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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (3): 24-31.doi: 10.6040/j.issn.1671-9352.2.2016.108

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一类新的周期为p3的GF(l)上广义割圆序列的线性复杂度

刘龙飞,杨晓元   

  1. 武警工程大学网络与信息安全武警部队重点实验室, 陕西 西安 710086
  • 收稿日期:2016-08-18 出版日期:2017-03-20 发布日期:2017-03-20
  • 作者简介:刘龙飞(1990— ),男,硕士,讲师,研究方向为流密码和编码. E-mail: ya_zhou_521@163.com
  • 基金资助:
    国家自然科学基金资助项目(61562077,61462077);国家社会科学基金资助项目(16BTJ033);武警工程大学基础研究基金(WJY201518);武警工程大学军事理论研究项目(JLX201648)

On the linear complexity of a new generalized cyclotomic sequence with length p3 over GF(l)

LIU Long-fei, YANG Xiao-yuan   

  1. Key Laboratory of Network &
    Information Security of Armed Police Force, Engineering University of Armed Police Force, Xian 710086, Shaanxi, China
  • Received:2016-08-18 Online:2017-03-20 Published:2017-03-20

摘要: 线性复杂度是度量序列随机性的一个重要指标。基于Ding-广义割圆序列,构造了GF(l)上一类新的周期为p3的广义割圆序列(其中l为一奇素数h的幂),且该序列为平衡序列,并通过有限域上的多项式理论确定了该序列的线性复杂度。结果表明,该类序列具有良好的线性复杂度性质,以它们做密钥流序列的密码系统具有抵抗B-M算法攻击的能力。

关键词: 密码学, 流密码, 伪随机序列, 线性复杂度, 广义割圆类

Abstract: Linear complexity is the most important index for measuring the randomness properties of sequences. Based on the Ding-generalized cyclotomy, a new class of generalized cyclotomic sequences with length p3 over the finite field of power of odd prime order is constructed, and the sequence is balanced. The linear complexity of the sequences is determined using the theory of polynomial over finite field. It is shown that the sequence has good linear complexity, and it can resist attacks from the application of the Berlekamp-Massey algorithm.

Key words: pseudo-random sequence, generalized cyclotomy, cryptography, linear complexity, stream cipher

中图分类号: 

  • TP309
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