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

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