基于布尔函数正规性的广义Bent函数构造

摘要

基于广义Bent函数的正规性,结合子空间上的特征函数,分析广义正规Bent函数的Chrestenson谱特征.利用间接构造Bent函数的方法,在整数模m的剩余类环Zm以及p元域Zp上,给出2类新的n元广义Bent函数.理论分析结果表明,与传统构造方法相比,该方法可构造出更多的n元广义Bent函数.%This paper is based on the normality of generalized Bent functions, combines the characteristic functions of linear subspace. The Chrestenson spectral characteristics of generalized nonnal Bent functions are studied. According to the indirect construction method, two new classes of generalized Bent functions of n variables over integers module m residue class Zm and p meta-field Zp are presented. Theory analysis result shows that more generalized Bent functions can be constructed by using the proposed construction method compared with the traditional construction method.