三元
3n
周期序列的
k
错线性复杂度的性质

doi:10.3969/j.issn.0253-2778.2015.02.003

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (2): 107-111.DOI: 10.3969/j.issn.0253-2778.2015.02.003

三元 3n 周期序列的 k 错线性复杂度的性质

唐淼

1.安徽农业大学应用数学系,安徽合肥 230036；2.合肥工业大学数学学院, 安徽合肥 230009

收稿日期:2013-03-12 修回日期:2014-05-28 出版日期:2015-02-28 发布日期:2015-02-28
通讯作者: 开晓山
作者简介:唐淼,男,1981年生,硕士/讲师. 研究方向:编码与密码. E-mail: tangmiao@ahau.edu.cn
基金资助:
安徽省自然科学基金(1208085MA14)，安徽农业大学数学学科建设专项（2014XKJS-307）资助.

Some properties of the k -error linear complexity of ternary 3n -periodic sequences

TANG Miao

1.Department of Applied Mathematics, Anhui Agricultural University, Hefei 230036, China; 2.School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received:2013-03-12 Revised:2014-05-28 Online:2015-02-28 Published:2015-02-28

摘要/Abstract

摘要： 周期序列的线性复杂度和k错线性复杂度是衡量流密码系统的安全性能的两个重要指标.讨论了有限域F3上的3n周期序列的k错线性复杂度，得到了关于该类序列的k错线性复杂度和差错序列之间的一些性质.并且利用这些性质导出了一个结论，该结论显示了关于3n周期序列k错线性复杂度的计算如何转化成关于3n－1周期序列k错线性复杂度的计算，n为任意的正整数.

关键词: 流密码, 周期序列, 线性复杂度, k错线性复杂度, 差错序列

Abstract: Linear complexity and k-error linear complexity of periodic sequences are two important security indices of stream cipher systems. The k-error linear complexity of 3n-periodic sequences over the finite field F3 was discussed, and some of its properties and error sequences were obtained. By means of the properties, a result was presented, showing how the computation of the k-error linear complexity of a sequences with period 3n can be reduced to the same computation for sequences with period 3n－1, for any positive integer n.

Key words: stream cipher, periodic sequence, linear complexity, k-error linear complexity, error sequence

唐淼，开晓山. 三元 3n 周期序列的 k 错线性复杂度的性质[J]. 中国科学技术大学学报, 2015, 45(2): 107-111.

TANG Miao, KAI Xiaoshan. Some properties of the k -error linear complexity of ternary 3n -periodic sequences[J]. Journal of University of Science and Technology of China, 2015, 45(2): 107-111.

三元 3n 周期序列的 k 错线性复杂度的性质

Some properties of the k -error linear complexity of ternary 3n -periodic sequences

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