This was no longer possible; any one of the 288 Grunds might have been used and there was no way of telling which as the indicators could not be bigrammed and looked up in the K book. A certain number of bigrams could, however, be discovered in the normal way from keys not using the Grund tables - Sucker, Shark and Narwhal. If we than found a Dolphin message with two bigrams known we should be able to discover the correct Grund as follows:
| Indicators | P N B O | C D D L |
PN and BO are known so the tetragram will be A L ? ?
and the message decodes at B
R G D.
The correct Grund will have the pairing A = B in the first alphabet and the
L = R in the second; of the 288 Grunds 11 will have A = B and 11 L = R and
only one both; this will be the correct Grund and at it the set-up can be
transposed and 2 further bigrams known. If only one bigram is known, i.e.
if the tetragram is A ? ? ? there will, of course, be 11 possible Grunds but
it is possible to discriminate between them: if the set-up is transposed at
all 11, we have 11 possible tetragrams and the first 3 letters of the tetragram,
if looked up in the K book, must give an encircled number which, in the case
of the correct Grund, will coincide with the column of the Grund table in
which the Grund occurs - this is implicit in the system of Grund indication.
By this method the right Grund should be discovered though as often as not
there will be a second possible answer; thus 1 or 2 values will be found for
3 further bigrams, if 2 an attempt to confirm or contradict one of the alternatives
has to be made as soon as possible.
If this process was to be a practical proposition the alphabets for all known Grunds had to be listed daily for both keys and sorted into a convenient catalogue form; this very large job was undertaken by Mr. Freeborn's Section. If the April Grund sheet had remained in force in May, the catalogue would have had to cover nearly all the 288 Grunds but as both tables were new on May 1st it would cover only such Grunds as could be broken between May 1st and May 5th.
We were never to know how this scheme would have worked in practice. At the beginning of the month we set to work to obtain as many Grunds as possible before May 5th and extremely successful use was made both of Hypo in America and of the now very large amount of machinery for breaking individual messages in this country. Presumably owing to difficulties of distribution, the bigram tables did not change on May 5th and few days later work was stopped when we heard that the Grund tables had been captured.
The subsequent surrender of cypher material revealed that the problem was worse than we believed as the number of bigram tables had been increased from 9 to 15: also the Grund tables were due to
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