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Dembowski-Ostrom polynomials from reversed Dickson polynomials

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Abstract

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.

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Author information

Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoming Zhang, Baofeng Wu & Zhuojun Liu

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Baofeng Wu

Authors
  1. Xiaoming Zhang
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  2. Baofeng Wu
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  3. Zhuojun Liu
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Corresponding author

Correspondence to Baofeng Wu.

Additional information

This research was supported by the National Basic Research Program of China under Grant No. 2011CB302400.

This paper was recommended for publication by Editor DENG Yingpu.

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Zhang, X., Wu, B. & Liu, Z. Dembowski-Ostrom polynomials from reversed Dickson polynomials. J Syst Sci Complex 29, 259–271 (2016). https://doi.org/10.1007/s11424-015-4110-4

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  • DOI: https://doi.org/10.1007/s11424-015-4110-4

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