# The Special Fish Report

## Albert W. Small (December 1944)

### Page 2

Tony Sale's
Codes and Ciphers

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CX/MSS TOP SECRET Special Fish Report Page 2

and that now existing at G.C. & C.S. We have all the elements of the story

-- in fact, many more elements than are used in the story -- and we lack

only the operational perspective to piece them together. It is a perspective

that we can hardly attain unless we ourselves do operations on an

"assembly line" basis.

(Tony Sale: Notes written in pencil)

The formula* for the Fish machine is:

(Plain + periodic key + aperiodic key = cipher)
P + X + PSI' = Z

and since arithmetic is modulo 2:

Z + X = PSI' + P

and this may be expressed by the parametric equations:

(cipher + periodic = pseudo plain)
(l) Z + X = D

(2) D + PSI' = P.
(pseudo + aperiodic = real plain)

G.C. & C.S. Fish sections are organized on the basis of these

parametric equations. Mr. Newman must solve the former, obtaining pseudo

plain text D from cipher text Z. Major Tester must solve the latter,

obtaining plain text P from pseudo cipher text D.

Operations (1) and (2) are equally important, since no plain text

can be read unless both are solved. However we can say that solution of

equation (1) has taken the greatest amount of statistical science, and is of

great primary interest to Arlington Hall. Equation (2) has taken much

knowledge of language and is of great interest as an art.

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*There is appended a list of symbols and meanings.
To give a better understanding of G.C. & C.S., it is necessary to retell much
that is already known to Arlington, and at the same time to assume a fair
knowledge of the Fish on the part of the reader.

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