m子序列的密码学性质研究*

文中所提m子序列是根据m序列的状态转换特征，通过交叉改变状态转换次序而形成新的序列。通过随机性测试软件（NIST）验证m子序列具有和m序列相似的随机性，使用BM算法可以得出这种伪随机序列具有非常高的线性复杂度，同时验证了其补序列也具有非常高的线性复杂度，并说明m子序列具有良好的线性复杂度谱，抗线性攻击能力强。m子序列的数量庞大，一个周期为 的m序列，改变反馈函数就可以至少产生 个m子序列。产生m子序列的反馈函数经证明具有良好的代数免疫度，抗代数攻击能力较强。m子序列具有良好的密码学性质，应用前景良好。

Research on Cryptographic Properties of m Subsequences

The m subsequence was formed by changing the m sequence of state transitions in this paper. It verified that the m subsequence have random similarity with m sequence by the random test software (NIST). It verified that the m subsequence have very high linear complexity using BM algorithm, and verified the complementary sequence also have very high linear complexity. The m subsequences have good linear complexity spectrum. It has strong ability to resist linear attack. It has a large number of m subsequence by changing feedback functions of m sequence, m sequence, such as a cycle of can produce m subsequences. The feedback function of m subsequences have good algebraic immunity and strong ability of resisting of algebraic attack. The m subsequences have good cryptographic properties and good application prospects.