The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report Page 99
Positions of tapes relative to each other are shown on the
run as the first four digits dawn the columns, and the scores at such
positions are shown as the last four digits. The P tape was 2,510 long.
The Z tape was 2,512 long, of which only 1,222 characters were due to the
Z text and 1,290 were blank. (That is, the crib as 1,288 longer than
the cipher.) Start and stop impulses were placed on the Z tape.
The Z tape was made two positions longer than the P tape, so that as the
two revolved side by side in the Robinson "bedstead" (tape rack), the first
position of the Z tape changed relative to the P tape by two notches each
revolution. For this reason the setting "1052" shown on the accompanying
Robinson run really means position 2 x 1052 or 2104. (This was an even
run. On odd runs the position is one less than twice the recorded position.)
In this particular crib run it should be noted that
if the first position of the Z tape was set along 2,104 positions on the P
tape, then the first 406 characters of the Z tape matched the last
406 of the P tape. The remaining 816 characters of the text (non-blank) part
of the Z tape have been matched against the beginning of the P tape
(and are therefore random) This is considered better procedure however than
to let the Z tape "run off the end" of the P tape, in which case average
random scores would have to be re-figured at each of such positions.
The random score in the sample is obviously 1/16 times 1,222 = 76.4.
Sigma is (1,222*(1/16)*(15/16))^1/2 = 8.46. A score of 114 is therefore 4.5 sigma.
This was attained in spite of the fact that only 406 characters counted
toward the causal score, whereas 816 were random!
These 406 characters actually represent 406+341 or 747 letters of