This depth was much easier to read than the earlier depths had been, for
at any stage the next letter of clear language in the less advanced message could
be predicted from the clear language already derived for the other. The messages
were in fact decoded over the entire length of the shorter message, so that the
ambiguity in the key was resolved. The practice of giving the serial number
externally and internally had ceased some weeks previously.
From this depth a length of subtractor key of 3,976 letters was
reconstructed (with a few of the letters doubtful, of course). During the
remaining months of the year 1941 the Research section were engaged in attempt to
analyse this key, and so discover the nature of the machine which had produced it.
The Germans may have noticed this breach of security, for the traffic almost
stopped for a few days, and no more true depths are on record for the remainder of
Besides the depths in July and August there were a number of "near-depths".
These were pairs of messages sent out on the same day whose indicators differed
only in one or two letters. One pair whose indicators differed only in the first
letter was decoded successfully for 20 or 30 letters on the assumption that the
two subtractor keys differed only in the first impulse. Then another pair whose
indicators differed only in the first two letters was decoded for a dozen or so on
the assumption that its two subtractor keys differed only in the first and second
It was deduced from this that the first letter of the indicator affected
only the first impulse and the second letter only the second impulse of the
subtractor key. No further positive information was obtained from near-depths at
Mention should also be made of some pairs of messages having the same
indicator, but not sent on the same day. All attempts to decode the beginnings of
these pairs failed.
With luck, we might have had at this early stage a near depth whose
indicators differed only in one or two of the last five letters. Such a depth, we
now know, should have given very important information. However no such depth
seems to have been intercepted until March 1942, except for a hopelessly corrupt
one in the January of that year.
41D KEY ANALYSED
(a) Study of Indicators
For a long time no progress was made in the analysis of the subtractor key
of the depth H Q I B P E X E Z M U G. This was due to concentration on a
hypothesis now known to be wrong - that each impulse was the sum of two or more
periodic components, the periods being small.
In fact the only positive information obtained during the rest of 1941 was
obtained by a study of the indicators used. It was found that, in any particular
month, there were two letters (apart from J) which could not appear in the twelfth
place of the indicator. This pair varied from month to month. One other fact
about the indicators was established: the letters most frequently used were those
in the middle of the alphabet, and those at the ends of the alphabet were
The reason for the latter effect remains obscure though there