有限域上二次Bent函数的构造  

Constructions of Quadratic Bent Functions over Finite Fields

作　　者：张凤荣[1] 胡予濮[1] 谢敏[1,2] 高军涛[1] 

机构地区：[1]西安电子科技大学计算机网络与信息安全教育部重点实验室,西安710071 [2]广东省信息安全技术重点实验室(广州大学),广州510405

出　　处：《北京邮电大学学报》2010年第3期52-56,共5页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(60833008;60503010;60832001);国家重点基础研究发展计划项目(2007CB311201)

摘　　要：针对MaWP等给出的二次多项式函数是Bent函数的充要条件以及CharpinP等给出的二次三项函数是semi-Bent函数的充要条件这2个结论进行了研究,结果表明,MaWP等文章中的推论5、6和CharpinP等文章中的定理5、6是不完全正确的.结合有限域上的二次多项式理论,给出了相应的正确结果,并构造了一类三项式和四项式Bent函数.借助多项式置换,提出了一种利用二次二项Bent函数构造多项式Bent函数的新方法.A sufficient and necessary condition that a quadratic polynomial function is a bent function was presented by Ma W P,et al.in 2005.In the same year,Charpin P,et al proposed a sufficient and necessary condition that a polynomial function is a quadratic semi-Bent function with three trace terms in a paper.Corollary 5,6 of the former and Theorem 5,6 of the latter are not quite right by further investigating these conditions.Based on the theory of quadratic polynomial over finite fields,the correct conditions are presented.Moreover,some quadratic bent functions with three or four trace terms are constructed.Finally,a new method for constructing bent functions in polynomial forms is provided by using bent functions of two trace terms and permutation of polynomial.

关 键 词：密码函数 Boolean函数 BENT函数 最大非线性度 

分 类 号：TN918.1[电子电信—通信与信息系统]