基于费马商的r元序列的迹表示  

Trace Representation of r-ary Sequences Derived from Fermat Quotients

作　　者：杜小妮 李芝霞 万韫琦 李晓丹 

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：《电子学报》2017年第10期2439-2442,共4页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61462077;No.61772022);安徽省自然科学基金(No.1608085MF143);上海市自然科学基金(No.16ZR1411200)

摘　　要：基于费马商构造的伪随机序列均具有良好的密码学性质,本文根据有限域上迹函数理论及陪集理论,通过确定基于费马商构造的r元序列的离散傅里叶变换,研究得到该序列的迹函数表示.所给出的迹函数表示不仅对序列的工程实现有重要意义,而且对分析序列的其他伪随机性质提供了新的工具和方法.Families of pseudorandom sequences derived from Fermat quotients possess good cryptographic properties.In this paper,based on the theory of trace function in the finite field and cosets,we firstly determine the discrete Fourier transform（ DFT） of the r-ary sequences derived from Fermat quotients. Then from which we obtain the sequences＇ trace representation. The trace representation we determined plays an important role in the engineering realization of the sequences,and also provides a newtool for analyzing the pseudorandom properties of the sequences.

关 键 词：r元序列 费马商 离散傅里叶变换 迹表示 

分 类 号：TN918.4[电子电信—通信与信息系统]