Dembowski-Ostrom polynomials from reversed Dickson polynomials

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• 作者：Xiaoming Zhang ; Baofeng Wu ; Zhuojun Liu
• 关键词：Almost perfect nonlinear function ; Dembowski ; Ostrom polynomial ; linearized polynomial ; reversed Dickson polynomial
• 刊名：Journal of Systems Science and Complexity
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：29
• 期：1
• 页码：259-271
• 全文大小：207 KB
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• 作者单位：Xiaoming Zhang (1)
  Baofeng Wu (1) (2)
  Zhuojun Liu (1)
  
  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
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067

文摘

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 \({x^{1 + {2^\alpha }}}\) 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. Keywords Almost perfect nonlinear function Dembowski-Ostrom polynomial linearized polynomial reversed Dickson polynomial