m子序列的密码学性质研究

摘要

The m subsequence is formed by changing the state transitions of m sequence.This paper verified that the m subsequence had random similarity with m sequence by the random test software (NIST).It verified that the m subsequence had very high linear complexity using BM algorithm,and verified the complementary sequence also had very high linear complexity.The m subsequences had good linear complexity spectrum.It had strong ability to resist linear attack.It had a large number of m subsequence by changing feedback functions of m sequence,m sequence,such as a cycle of 2n-1 could produce (2n-1-1) × (2n-1-2)/6 m subsequences.The feedback function of m subsequences have good algebraic immunity and strong ability of resisting of algebraic attack.The m subsequences has good cryptographic properties and good application prospects.%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子序列具有与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2n-1的m序列,改变反馈函数就可以至少产生(2n-1-1)(2n-1-2)/6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.