Z_(4)上两类具有最优自相关四元序列的线性复杂度研究  

On the Linear Complexity of Two Classes of Quaternary Sequences over Z_(4)with Optimal Autocorrelation

作　　者：赵璐 刘春红[2] 杜蛟[3,4] 曹天庆 ZHAO Lu;LIU Chun-hong;DU Jiao;CAO Tian-qing(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China;College of Computer and Information Engineering,Henan Normal University,Xinxiang,Henan 453007,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang,Henan 453007,China;Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University,Xinxiang,Henan 453007,China)

机构地区：[1]天津工业大学数学科学学院,天津300387 [2]河南师范大学计算机与信息工程学院,河南新乡453007 [3]河南师范大学数学与信息科学学院,河南新乡453007 [4]河南师范大学大数据统计与优化控制河南省工程实验室,河南新乡453007

出　　处：《电子学报》2021年第4期631-636,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61701343,No.11971004);河南省重点研发与推广专项(科技攻关)(No.202102210163);河南省高等教学改革研究与实践(No.2019SJGLX033Y)。

摘　　要：线性复杂度是序列密码中重要的安全性指标.针对Z_(4)上两类具有最优自相关的四元序列,对其线性复杂度进行研究.利用Galois理论,分别得到了由Legendre序列、双素数序列及广义GMW序列构造的四元序列线性复杂度的精确值.The linear complexity of quaternary sequences plays an important role in stream ciphers.In this paper,we investigate the linear complexity of two classes of quaternary sequences over Z_(4)with optimal autocorrelation.Furthermore,by the theory of Galois rings,the exact value of the linear complexity of sequences constructed from Legendre sequences,twin-prime sequences and generalized GMW sequences are derived,respectively.

关 键 词：密码学 线性复杂度 四元序列 GALOIS环 

分 类 号：TN918.4[电子电信—通信与信息系统]