General Report on Tunny

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22F Page 53

This multiplication property is first mentioned in R1 p. 20.

22F     THE KEY STREAM

	K	=   Χ +   Ψ'
	∴ ΔK	= ΔΧ + Δ Ψ'

The undifferenced Ψ' stream is flat, therefore the undifferenced K stream is random and unrecognisable statistically [(E3)]

(a) Recognising key on any limitation.

		(F1)

Differencing at distance ω_i where ω_i is the length of Χ_i (R3 p. 62)

since we are in effect adding two streams in which ΔK_ij → ΔΧ_ij with proportinal bulge β

	Now
		(F2)

Similarly, differencing at ω_i ω_j (e.g. 26 x 23 for Χ₄ and Χ₅)

(F3)

This result shows that all key maybe recognised by an excess of dots over crosses in Δ₅₉₈(ΔK₄₅). (R2 p. 90)

(b) Recognising key on Χ₂ limitation.

		(F4)

and differencing at 31(R2 p. 70) we get

(F5)

(c) Δ²K.

In cases where Δ²Χ_i and Δ²Χ_j each → x with high probability Δ²Χ_ij → dot

Now Δ²Ψ'_ij → dot

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