向量值函数的代数免疫度与非线性度

The Algebraic Immunity and Nonlinearity of Vectorial Boolean Functions

本文讨论了向量值函数代数免疫度的定义,给出了向量值函数的代数免疫度与其非线性度之间的关系,研究了布尔函数的重量与其代数免疫度之间的关系,利用该关系,给出了达到最大代数免疫度的平衡布尔函数个数的一个下界。

This paper discusses the definition of algebraic immunity of the vectorial Boolean functions, and exhibits the connection between the algebraic immunity and nonliearity of vectorial Boolean functions. We also investigate the relationship between the weight and algebraic immunity of Boolean functions, by which we give a lower bound of the number of balanced Boolean functions which have the maxmal algebraic immunity.