Dembowski-Ostrom Polynomials from Reversed Dickson Polynomials  

作　　者：ZHANG Xiaoming WU Baofeng LIU Zhuojun 

机构地区：[1]Key Laboratory of Mathematics Mechanization,Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100190, China [2]State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences, Beijing 100093, China

出　　处：《Journal of Systems Science & Complexity》2016年第1期259-271,共13页系统科学与复杂性学报（英文版）

基　　金：supported by the National Basic Research Program of China under Grant No.2011CB302400

摘　　要：This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.

关 键 词：Almost perfect nonlinear function Dembowski-Ostrom polynomial linearized polynomial reversed Dickson polynomial 

分 类 号：O174.14[理学—数学]