Permutation polynomials x^2^k+1+3+ax^2^k+2+bx over F2^2k and their differential uniformity  

作　　者：Jie PENG Lijing ZHENG Chunsheng WU Haibin KAN 

机构地区：[1]Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China [2]School of Mathematics and Physics,University of South China,Hengyang 421001,China [3]Department of Mathematics,Lianyungang Normal University,Lianyungang 222006,China [4]Shanghai Key Laboratory of Intelligent Information Processing,School of Computer Science,Fudan University,Shanghai 200433,China [5]Fudan-Zhongan Joint Laboratory of Blockchain and Information Security,Shanghai Blockchain Engineering Research Center,Shanghai 200433,China [6]Shanghai Institute for Advanced Communication and Data Science,Shanghai 200433,China [7]Shanghai Institute of Intelligent Electronics&Systems,Shanghai 200433,China

出　　处：《Science China(Information Sciences)》2020年第10期251-253,共3页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61672166,11701488);Shanghai Excellent Academic Leader(Grant No.16XD1400200);Shanghai Innovation Plan of Science&Technology(Grant No.16JC1402700);Scientific Research Fund of Hunan Provincial Education Department(Grant No.17B040)。

摘　　要：Dear editor,A polynomial f(x)∈Fq[x]is called a permutation polynomial(PP)over the finite field Fq if the associated mapping f:c→f(c)from Fq to itself is bijective.A PP f is called a complete permutation polynomial if f(x)+x is a PP.PPs over finite fields of even characteristic have wide applications,including cryptography,coding theory,and communication theory.In many block ciphers with substitution-permutation network structure,the substitution box is usually a PP over F22kfor some positive integer k.

关 键 词：theory. polynomial PERMUTATION 

分 类 号：O174.14[理学—数学]