布尔函数性质的谱特征  

Spectrum characteristic of Boolean function properties

作　　者：刘楠楠[1] 张引兵[1] 周玉凤[1] 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《沈阳师范大学学报（自然科学版）》2011年第3期356-358,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10801023);淮北师范大学教研项目(2010-41)

摘　　要：布尔函数对于分组密码及流密码的安全性起着重要的作用。为了抵抗几种对密码体制的攻击,布尔函数需要具有几种相应的准则:平衡性,高代数次数,高非线性度和高相关免疫度等。Walsh变换和Walsh谱技术是研究布尔函数性质的有效方法,利用Walsh谱技术研究布尔函数的一些重要性质,将这些性质(平衡性、非线性度、相关免疫性、扩散准则、严格雪崩准则、代数免疫性)进行量化。主要研究了布尔函数的Walsh谱及相关的性质,重点介绍了布尔函数的几种密码学性质及Walsh谱与其他密码学性质之间的关系,得到了布尔函数性质的一些结果:首先介绍了布尔函数Walsh谱及其他的密码学性质,然后分析了布尔函数Walsh谱与其他性质之间的关系,包括与汉明重量、平衡性、非线性度、相关免疫性、扩散性、严格雪崩性、代数免疫性之间关系。Boolean functions play a central role in security of block ciphers and stream ciphers.To withstand several known attacks on the cryptosystem,Boolean functions should possess several criteria： balancedness,high algebraic degree,high nonlinearity and high correlation immunity,etc.Walsh transform and Walsh spectrum are effective method to study properties of Boolean function.In this paper,properties of Boolean function are quantified by Walsh spectrum.The properties include balancedness,nonlinearity,correlation immunity,SAC,PC,and algebraic immunity.This paper investigates mainly Walsh spectrum of Boolean functions and associative properties,and shows several cryptographic properties of Boolean functions accordingly and analyzes the relationship between Walsh spectrum and other cryptographic properties,and obtains main result as follows： both Walsh transform of Boolean functions and other cryptographic properties are introduced at first,and then the author studies the relationships between Walsh spectrum of Boolean functions and other cryptographic properties such as Hamming weight,balancedness,nonlinearity,correlation immunity,SAC,PC,and algebraic immunity.

关 键 词：布尔函数性质 WALSH变换 WALSH谱 

分 类 号：TN918[电子电信—通信与信息系统]