布尔函数的迹Walsh谱  

Trace Walsh Spectrum of Boolean Functions

作　　者：祁传达[1] 谢晓[1] 邵辉[1] 袁小转[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《数学的实践与认识》2015年第18期161-166,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61272465);河南省自然科学基金项目(102102210242)

摘　　要：布尔函数线性Walsh谱和高阶Walsh谱的研究对构造能够抵抗线性逼近攻击和二次或较高次逼近攻击的密码函数发挥了重要作用.为了抵抗采样攻击,提出了布尔函数迹Walsh谱和迹Walsh循环谱概念,并给出该Walsh谱的一些简单性质.利用这一谱值的分布特性,可以很好地分析布尔函数的迹函数逼近问题,对序列密码采样攻击研究具有重要意义.The study of Boolean function＇s linear Walsh spectrum and higher order Walsh spectrum plays an important rule in constructing the cipher function against linear function approximation attack and quadratic or higher order function approximation attack.In order to resist decimation attacks,two concepts,trace Walsh spectrum and trace Walsh cyclic spectrum,are presented in this article.And some simple properties of them are also provided.By using the distribution characteristics of the two spectrums,the approximate problem of trace function can be effectively analyzed,which is of important meaning to the study of decimation attack of stream ciphers.

关 键 词：布尔函数 线性Walsh谱 高阶Walsh谱 迹Walsh谱 

分 类 号：TN918.1[电子电信—通信与信息系统]