The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report - 9
From the table of Delta-D impulse characteristics, it is easy to see
that (1p2)= . is an admirable characteristic to "shoot for" in wheel setting
runs, since the average count of (1p2) in a 3,200 letter message set
correctly on x1x2 is 113 dots more than the number of dots expected by
random. This is 1600 + 4((1/4)*3200)^1/2 or "four sigma" above, and the
odds against this being attained in the wrong place are 1/41 x 1/31 x 33,000
(from the normal distribution tables) or 25:1. In fact, the ease of
setting 1p2/ runs has been found to be a rough measure of the ease of
solving the whole message.
Therefore in a X-wheel setting procedure, a message tape is
placed on Colossus; X1, X2, X3, X4, and X5 patterns are plugged up; the
machine is set to Delta-ize; and the counters are switched so as to
count all the occurrences of (DeltaXl+DeltaZl)+(DeltaX2+DeltaZ2)= . throughout
the message, given in turn each of the 1,271 possible initial settings of
Xl and X2; and the electromatic typewriter to record all totals which
exceed 2.5 sigma above random (which is the conventional "set total" for
Below and following is a set of Colossus runs, made in an
attempt to set message number SG 908. (These are carbon copies of the
electromatic typewriter tape.) The first such run represents 1p2/.
Colossus #3 was used. Message date was October 22; filing time, 11:28.
Total length of message, 2,683. Expected random score for 1p2/ was 1341.
Sigma of random score was 25.5 Set total was 1,404. Wheel settings are shown
for XI and X2 ("K1 K2") together with the "counter letter" and the score.
(Five counters are used at once in "multiple testing" to cut the time in one