# General Report on Tunny

22A Page 45

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22   STATISTICAL FOUNDATIONS
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 22A Introductory 22B The Chi Stream 22C The Motor Stream 22D The Psi Stream 22E The Sum of Two Streams 22F The Key Stream 22G The Plain Language Stream 22H The De-chi Stream 22J The Cipher Stream 22K Sampling Errors in Alphabetical Counts 22W Some further Streams 22X The Algebra of Proportional Bulges 22Y The Amount of Evidence derived from a Letter Count

22A     INTRODUCTORY

Statistical methods of Tunny breaking are possible because (and only because) cipher, plain, key, chi, extended psi, de-chi and motor streams can - with suitable treatment - be made to exhibit marked characteristics which will distinguish them from a random sequence of letters. In this chapter we analyse these characteristics, and in subsequent chapters we show how they are exhibited.

(a) Notation.

The letters Z, P, K, Χ, Ψ', D are used to denote the operative letters of the Cipher, Plain, Key, Chi, Extended psi and de-chi Streams at any given ciphering position. They are connected by the equations:

 Z = P + K K = Χ + Ψ' D = Z + Χ = P + Ψ'

The suffixes 1, 2, 3, 4, 5 are used when a particular impulse is specified so that (using a generalised form) Ui denotes the operative