奇特征域上的一类二次Bent函数  

Class of Quadratic Bent Functions over the Finite Fields of Odd Characteristic

作　　者：肖理 张习勇[1] 

机构地区：[1]信息工程大学网络空间安全学院,河南郑州450001

出　　处：《信息工程大学学报》2012年第6期641-645,共5页Journal of Information Engineering University

基　　金：国家自然科学基金资助项目(60803154)

摘　　要：Bent函数在编码理论、通信领域以及密码学中具有广泛的应用。文章利用二次型理论构造了定义在奇特征域Fpn上的二次Bent函数∑m/2-1i=1ciTrn1(βx1+pei)+cm/2Trn/21(βx1+pn/2),其中,p是奇素数,ci∈Fp,n=em,且满足m是偶数;给出了这类函数是p-ary Bent的充分必要条件。进一步地,当m=2pvq,v≥0,q是一个奇素数且满足p是模q的原根,给出了这种情况下的此类二次Bent函数的个数。Bent functions are widely used in the fields of coding theory, communications and cryptog-raphy. This paper constructs a class of quadratic bent functions having the form ∑i=1^m/2-1ciTr1^n（βx^1＋pei）＋cm/2Tr1^n/2（βx1＋p^n/2）for even n with n = em,ci E Fp over the finite field of Fp~ of odd characteristic p by using the theory of quadratic forms over finite fields. Moreover, the necessary and sufficient con- ditions are presented. Further, when m = 2p^q,v 〉I O,q is an odd prime and p a primitive root mod- ulo q. The enumerations of this class of bent functions are also considered.

关 键 词：BENT函数 二次型理论 奇特征域 p-ary BENT函数 指数和 

分 类 号：TN918.1[电子电信—通信与信息系统]