m序列频谱免疫度的研究

doi:10.3778/j.issn.1002-8331.1603-0207

计算机工程与应用 ›› 2017, Vol. 53 ›› Issue (16): 74-78.DOI: 10.3778/j.issn.1002-8331.1603-0207

m序列频谱免疫度的研究

胡建勇1，张文政1，陈克非2，董新锋1

1.保密通信重点实验室，成都 610041
2.上海交通大学，上海 200240

出版日期:2017-08-15 发布日期:2017-08-31

Research on spectral immunity of m-sequences

HU Jianyong1, ZHANG Wenzheng1, CHEN Keifei2, DONG Xinfeng1

1.Science and Technology on Communication Security Laboratory, Chengdu 610041, China
2.Shanghai Jiaotong University, Shanghai 200240, China

Online:2017-08-15 Published:2017-08-31

摘要/Abstract

摘要： 频谱免疫度是度量周期序列抵抗离散傅里叶频谱攻击的重要指标。周期序列的频谱免疫度越大，抵抗离散傅里叶频谱攻击的能力越强。通过搜索[m]序列的零化子，计算其频谱重量，提出猜想：[n]级[m]序列的零化子最低频谱重量是[n+1]，而该[m]序列的补序列恰恰是其一个最低频重零化子。研究了[m]序列零化子及其补序列的性质，从理论上证明了该猜想。分析了[m]序列补序列的零化子性质，得出结论：[n]级[m]序列的频谱免疫度为[n]；说明了[m]序列难以抵抗离散傅里叶频谱攻击。

关键词: m序列, 频谱免疫度, 零化子, 离散傅里叶频谱攻击

Abstract: Spectral immunity measures the resistance of a period sequence against discrete Fourier spectra attack. With bigger spectral immunity, the ability to resist spectral attack is stronger. By searching the annihilators of m-sequences and calculating their spectral weights, a conjecture is put forward. The lowest spectral weight of all the annihilators of m-sequences with degree n is n+1, and its complementary sequence is just one of the lowest spectral weight annihilators. Then, by studying the properties of annihilators and complementary sequences of m-sequences, the conjecture is proved theoretically. Finally, the annihilator properties of complementary sequences are analyzed. As a result, the spectral immunity of m-sequences with degree n is n. And it shows that m-sequences are vulnerable to resist fast discrete Fourier spectra attack.

Key words: m-sequence, spectral immunity, annihilator, discrete Fourier spectra attack

胡建勇1，张文政1，陈克非2，董新锋1. m序列频谱免疫度的研究[J]. 计算机工程与应用, 2017, 53(16): 74-78.

HU Jianyong1, ZHANG Wenzheng1, CHEN Keifei2, DONG Xinfeng1. Research on spectral immunity of m-sequences[J]. Computer Engineering and Applications, 2017, 53(16): 74-78.

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m序列频谱免疫度的研究

Research on spectral immunity of m-sequences

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