12B Page 17
A typical operation in Tunny breaking consists in using these characteristics to separate out a stream of letters such as a K-stream into its component streams (e.g. Χ and Ψ'). This may be described as the solution of an equation; in the example quoted the equation is K = Χ + Ψ'.
Several equations of this form are soluble given streams of sufficient length. In some cases the solution is a job for a linguist, in others for statistician, and mechanical aid may or may not be required.
(d) Early methods.
In the early days comparatively simple hand methods of analysis were possible. Before the QEP system was introduced indicators could be used not only to set messages on one or more wheels (when the substitution equivalents were known) but also to recognise depths and near-depths (messages with common settings on nearly all wheels) and even to break wheel patterns. With depths, near depths and partly set messages, the plain language could sometimes be inferred and a stretch of key obtained.
This key could be easily analysed as long as ab ≠ ½
|K = Χ + Ψ'|
|∴ΔK = ΔΧ + ΔΨ'|
For when, ab ≠ ½ there is a surplus of dots over crosses in each impulse of ΔΨ', and therefore it is immediately possible to deduce the pattern (or setting) of any ΔΧ from a long enough stretch of that impulse of Δkey.
These methods are described in some detail in Part 4, but the bulk of this report is designed to show the more complex methods required when wheels and indicating system were constructed so as to invalidate the more simple-minded approaches. In the pages that follow it is assumed that ab = ½, and that indicators give no information about the settings used. All methods described, apply to the Tunny machine with limitation; the only simplifications which are possible for Tunny with no limitation are trivial and easily deduceable.
12B MODERN STRATEGY.
There are three main methods of Tunny analysis each of which can (in suitable circumstances) be used for wheel-breaking or setting. The stages by which Z is broken down into Χ, Ψ', P and Motors in each method are shown diagramatically in fig. 12 (I) and listed below.
(a) 1st Method.
Stage I. Solution of Z = Χ + D. Various Χ-patterns (or settings) are tried mechanically and the correct one is distinguished by the statistical properties of ΔD.
Stage II. Solution of D = P + Ψ'. This is a hand job for a cryptographer who can recognise plain language and extended psi stream. Ψ-patterns (or settings) follow at once from the Ψ' stream.
Stage III. Solution of motor patterns (or settings), by hand from the extended psi-stream.
This method is the general method of wheel-breaking and setting when the motors are not known and Stage III is still in progress. The use of the method is limited by the minimum length required to obtain reliable chi-patterns or settings in Stage I. For chi-breaking the minimum length is