# The Special Fish Report

## Albert W. Small (December 1944)

### Page 3 Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 3

Characterisation of D

To solve (1) for pseudo plain text D, it is necessary to know

the characteristics of D, as resulting from equation (2).

Individual letters of D are random in appearance, since D

results from the enciphering of plain text P by the addition of PSI' key,

the letters of which are fairly random when distributed singly.

However the successive letters of PSI' text are non-random in their pairings,

since PSI' is generated from PSI wheels which either all move with probability

of "a," or all don't move with a probability of "l-a." A letter in the

PSI' key will be repeated when the Mtotal= . ; or when the, Mtotal = x and every

one of the five signs of PSI, remains the same. Thus a double letter

in the PSI' text has a probability of occurrence of (1-a) + a(l-b)^5.

Similarly, a letter which is the exact inverse will follow a PSI' character

with a probability of ab^5.

In teletype modulo-two arithmetic, if a letter is added to

itself the result to always the teletype character "/" and if it is

added to its inverse the result is always an "8". Thus by taking each

letter of the PSI' text and adding it to a letter equal to the letter

following it, this resultant text, called Delta-PSI' text, shows a slant for

every double letter. Thus, / has a probability of occurrence of

(1 - a) + a(l - b)^5. Similarly, 8 has a probability of occurrence in

Delta-PSI' of ab^5. The probabilities of Delta-PSI' text characters are as shown

in the following table:

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