12D Page 22
12D MOTOR AND PSI BREAKING AND SETTING Solution of D = P + Ψ'.
(a) Psi-breaking and setting by hand.
When chi-wheels and settings for a message are known the chi stream and Z stream can be added together and de-chi stream found. A stretch of de-chi can be converted by eye into the sum of P and psi by a skilled cryptographer with knowledge of "Tunny-German" and the power of instantaneous mental addition of letters of the Teleprint alphabet.
A start can be made as follows : it is very likely that somewhere in every message a full-stop (say 5M89) in P will occur at the same place as a long extension of the psis (say TTTT). Experienced men know at sight that
|JNKH =||5M89 + TTTT|
|NJ3W =||5M89 + QQQQ|
|Part of the de-chi stream (data)||:||C||Q||P||Q||V||B||G||Q||F||F||Y||J||E||B||4||L||T|
|P stream (inferred)||:||9||I||N||F||5||M||8||9||D||I||V||5||M||8||9|
|Ψ' stream (inferred)||:||R||Z||G||G||S||S||S||W||9||J||J||T||X||I||I|
From Ψ' obtained in this way the unextended psi is easily found. If there are 59 letters of it, the sequence will give us the complete pattern of dots and crosses on psi 5 (unconfirmed) and a complete pattern (partly confirmed) on the other psis. Fewer letters of psi (about 10) are required to find the settings of wheels whose patterns are already known.
As the dottage and number of extensions increases, reading a de-chi becomes correspondingly easier although more letters of Ψ' are required to give an adequate stretch of psi.
(b) Motor-breaking and setting given ΔΨ'.
When the psi patterns (or settings) for some point in a message have been found, it is necessary
(i) To find the psi settings for the start of the message.
(ii) To recover a sufficiently long stretch of Ψ' to enable the motor patterns (or settings) to be determined.
In order that motor settings for the beginning of the message may be found directly, these two jobs are usually done in unison. The approximate psi settings for the start of the message may be calculated and the psi stream generated. This can be fitted on to the de-chi stream and used to separate into P and Ψ' a longish stretch of de-chi near the start - the psi being extended wherever this is required to make sense of the P.
When a longish stretch has been read the motor can be worked out. The Ψ' shows where the TM dots occur. There is a BM dot at all these places and a BM cross at every other place which has a limitation cross, the character of the limitation being determined since chi, psi and P are known.
Consequently, certain dots and crosses in the BM stream can be placed: when enough have been placed it is possible to find a unique pattern of motor wheels (or a unique position of motor wheels) which will fit these BM dots and crosses without contradiction.
The length of Ψ' required depends on the dottage; the normal minima are 300 letters for motor breaking and 120 letters for motor setting.
(c) Motor and psi-settings by machine.
It has already been shown that a ΔD count consists of the sum of the count against TM dots, where ΔD = ΔP, and the count against TM crosses which is nearly random. The strong letters in ΔD therefore derive a proportion of their strength from BM dots which is greater than the proportion of BM dots in the whole message. We can therefore - in favourable