# Captain Walter Fried's Fish Notes March 1944 to January 1945

### Page 7

Tony Sale's
Codes and Ciphers

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-2-
Report #F 14 (continued)

If we use logs to base e the foregoing can be approximated and simpli-
fied through the logarithmic series

How big a score in centibans should be ainad at in setting patterns?
In the first place the a priori odds tItat a given setting is wrong
vary from 597:1 (for X45) to 1270:1 (for X12). The Brttish average
this at 1000:1 for a 2 wheel run in order to avoid a separate set of
computations for each pair ot wheels. Furthermore, they adopt 10:1
as the standard of odds required of a favorable result. Therefore F
must be 10,000 in order to make it 10:1 that the settng is correct
notwithstanding a 1000:1 a priori probability or incorrectness. Since
the log of F to base 10 must be 4, a score or 400 centibans is neces-
sary. The length of message necessary to achieve this score is easily
determined.

400 = 86.86 lambda^2 n

ri = 4.6/lambda^2

400 centibans is the average for a message of this length. Therefore,
we should get a score of 400 centibans or greater just half the time.
Similarly, lambda = sqrt (4.6/n)

From this we can, if we know the characteristics of the motor or Psi
patterns, compute the bulge in Delta Pij necessary to achieve the required
degree of access with a message of length n.

ARMY SECRET

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