具有最优代数免疫阶的1阶弹性函数的构造  

Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity

作　　者：董新锋 张凤荣[2] 谯通旭 张文政 

机构地区：[1]现代通信国家重点实验室,四川成都610041 [2]西安电子科技大学计算机网络与信息安全教育部重点实验室,陕西西安710071

出　　处：《信息安全与通信保密》2010年第12期112-115,共4页Information Security and Communications Privacy

基　　金：现代通信国家重点实验室基金资助项目(编号:9140C1102020802)

摘　　要：这里研究了两种二阶级联构造的密码学性质,发现对初始函数增加2个变元,构造方法I和Ⅱ都能使代数免疫阶增加1阶,同时分别获得高的非线性度和1阶弹性。通过选择置换s,构造I能迭代产生非线性度高的代数免疫最优的布尔函数。最后利用级联构造I和II给出了一种具有1阶弹性的代数免疫最优布尔函数的构造方法.The two second-order concatenating constructions are cryptographically studied.Adding 2 variables to the initial function,the first construction could raise the nonlinearity of the newly-built function effectively,and the second construction could creat 1 order of resiliency,meanwhile the algebraic immunity increases 1.By proper choice of permutation s,the first construction could iteratively construct Boolean functions with high non-linearity and optimal algebraic immunity.Finally a method for constructing 1-resilient Boolean functions with optimal algebraic immunity is provided.

关 键 词：代数免疫 二阶级联 非线性度 弹性 布尔函数 

分 类 号：TN918.1[电子电信—通信与信息系统]