The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report Page 27
Thus a wheel-breaking run on Colossus is merely a means of
converging into a pattern from any given data, by crude convergence, and
using Colossus as a rapid adding machine.
It is necessary at this time to describe the decibanning of a
Let: r = total number of values of Delta-Z ipj looked at in converging
one given character of the unknown wheel.
r/2 + x/2 = number of dots counted.
r/2 - x/2 = number of crosses counted.
x = excess of dots over crosses.
Therefore "x" is the score given in the wheel-breaking run: the "pippage"
for any given character of the unknown wheel.
Now the factor that the wheel was originally a dot in the
character giving the score x, are estimated as:
Therefore (r+x)/(r-x) is the "value of a pip" (numerically) for that particular
character of the wheel.
It is impossible to evaluate this for each character each time;
so the average value may be considered as an estimate:
R + X
R - X
wherein R = Sum ri or the total number of letters looked at in the whole run;
end X = Sum |xi| if we assume the best possible score to be the true score.