It was argued that if a pair of messages (a,b,) with the same indicators
were really in depth, the sum of the two cipher messages must be equal to the sum
of the two clear messages, it being assumed that the cipher was a letter
Now when the sums Za + Zb were formed for a number of depths of two it was
noticed that some pairs of them began with the same sequence of five or six
letters. This was regarded as a proof of the assumptions that had been made,
namely that the cipher was a letter subtractor, and that the law of addition had
been inferred correctly. The effect would be expected to arise if stereotyped
beginnings were being used.
The proof was completed when about 15 letters of one of the depths were
decoded. When a group ++zzz88, which had appeared occasionally in clear preambles
was tried as the clear of one message, the clear of the other message, came out as
the first letters of the word S P R U C H N U M M E R (serial number).
41C A DEPTH READ
(a) Problems of depth reading
The first attempts to reconstruct long key-sequences from depths of two were
failures. Depth breakers then had no previous experience of the traffic, and so
depth breaking was much slower and much more difficult than it was in later years.
Apart from this there was one very serious obstacle in an ambiguity which is
inseparable from a depth of two.
For in the process of depth breaking the first step is to construct the
sequence Za + Zb , and then to express this as the sum of two passages of plain
language, which are assumed to be Pa and Pb . But there is usually no way of
telling which of the passages is Pa and which is Pb . It can be done when cribs
to the messages are known; for example, as in the early days when the serial
numbers were given both internally and externally: and it can also be done when
the decoding process is carried on to the end of the shorter message, for then the
clear message which comes to an end must be associated with the shorter cipher
message. But it cannot be done by the depth breaking process alone, without
In the depths which were first attacked, the clear language obtained was not
continuous, and the short sequences obtained could not be correlated with one
another, so the ambiguity arose fresh in each section.
It is not surprising therefore that for some time little progress was made
with the "Tunny" cipher. The construction of long pieces of key was very
difficult, and even when it was possible the results were not unique.
(b) The depth "HQIBPEXEZMUG"
On 30th August, 1941 the German cipher operators came to the rescue.
On that date two very long messages, with the same indicators HQIBPEXEZMUG
were sent out from the same end of the link. When a depth was broken into, it was
found that the messages were essentially the same, but the spacing, the mis-
spellings and the corrections were different. Evidently the same message had been
typed out twice, by hand. As a result the two versions, at the same number of
letters from the beginning, would be at slightly different places in the true
text of the message. This divergence increased slowly, until at the 3,976th
letter, where the shorter message came to an end, it had increase to more than one