The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report page - 8
In the preceding table, "Expected sigmage" is the excess
of the average observed causal score over random score, divided by
random sigma. The variance of such sigmage is assumed to be the
sum of the variances of the sigmages of the letters involved. (These
individual variances are in turn the mean square deviation-from-average-sigmage
in the 16 messages.) The "estimated standard deviation" is the square root
of the variance so computed. "Actual standard deviation of sigmage" is
computed from sigmages recorded in runs.
It might almost be said that the whole story of the Newmanry is
told in the preceding table, and for this reason such a table deserves
close scrutiny. Different traffic networks would or course have different
tables, and while such have not been computed for all cases where they
are needed, they exist in the minds and experience of the Colossus operators.
A thorough knowledge of Delta-D characteristics is needed either for
setting known X wheels or for breaking unknown wheels.
Setting known X's is of course easier. In an ideal world the basis
for setting them would be to "run" all positions of Delta(X1, X2, X3, X4, X5)
against Delta-Z text; and to match the resultant Delta-D text against the
theoretical distribution. Where the match would be greatest, there would be
the most probable answer. Since 41x31x29x26x23 settings would require a
run of the Z tape 22,041,684 times through Colossus, this is obviously impossible
on today's machinery. Compromises must be found. Accordingly the X's are
set in smaller combinations rather than in toto; and this is the reason the
table of Delta-D impulse combinations is so important. Any run involving the
setting of two X wheels at once is called a "long run;" any involving the setting
of only one X wheel is called a "short run". The average long run takes 8
minutes* as against 2 minutes for a short run.
*Utilising five counters in "multiple testing" to cut the time in one fifth.