计算机工程

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周期为2pq的四元序列线性复杂度研究

魏万银,杜小妮,王国辉   

  1. (西北师范大学数学与统计学院,兰州 730070)
  • 收稿日期:2015-01-28 出版日期:2016-03-15 发布日期:2016-03-15
  • 作者简介:魏万银(1989-),女,硕士研究生,主研方向为密码学;杜小妮,教授、博士;王国辉,硕士研究生。
  • 基金项目:

    国家自然科学基金资助项目(61202395,61462077);教育部“新世纪优秀人才计划”基金资助项目(NCET-12-0620)。

Research on Linear Complexity of Quaternary Sequences with Period 2pq

WEI Wanyin,DU Xiaoni,WANG Guohui   

  1. (College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)
  • Received:2015-01-28 Online:2016-03-15 Published:2016-03-15

摘要:

线性复杂度是度量序列随机性的一个重要指标。基于广义分圆理论,在有限域F4上构造一类周期为2pq的四元平衡广义分圆序列。利用有限域上多项式根理论,通过分析序列的生成多项式与x2pq-1在F4代数闭包中公共根的个数,确定其线性复杂度的精确值。分析结果表明,新序列有较高的线性复杂度和较好的密码学性质。

关键词: 流密码, 伪随机序列, 广义分圆, 四元序列, 线性复杂度, B-M算法

Abstract:

Linear complexity is an important index for measuring the randomness properties of the sequences.Based on the theory of generalized cyclotomic,a new class of quaternary balanced generalized cyclotomic sequences with period 2pq over finite field F4 is constructed.Using the theory of polynomial roots over finite field,linear complexity is determined by examining the common root of generating polynomial of the sequences and polynomial x2pq-1 over the algebra closure of F4.The results show that the new sequence has high linear complexity.It is a good sequence from the viewpoint of cryptography.

Key words: stream cipher, pseudo-random sequence, generalized cyclotomic, quaternary sequences, linear complexity, B-M algorithm

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