General Report on Tunny

23A page 78


(a) The problem of chi-setting.

The problem of chi-setting is: given the cipher Z and the chi-patterns, to find the settings of the chis relative to Z and so obtain

D ≡ Z + Χ

(b) The evidence available.

The evidence available is that of the ΔD letter count, which has non-random bulges: the method is to find settings which make these bulges as large as is possible, discriminating in favour of settings whose bulges are on the right letters. Unless the bulges are so large as to be unlikely to have occurred at random, the chis cannot be regarded as set.

(c) The ideal method.

The ideal method would be to examine the 32 letter count at all possible settings, but this means 41 x 31 x 29 x 26 x 23 = 23,561,898 letter counts.

(d) Practical chi-setting.

Practical chi-setting must be completed in a reasonable time, so that it will be necessary at each stage to set a smaller number of chis and to examine not the whole letter count, but only its strongest feature. Runs are classified as one-wheel or short, 2-wheel or long, 3-wheel, and 4-wheel.

(e) The art of chi-setting.

The art of chi-setting consists of:
         (i) choosing runs so as to obtain significant scores as quickly as possible.
         (ii) knowing how significant the scores obtained are; in particular, knowing
         when they are "good" or "certain".

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