基于欧拉商的二元序列的迹表示  

Trace representation of binary sequences derived from Euler quotients

作　　者：杜小妮[1] 李芝霞[1] 万韫琦 李晓丹[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2017年第1期18-21,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61462077;61562077);教育部"新世纪优秀人才支持计划"基金资助项目(NCET-12-0620);安徽省自然科学基金资助项目(1608085MFI43)

摘　　要：基于费马商和欧拉商构造的伪随机序列均具有良好的密码学性质.本文基于有限域理论及定义对思想,确定了基于欧拉商的二元序列的定义对,并由此出发得到该序列的迹函数表示,从而确定了序列的线性复杂度.所给序列的迹函数表示为分析序列的伪随机性质提供了新的工具.Families of pseudorandom sequences derived from Fermat quotients and Euler quotients possess good cryptographic properties. In this paper, based on the theory of finite fields and defining pairs, the defining pairs of binary sequence based on Euler quotient are determined firstly, and then from which the sequences＇ trace representation is obtained. Finally the linear complexity of the sequence is given. The trace representation can provide a new tool for analyzing other pseudorandom properties of the sequence.

关 键 词：二元序列 欧拉商 费马商 定义对 迹函数 线性复杂度 

分 类 号：TN918.4[电子电信—通信与信息系统]