# The Special Fish Report

## Albert W. Small (December 1944)

### Page 65

Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 65

cross. In such case, the distance between the two corresponding stretches

of recovered psi is known, and it may be possible from the two stretches

together to fit in all the psi wheels.

As soon as all five psi's are set uniquely, the worksheets are sent

into the "setters' room"* where they compute the approximate position

of the psi's at the beginning of the message, type out a PSI' stream on a

Tunny machine, and drag this stream through the beginning of the message

until they have established the original starting point of the psi's.

Then they decipher about 120 letters of text by anagramming, with which

to set the motor wheels.

On page 63 a table for (DeltaPSI')A plus (DeltaPSI')B characteristics was
discussed.
The mathematics leading to the tables, and the tables themselves, follow:

It is known that: (Assuming M37=20 dots.)

P(0 crosses in DeltaPSI') = 1-a + a(1-b)^5 = .273 = A0

1/5*P(l crosses in DeltaPSI') = ab(l-b)^4 = .005 = A1

1/10*P(2 crosses in DeltaPSI') = a(b^2)(l-b)^3 = .011 = A2

1/10*P3 = .023 = A3

1/5*P4 = .050 = A4

P5 = .110 = A5

And therefore, since we are after the sum of two delta-psi-

prime streams:

*The room where the original psi setting had just been found for a stretch of
guessed-in plain-text, is called the "breakers' room." This is probably due to
the fact that even when psi patterns are known, it is necessary to "break" a
stretch of psi prime, before psi wheels can be matched to it. But "setters"
have only to set the psi wheels at the beginning of the message, and then set
the motor wheels.

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