二元周期序列的k-错线性复杂度研究  

Research on k-error Linear Complexity of Periodic Binary Sequences

作　　者：周建钦[1] 剌锋[1] 

机构地区：[1]杭州电子科技大学通信工程学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2011年第5期41-44,共4页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金委与中国工程物理研究院联合基金资助项目(10776077);浙江省自然科学基金资助项目(Y1100318;R1090138);上海市信息安全综合管理技术研究重点实验室开放课题资助项目(AGK2009007)

摘　　要：线性复杂度和k-错线性复杂度是度量密钥流序列的密码强度的重要指标。通过研究周期为2n的二元序列的线性复杂度,该文提出将k-错线性复杂度的计算转化为求Hamming重量最小的错误序列。基于Games-Chan算法,讨论了线性复杂度为2n-m的2n-周期二元序列的k-错线性复杂度分布情况。当(m,k)=(5,4),(6,4),(7,8),(8,2)时,分别给出了对应k-错线性复杂度序列的计算公式。对于一般的m,也可以使用该方法给出对应k-错线性复杂度序列的计算公式。The linear complexity and k-error linear complexity of a sequence have been used as important measures of keystream sequence strength.By studying linear complexity of binary sequences with period 2n,it is proposed that the computation of k-error linear complexity should be converted to finding error sequences with minimal Hamming weight.Based on Games-Chan algorithm,k-error linear complexity distribution of 2n-periodic binary sequences with linear complexity 2n-m is discussed.When（m,k）=（5,4）,（6,4）,（7,8）,（8,2）,the complete counting functions on the k-error linear complexity of 2n-periodic binary sequences are presented separately.For general m,the complete counting functions on the k-error linear complexity of 2n-periodic binary sequences with linear complexity 2n-m can be obtained using a similar approach.

关 键 词：周期序列 线性复杂度 错误线性复杂度 错误线性复杂度分布 

分 类 号：TN918.1[电子电信—通信与信息系统]