Bent函数的性质与构造

The Properties and Construction of Bent Functions

给出了形如F(x, y) = f (x +τ(y))q(y) + g(y) 的布尔函数是Bent 函数的充分必要条件,并据此给出了二次Bent 函数的已拥有等价类. 另,文中还给出了Bent 函数的几种构造方法. 特别地,给出了Bent 基函数的完全构造.

In this paper, the necessary and sufficient conditions of a Boolean function F(x, y) = f (x +τ (y))q(y) + g(y) are given, which is a Bent function. On the basis of this, all equivalent classes of Bent functions with degree two are given. Then some methods for constructing new Bent functions from known Bent functions are presented. In addition the complete construction of Bent basis functions is given.