Reversed Dickson polynomials over finite fields

被引：50

作者：

Hou, Xiang-dong ^{[3
]}

Mullen, Gary L. ^{[2
]}

Sellers, James A. ^{[2
]}

Yucas, Joseph L. ^{[1
]}

机构：

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Univ S Florida, Dept Math, Tampa, FL 33620 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2009年 / 15卷 / 06期

关键词：

Almost perfect nonlinear function; Dickson polynomial; Finite field; Reversed Dickson polynomial;

D O I：

10.1016/j.ffa.2009.06.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials D-n(x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear (APN) functions. We find several families of nontrivial RDPPs over finite fields: some of them arise from known APN functions and others are new. Among RDPPs on F-q with q < 200, with only one exception, all belong to the RDPP families established in this paper. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：748 / 773

页数：26

共 17 条

[1] Two classes of quadratic APN binomials inequivalent to power functions [J].