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 Χ_{4} and Χ_{5})

(F3) |

This result shows that all key maybe recognised by an excess of dots over crosses in Δ_{598}(ΔK_{45}). (R2 p. 90)

(b) Recognising key on Χ_{2} limitation.

(F4) |

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

(F5) |

(c) Δ^{2}K.

In cases where Δ^{2}Χ_{i} and Δ^{2}Χ_{j} each → x with high probability Δ^{2}Χ_{ij} → dot

Now Δ^{2}Ψ'_{ij} → dot

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