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<p>The authors prove a theorem that establishes an explicit expression of the probability of the coincidence of two adjacent signs of the output sequence of an arbitrary keystream combination generator based on linear shift registers, each of which is either idle or shifts by one step in each clock cycle. The result allows us to calculate this probability directly from the known principle of motion of the linear shift registers and the Walsh–Hadamard transform of the combination function.</p>

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Analytical Expression of the Coincidence Probability of the Adjacent Signs of the Output Sequence of Keystream Combination Generator Based on Shift Registers Moving with Idle Periods

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • A. N. Alekseychuk,
  • A. A. Matiyko

摘要

The authors prove a theorem that establishes an explicit expression of the probability of the coincidence of two adjacent signs of the output sequence of an arbitrary keystream combination generator based on linear shift registers, each of which is either idle or shifts by one step in each clock cycle. The result allows us to calculate this probability directly from the known principle of motion of the linear shift registers and the Walsh–Hadamard transform of the combination function.