基于RM码最优代数免疫度奇元布尔函数的构造

摘要

The support set of the Majority function is revised according to new vector sets given by three-type odd numbers and vector sets sorted by Hamming weight,and a new construction of odd-variable Boolean functions with optimal algebraic immunity based on Reed-Muller code is proposed.It can be proved that the constructed odd-variable function has optimum algebraic immunity degree and high nonlinearity.With the help of computer programs,it is verified that,as the input variable n =11,13,15,this function has near sub optimal ability to resist fast algebraic attacks.%根据按照奇数的3种情况分别给出的新向量集合和按照汉明重量划分的向量集合,对“择多”函数支撑集加以修改,提出了一种新的基于RM码最优代数免疫度的奇元布尔函数的构造方案.证明了该构造方案生成的奇元布尔函数具有最优的代数免疫度以及较高的非线性度.利用计算机程序验证了输入变量值n=11,13,15时所构造的函数具有接近次优的抵抗快速代数攻击的能力.所构造的奇元布尔函数为设计流密码的非线性组件提供了一种选择.