## The Newmanry History## Part of the General Report on Tunny(1945)## Page 300 |
Tony Sale's Codes and Ciphers |

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- 41D Page 300

nature of the machine and of the indicator system. The first effect suggested

that the last letter of the indicator controlled the setting of a wheel of

period 23.

(b) Chis, Psis and extensions.

- The first success in the analysis or the key was obtained towards the end of

the first impulse of the key at intervals which were multiples of 41. This

suggested that this first impulse was the sum or a periodic sequence (of period

41) and of an aperiodic but non-random sequence. We here denote the periodic

sequence by X and the non-periodic sequence by PSI.

- In order to reconstruct the sequences X and PSI , the first impulse was

was made of the five consecutive characters which occupied these columns. When

two such counts were made it was found that they were closely related; by adding a

constant set of five consecutive characters to each of the five character

sequences in one of the sets of columns, the frequency count of this set could be

brought into close agreement with that of the other. It was found that these

constant five-character sequences could be so chosen as not only to bring all the

frequency counts into good agreement, but also to fit together in their proper

order to form a periodic sequence of period 41. This sequence was denoted by X

and the result of adding it to the first impulse was denoted by PSI .

- When PSI was examined with the object of determining its non-random

(1) Consecutive signs in the sequence PSI tended to be equal.

- In fact there was equality in about 3/4 of the cases.

- even when the result (i) was taken into account.

It was then seen that the X pattern could have been reconstructed by

of the method was not appreciably increased by taking five columns rather than

three. When the method came to be applied to other depths, the counts were

therefore made on sets of three consecutive columns.

- The most striking property of PSI, was that it was roughly periodic; it

replacing some dots by sequences of two or more consecutive dots, and some crosses

by sequences of two or more consecutive crosses. The PSI sequence was evidently

generated by a wheel of period 43 which sometimes moved on one place, and

sometimes stayed still when the cipher machine moved from one of its states to the

next.

- We may here introduce a slight change of notation. The extended key which

periodic sequence from which it is derived by extension.

- We have now reached the stage at which the first impulse was shown to be the

from a periodic sequence PSI of period 43. An ambiguity arose here, for the

pattern of X and PSI could both be reversed (by replacing dots by crosses, and

crosses by dots) without affecting their sum, but this was evidently of very

little importance.

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