几类对称布尔函数的非线性度、代数次数和代数免疫阶

On the Nonlinearity,Algebraic Degree and Algebraic Immunity of Some Symmetric Boolean Functions

该文讨论了几类偶数个变元n的对称布尔函数的一些密码性质,包括非线性度、代数次数、代数免疫阶、严格雪崩准则和相关免疫性等.我们的讨论显示这些对称布尔函数有好的非线性度和代数次数,并且有两类对称布尔函数的代数免疫阶达到最大n/2,一类对称布尔函数的代数免疫阶为1,但是它们基本上不具有相关免疫性和不满足严格雪崩准则,因此这些布尔函数都不能直接应用到密码系统中.

This paper studies the nonlinearity,algebraic degree,algebraic immunity,strict avalanche criterion and correlation immunity of certain type of symmetric Boolean functions on even number of input variables n.Our study shows that these functions have high nonlinearity and algebraic degree,and two classes of them have maximal algebraic immunity n/2 and a class has algebraic immunity 1.However they do not include the correlation immunity and satisfy the strict avalanche criterion,so they can not be applied in cryptosystem.