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Asymptotic analysis on the normalized k-error linear complexity of binary sequences

机译：二元序列归一化k误差线性复杂度的渐近分析

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摘要

Linear complexity and k-error linear complexity are the important measures for sequences in stream ciphers. This paper discusses the asymptotic behavior of the normalized k-error linear complexity L_(n,k){s) of random binary sequences s, which is based on one of Niederreiter's open problems. For k = nθ, where 0 < 9 < 1/2 is a fixed ratio, the lower and upper bounds on accumulation points of L_(n,k)(s) are derived, which holds with probability 1. On the other hand, for any fixed k it is shown that lim_(n-∞) L_(n,k)(s) = 1/2 holds with probability 1. The asymptotic bounds on the expected value of normalized k-error linear complexity of binary sequences are also presented.
机译：线性复杂度和k误差线性复杂度是流密码序列的重要度量。本文讨论了随机二进序列s的归一化k误差线性复杂度L_（n，k）{s）/ n的渐近行为，该行为基于Niederreiter的开放问题之一。对于k =nθ，其中0 <9 <1/2是固定比率，则得出L_（n，k）（s）/ n的累积点的上下限，其概率为1。另一方面，对于任何固定的k，表明lim_（n-∞）L_（n，k）（s）/ n = 1/2且概率为1成立。归一化k误差线性复杂度的期望值的渐近界还介绍了二进制序列。

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  • 来源
    《Designs, Codes and Crytography》 |2012年第3期|p.313-321|共9页
  • 作者

    Lin Tan; Wen-Feng Qi; Hong Xu;

  • 作者单位

    Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, P.O. Box 1001-745, 450002 Zhengzhou, People's Republic of China;

    Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, P.O. Box 1001-745, 450002 Zhengzhou, People's Republic of China;

    Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, P.O. Box 1001-745, 450002 Zhengzhou, People's Republic of China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    stream ciphers; binary sequences; linear complexity; k-error linear complexity;

    机译：流密码;二进制序列线性复杂度;k误差线性复杂度;

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