l次扩散函数的特征和结构研究综述

Characteristics and Constructions of Functions with Propagation of Degree l

扩散准则是衡量布尔函数非线性的重要指标。本文主要对近年来国内外研究满足扩散准则的布尔函数的特征、结构和相关构造方法的重要成果进行了综述 ,给出了满足两种特殊扩散准则的布尔函数的简单构造 ,并用Bent函数构造了仅在个别向量处不满足扩散准则的布尔函数。

PC is an important indeX for judging nonlinear properties of Boolean functions.Two significant characteristics of PC and PC(l) are given in this paper.The constructions and functions of PC(l) and PC(l)/k are studied and some functions satisfying PC(l) or PC(l)/k are obtained.Finally,the functions without PC at a few vectors are pointed out.