12E Page 23
circumstances - select the correct motor settings by trying each pair of settings in turn and choosing those at which the frequency of the strongest ΔD letters against BM dots is a maximum.
With Χ2 limitation, the extended psi pattern corresponding to each possible settings of each psi is known as soon as the motors have been set, and the correct setting of each psi can be recognised by the marked characteristics D + Ψ' = P in each impulse. For unlike ΔD, which has an equal number of dots and crosses in each impulse as long as ab = ½, P1, P2, P4, P5 normally have an excess of dots and P3 an excess of crosses sufficient for it to be possible to set at least one psi wheel independently of the others.
For psi 1 (or P5) limitation a similar method can be used, provided psi 1 (or psi 5) are set first and no effort is made to set the other psis until the pattern of the Total Motor has been completely determined.
Colossus is designed to carry out both these jobs.
12E METHODS INVOLVING KEY Solution of Z = K + P, and K = Χ + Ψ'.
(a) Obtaining of key from depths.
As the key stream is the same for both messages (a and b) of a depth, we get
| Za + Pa = K = Zb + Pb |
| ∴Za + Zb = Pa + Pb |
Za and Zb are known. Za + Zb can be found by addition and a skilled cryptographer can separate this out into the sum of two stretches of plain language.
Example:
| Za | = | A O 9 V Y P B 8 S L K N 9 I I / P R 8 Y Q A H V 8 | |
| Zb | = | N N R Z Y A P Q U F C L I N C 3 A 4 L P 8 / K 9 Z | |
| Za + | Zb | = | K H C K / Y K 3 4 8 Y V 4 R 3 3 Y 3 F A 3 A 5 G C |
| Pa | = | 5 Q M 8 9 E N G L 5 M 8 9 I N F 5 M 8 9 D I V 5 M | |
| Pb | = | H A L T 9 H A L T 9 D E I N 9 S C H L U E S S E L |
from Za and Pa the stretch of key is found by addition.
(b) Obtaining of key from cribs.
At certain times in the history of Tunny certain routine reports were sent out from the "Berlin" end of two or more different links from the same P-tape. It may be possible to identify retransmission of this type from serial receipts and other forms of unciphered operators' chat before either version has been decoded, and as soon as one version has been decoded it is comparatively easy to do so.
When the report has been decoded on one link it is possible to find the point in the Z of the undeciphered link at which the P from the known decode starts. This is done by trying the various possible positions (on a Robinson) and testing P + Z at each position for the statistical characteristics of ΔK.
(c) Wheel-breaking from key.
Chi-breaking from key is analogous to chi-breaking from Z, the method being to select the patterns of ΔΧ wheels which will give the strongest count for ΔΨ'. It is, in fact, equivalent to chi-breaking from Z when the P-stream consists entirely of strokes.
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