一类多输出半Bent函数的构造及其密码学性质  

The Construction of a Class of Multi-output Semi-bent Functions and Their Cryptographic Properties

作　　者：刘志高[1] 张福泰[1] 徐倩[1] 

机构地区：[1]南京师范大学数学与计算机科学学院

出　　处：《南京师范大学学报（工程技术版）》2006年第1期38-42,共5页Journal of Nanjing Normal University(Engineering and Technology Edition)

基　　金：江苏省高校自然科学研究计划重点资助项目(03KJA520066);教育部网络与信息安全重点实验室(西安电子科技大学)开放课题资助项目

摘　　要：给出了多输出半Bent函数的一种构造方法.该方法通过级联两个低阶多输出Bent函数得到高阶多输出半Bent函数.由于在多输出Bent函数的构造方面,目前已有许多较好的结果,因此新方法是一个非常有效的方法,能构造出大量的多输出半Bent函数.还进一步讨论了这类函数的平衡性、非线性性、稳定性及扩散性等密码学性质.这些性质显示,多输出半Bent函数是一类密码学性质良好的奇数元多输出函数,除了可应用于多输出前馈网,它还可用作分组密码体制的非线性组合器.A method to construct multi-output semi-bent functions is presented. In the method, a higher order muhioutput semi-bent function is constructed by concatenating two lower order multi-output bent functions. Since many good results on the construction of multi-output bent functions have been given, the new method is very effective and many multi-output semi-bent functions can be constructed by it. Furthermore, some cryptographic properties of this kind of functions such as balance, nonlinearity, stability and propagation characters etc, are discussed. The discussion shows that the multi-output semi-bent function is a class of multi-output functions with odd variables that hold good cryptographic properties. Besides applications in multi-output feedforward networks, multi-output semi-bent functions can also be used as nonlinear combiner in block ciphers.

关 键 词：BENT函数 多输出Bent函数 多输出半Bent函数 Walsh循环谱 

分 类 号：O236.2[理学—运筹学与控制论] O157.4[理学—数学]