基于T-D猜想上MAI函数的构造  

Construction of MAI Function Based on T-D Conjecture

作　　者：张喆琳 周梦[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院LMIB,北京100191

出　　处：《计算机科学》2013年第11期94-97,111,共5页Computer Science

基　　金：国家自然科学基金(NSFC11271040)资助

摘　　要：对涂自然等人提出的组合猜想上的构造方法及有关结论进行了改良推广,在假设更一般的组合猜想成立的前提下构造了一种具有最优代数免疫度的偶数元布尔函数f,同时还利用f构造了一种具有最优代数免疫度的平衡的偶数元布尔函数F。且这些函数也具有很高的代数次数和非线性度,对代数攻击具有较强的抵抗能力。An improvement was made on the construction method and the relevant conclusions of combinatorial conjec- ture proposed by Ziran Tu. Under the premise that the more general combinatorial conjecture is still rational, a class of Boolean functions f with the maximum algebraic immunity on even number of variables was presented, and using the functions f, a new class of balanced Boolean functions F with the maximum algebraic immunity on even number of vari- ables was gotten. These functions not only have higher algebraic degree and nonlinearity, but also have strong resistance against algebraic attacks.

关 键 词：布尔函数 代数免疫度 平衡性 非线性度 代数次数 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]