一类对称布尔函数的研究  

On one class of symmetric Boolean functions

作　　者：欧智慧 赵亚群[1,2] 

机构地区：[1]信息工程大学四院,河南郑州450002 [2]信息工程大学数字工程与先进计算国家重点实验室,河南郑州450002

出　　处：《通信学报》2013年第1期89-95,104,共8页Journal on Communications

基　　金：国家自然科学基金资助项目(61072046)~~

摘　　要：主要讨论了一类对称布尔函数(记为)的性质。提供了不同的方法证明的一个子类具有最大代数免疫阶。给出了中函数达到最大代数免疫阶的一个必要条件,并得到了满足此必要条件的布尔函数个数的下界。同时给出了中大部分函数的代数次数,分析了中函数的线性结构和相关免疫性。结果表明,中函数没有非零的线性结构且仅有2个函数具有一阶相关免疫性。The properties of one class of symmetric Boolean functions which was denoted by R was discussed, a dif-ferent method for proving that one subclass of R having maximum algebraic immunity was presented. A necessary condition was proposed for the functions of R with maximum algebraic immunity, of which a lower bound of the number was also given. Meanwhile, the algebraic degree of most functions of R was determined and linear structure and correlation immunity of R were also analyzed. The results show that the functions of R have no non-zero linear struc-ture and only two functions of R have 1-correlation immunity.

关 键 词：对称布尔函数 代数免疫阶 相关免疫性 非线性度 

分 类 号：TN918.1[电子电信—通信与信息系统]