具有最优代数免疫阶平衡布尔函数的递归构造  

Recursive construction of balanced Boolean function with optimum algebraic immunity

作　　者：曹浩[1] 卓泽朋[2] CAO Hao;ZHUO Zepeng(Institute of Information and Network Engineering, Anhui Science & Technology University, Chuzhou, Anhui 233100, China;School of Mathematical Science, Huaibei Normal University, Huaibei, Anhui 235000, China)

机构地区：[1]安徽科技学院信息与网络工程学院,安徽滁州233100 [2]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《计算机工程与应用》2017年第7期133-135,140,共4页Computer Engineering and Applications

基　　金：安徽高校省级自然科学研究重点项目(No.KJ2014A220);安徽高校省级自然科学研究一般项目(No.KJ2013B083);安徽科技学院自然科学研究项目(No.ZRC2014425)

摘　　要：针对密码学中布尔函数的代数免疫性和构造需求,通过选取适当次数的布尔函数,利用布尔函数的级联性质,提出了一种提高布尔函数代数免疫阶的递归构造法;同时证明了该构造法中所构造的布尔函数比原布尔函数的代数免疫阶高,利用该方法可以递归构造具有最优代数免疫阶平衡布尔函数,最后给出了一个具体实例。Focusing on the algebraic immunity of Boolean function and its demands of construction,a recursive constructionmethod to increase algebraic immunity of Boolean functions is proposed.In this method,the cascade properties ofBoolean functions are used and a Boolean function with proper algebraic degree is selected.Meanwhile,the inference thatthe algebraic immunity of constructed Boolean functions is higher than the original one is proved.Also,through the abovemethod,balanced Boolean functions with optimum algebraic immunity can be obtained.At the end,an example is given.

关 键 词：布尔函数 代数标准型 代数免疫阶 

分 类 号：TN918.1[电子电信—通信与信息系统]