9. In most attempts at message setting therefore, the groups S P R U C
H N U M M E R 9 + + or + + Z Z Z 8 8 9 8 S P R U C H were assumed as the clear
language in some position near to the beginning of the message. After the group 9
+ + the serial number of the message would be given in letter form. When this was
also given in the clear preamble the crib could be extended a little if necessary.
(This practice of giving the serial number in clear soon ceased.)
By adding the assumed clear language to the cipher text, a length of about
15 letters of possible keys was obtained. Each impulse of this was treated in the
following way. First the corresponding X wheel was added in all possible
settings, and then attempts were made to fit the PSI pattern, suitably extended,
to each of the set of sequences of dots and crosses thus obtained. Usually there
were two or three sequences which could be interpreted as extended parts of the
PSI patterns.
The possibilities were limited by the nature of the PSI patterns, which
contained so few singleton dots or crosses. A sequence containing several
singletons could be rejected at once.
After this process had been gone through for the five impulses the results
were compared to see if the same motor key could be fitted to five of the
possibilities, one in each impulse. If so, a possible setting or the 10 X and
PSI wheels had been obtained. It was finally tested by an attempt to decode more
of the message. This test depended on the principle that a message can be decoded
even when the motor key is unknown, provided that the other ten wheels are
correctly set. For suppose we have decoded a message up to the nth letter.
Then there are only two possibilities for the nth sign of the motor key, namely
cross and dot, and the ( n+1)th sign of the subtractor key can readily be
calculated for each possibility. By applying these two subtractor letters we get
two alternatives for the (n+1)th clear letter, and considerations of sense are
usually sufficient to decide between them. Thus the message can be decoded letter
by letter, the motor key being built up sign by sign at the same time.
For a long time the would be setters had no success, but at last came the
great day when the first single message was set and decoded.
By the end of April several other July messages had been set, and the
Research section was in a position to attack the July indicator system. But then
some messages were broken which were only about a month old. The message setters
thereupon forgot all about July 1941 and concentrated on March, 1942.
42B MACHINE BREAKING FOR MARCH 1942
(a) Depths in February
Interest in current traffic dormant for six months, revived at the end of