GF（q）上置换多项式与函数的相关免疫性  

PERMUTATION POLYNOMIALS AND CORRELATION IMMUNITY OF FUNCTIONS OVER GF(q)

作　　者：隆永红[1] 

机构地区：[1]中国科学院软件研究所

出　　处：《软件学报》1996年第7期442-448,共7页Journal of Software

基　　金：国家自然科学基金

摘　　要：本文提出了ＧＦ（ｑ）上（ｎ，ｋ）置换多项式的概念，建立了它与函数相关免疫性之间的联系，并研究了它们的性质．得到了ＧＦ（ｑ）（ｑ＞２）上一些特殊类型的函数是ｍ阶和所有二次多项式是最大阶相关免疫的充分必要条件．证明了在ＧＦ（ｑ）（ｑ＞４）上存在非线性的具有最大阶相关免疫阶的函数。The concept of (n,k) permutation polynomial over GF(q) is first introduced.The properties of (n,k) permutation polynomials and the relation to kth order correlationimmune functions have been studied. Sufficient and necessary conditions are proved forsome special n-ary functions to be mth(m<n) order correlation immune and all functionswith degree no greater than 2 to be (n- 1)th order correlation immune. The results showthat over GF(q) (q>4) are there nonlinear functions of highest possible correlation immunity order. An efficient method is put forward to construct functions of high nonlinearityfrom those of lower nonlinearity with the same correlation immunity order.

关 键 词：置换多项式 相关免疫 流密码 密码 

分 类 号：TN918.2[电子电信—通信与信息系统]