自对偶布尔函数的若干密码学性质研究  

Research on some cryptographical properties of self-dual Boolean function

作　　者：刘杨[1,2] 冯有前[1] 李瑞虎[1] 

机构地区：[1]空军工程大学理学院,西安710051 [2]空军第一航空学院,河南信阳464000

出　　处：《计算机工程与应用》2012年第9期63-66,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.60573040)

摘　　要：通过分析布尔函数的特征,建立了n元自对偶布尔函数和n-1元布尔函数之间的关系,根据此关系讨论了n元自对偶布尔函数的代数免疫度及其非线性度,得出自对偶布尔函数的非零次单项式个数为奇数,给出了n元n-1次自对偶布尔函数的个数和代数正规型表示的特征及其密码学性质,对其代数次数为t的单项式个数提出了猜想,对其中两种特殊情况进行了证明。By analyzing character of Boolean function, the connection between n -variables self-dual Boolean function and n- 1 -vari- ables Boolean function is set up, and according to this connection the algebraic immunity and nonlinearity of n -variables self-dual Boolean function are discussed. It is also obtained that terms ofmonomials with algebraic degree nonzero are odd. The number, algebraic norm formation and cryptographical property of n -variables self-dual function with algebraic degree n- 1 are presented. A conjecture about terms ofmonomials with algebraic degree t is proposed, and two special cases are proved out.

关 键 词：自对偶布尔函数 线性结构 代数免疫度 代数次数 单项式个数 

分 类 号：TN918.1[电子电信—通信与信息系统]