## The Newmanry History## Part of the General Report on Tunny(1945)## Page 321 |
Tony Sale's Codes and Ciphers |

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- 44B Page 321

44B SETTING - STATISTICAL METHODS

(a) First ideas - P characteristics.

- An attempt was made early in i942 to set X's and PSI's for a message by

impulse of ordinary Tunny plain language. This was not successful but the

possibility of using this effect was again investigated. The chief difficulty

was the irregular movement of the PSI wheels, but it was hoped that the PSI' key

could be approximated to sufficiently closely by using a standard motor key

instead of the unknown true motor key. The theoretical investigation showed that

success might just be possible with ab not = 1/2 but that no success could be

expected with ab = 1/2. The reason for this was closely connected with the

predominance of changes in the PSI pattern: when the assumed setting of a PSI

wheel was one place off the true setting, the resulting sign in the assumed PSI'

key was more likely to be wrong than right.

(b) Delta-PSI' characteristics.

- In another investigation, no attempt was made to use the periodicity of the

from a consideration of the other non-random properties of the PSI' key. These

are:

- (i) All five PSI wheels have the same movement

- frequent than continuation.

These properties, it was thought, could best be expressed in terms not of

Changes and continuation in PSI' are represented by crosses and dots respectively

in Delta-PSI'.

- At this time, as in March and April, 1942, the Germans always arranged that

Delta-PSI'. Hence no statistical method could be founded, it was thought, on the

statistical properties of Delta-PSI'.

- But suppose, it was argued, that two impulses of the Delta-PSI' key, say the

PSI'2 will have a dot in each position corresponding to a dot in the motor key,

and in the positions corresponding to crosses in the motor key, the proportion of

dots will be (b)^2 + (1 - b )^2 , and the proportion of crosses 2b ( 1 - b ), if,

as an approximation we take the same value of b for each impulse. But then the

proportion of crosses in the entire sequence will be

- 2 ab ( 1 - b ) = 1 - b

will be equal to b and about 70%.

- It was deduced that the first step in any statistical method of wheel

impulses of the resulting stream of letters.

- All now depended an the properties of Delta-P1 + Delta-P2. Counts

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