拟Bent函数的构造  

Constructions of Quasi-Bent Functions

作　　者：张习勇[1] 郭华[2] 滕吉红[2] 

机构地区：[1]解放军信息工程大学信息工程学院四系,郑州450002 [2]北京航空航天大学计算机学院,北京100083

出　　处：《工程数学学报》2010年第5期865-872,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60803154)~~

摘　　要：拟Bent函数在密码系统中可用作非线性组合函数和消息摘要函数,因而具有很好的密码学性质。本文通过计算布尔函数的Walsh谱,从映射的角度确定了变元个数不超过六的拟Bent函数的代数结构;提出了一般交换群上的扩展组合函数族的概念,研究了这类函数的性质,利用商群给出了扩展组合函数的下降构造,通过组合函数给出了提升构造法,从而得到了一种由扩展组合函数族构造拟Bent函数和Bent函数的递归构造法,由这种方法可以构造大量拟Bent函数和Bent函数。另外也构造了几种参数的布尔扩展组合函数。Qausi-Bent functions have good cryptographic properties and are employed as nonlinear combining functions and Hash functions in cryptography.In this paper,we firstly characterize the structures of quasi-Bent functions with variables not exceeding 6 by calculating Walsh spectrum of Boolean functions.We also introduce the concept of extended building functions（EBFs） in general finite Abelian groups and give some properties of this kind of functions.Using quotient group and the concept of building functions,we present a descending construction and a lifting construction,respectively. Thus we obtain a recursive construction of quasi-Bent functions and Bent functions by using the tool of EBFs.A great deal of quasi-Bent functions and Bent functions can thus be constructed. Using above methods,we give extended Boolean building functions with some parameters.

关 键 词：拟BENT函数 扩展组合函数族 组合函数族 递归构造 

分 类 号：TN918.1[电子电信—通信与信息系统]