The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report Page 101
therefore: 1/2(t+1)(t+1-1) + 1/2(4-t)(4-t -1) = T. The following table can
be made from this formula:
t T .
If at any given juxtaposition of the two tapes, we now make a count not only
of the 4-dot characters (as done in the crib run shown, for all juxtapositions)
but also of 3 dot 1 cross, 2 dot 2 cross, l dot 3 cross, and 0 dot 4 cross,
characters ("t" = 4, 3, 2, 1, 0) we can multiply such counts by the proper
T scores from the above table, and obtain the best possible scoring for
that particular given juxtaposition. This is easily done by setting the
tapes to the chosen juxtaposition, and making a "sixteen letter
count," and then grouping these letters into categories of "t," applying
the T values.
Since there are (1/2)*5*4*N or 10 N comparisons possible, the number
of dots expected at random is 5 N, and sigma is of course (2.5N)^1/2.
Thus after a crib run has been made as shown on page 98, a 16 letter count
is usually made at the juxtaposition suggested by the first run, the T score
computed, and resultant sigmage computed. If the resultant sigmage is above
that obtained from the original run, and is high (usually 5 sigma or better)
then the juxtaposition is accepted, and the key recovered from adding
crib and cipher together at that juxtaposition. In the present example
the sigmage from the 16 letter count (this count not shown) was 6.1 sigma,
so the setting was deemed proper.