On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over F_(2 2 m)  

作　　者：Mengyu Hu Nian Li Xiangyong Zeng 

机构地区：[1]Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan,China

出　　处：《Communications in Mathematical Research》2022年第2期223-245,共23页数学研究通讯（英文版）

基　　金：This work was supported by the Application Foundation Frontier Project of Wuhan Science and Technology Bureau(No.2020010601012189);the National Natural Science Foundation of China(Nos.61761166010,62072162).

摘　　要：Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field F_(2 2m) for an odd integer m. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.

关 键 词：Differential uniformity finite field NONLINEARITY permutation polynomial 

分 类 号：O17[理学—数学]