基于费马商的r元序列的迹表示

doi:10.3969/j.issn.0372-2112.2017.10.018

电子学报 ›› 2017, Vol. 45 ›› Issue (10): 2439-2442.DOI: 10.3969/j.issn.0372-2112.2017.10.018

基于费马商的r元序列的迹表示

杜小妮, 李芝霞, 万韫琦, 李晓丹

西北师范大学数学与统计学院, 甘肃兰州, 730070

收稿日期:2016-01-20 修回日期:2017-03-17 出版日期:2017-10-25
- 作者简介:
- 杜小妮,女,生于1972年,甘肃庆阳人.2000年毕业于兰州大学,并于2008年获西安电子科技大学密码学博士学位.现为西北师范大学数学与统计学院信息研究所副所长,博士生导师.主要研究方向:密码学、编码理论和信息安全.E-mail:ymldxn@126.com;李芝霞,女,生于1989年,甘肃兰州人.现就读于西北师范大学数学与统计学院,主修专业:密码学.E-mail:243248347@qq.com
- 基金资助:
- 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）

Trace Representation of r-ary Sequences Derived from Fermat Quotients

DU Xiao-ni, LI Zhi-xia, WAN Yun-qi, LI Xiao-dan

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Received:2016-01-20 Revised:2017-03-17 Online:2017-10-25 Published:2017-10-25

摘要/Abstract

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.

关键词: r元序列, 费马商, 离散傅里叶变换, 迹表示

Abstract: 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 new tool for analyzing the pseudorandom properties of the sequences.

Key words: r-ary sequences, Fermat quotients, discrete Fourier transform, trace representation

中图分类号:

TN918.4

杜小妮, 李芝霞, 万韫琦, 李晓丹. 基于费马商的r元序列的迹表示[J]. 电子学报, 2017, 45(10): 2439-2442.

DU Xiao-ni, LI Zhi-xia, WAN Yun-qi, LI Xiao-dan. Trace Representation of r-ary Sequences Derived from Fermat Quotients[J]. Acta Electronica Sinica, 2017, 45(10): 2439-2442.

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基于费马商的r元序列的迹表示

Trace Representation of r-ary Sequences Derived from Fermat Quotients

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