Trace Representation of r-ary Sequences Derived from Fermat Quotients

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

doi:10.3969/j.issn.0372-2112.2017.10.018

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Trace Representation of r-ary Sequences Derived from Fermat Quotients

更新时间：2025-07-16

- Trace Representation of r-ary Sequences Derived from Fermat Quotients
- Acta Electronica Sinica Vol. 45, Issue 10, Pages: 2439-2442(2017)
- 作者机构：
  
  西北师范大学数学与统计学院,甘肃,兰州,730070
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2017.10.018
  CLC： TN918.4
- Published：2017
- 稿件说明：
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DU Xiao-ni, LI Zhi-xia, WAN Yun-qi, et al. Trace Representation of r-ary Sequences Derived from Fermat Quotients[J]. Acta Electronica Sinica, 2017, 45(10): 2439-2442.
DOI：

DU Xiao-ni, LI Zhi-xia, WAN Yun-qi, et al. Trace Representation of r-ary Sequences Derived from Fermat Quotients[J]. Acta Electronica Sinica, 2017, 45(10): 2439-2442. DOI： 10.3969/j.issn.0372-2112.2017.10.018.

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

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.

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

-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.

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