基于RM码最优代数免疫度奇元布尔函数的构造  

Construction of odd-variable Boolean Functions with optimal algebraic immunity based on RM code

作　　者：赵庆兰[1] 刘航[1] 郑东[1] 

机构地区：[1]西安邮电大学通信与信息工程学院,陕西西安710121

出　　处：《西安邮电大学学报》2017年第4期43-51,56,共10页Journal of Xi’an University of Posts and Telecommunications

基　　金：国家自然科学基金资助项目(61472472;61402366);陕西省自然科学基础研究计划资助项目(2016JM6033)

摘　　要：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。The support set of the Ma jo r ity 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 a bility to resist fast algebraic attacks.

关 键 词：REED-MULLER码 代数免疫度 代数攻击 布尔函数 非线性度 

分 类 号：TN918.1[电子电信—通信与信息系统]