The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report Page 100
plain text cipher text coincidence, since the 4th level of the P tape came
from delta-ing the actual P text at interval 341, and therefore the tape
is that much shorter than the real text.
Consider for a moment the results of adding the two tapes as
described page 97 and as done in the run shown. Let us call
as the sums of the P and Z tapes at any given moment. These 4 levels of
delta/31.k *Q actually represent the result of summing:
But there are really 5*4/2 or 10 sums possible in (B) of which we have shown
in (A) only 4. It is desirable to use all 10 sums in any test proposed.
Now if there are "t" dots in the 4 levels of any Delta/31.k *Q
character from(A) that means that in (B), sign Qa agrees with "t" of the
signs Qa+93, Qa+124, Qa+279, Qa+341. There are therefor in (B) really
"t+1" signs alike and like Qa and "4-t" signs alike and unlike Qa.
The number of dots in the 10 possible combinations of (B) is