Reversed Dickson polynomials over finite fields

Xiang dong Hou, Gary L. Mullen, James A. Sellers, Joseph L. Yucas

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials Dn (x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear (APN) functions. We find several families of nontrivial RDPPs over finite fields; some of them arise from known APN functions and others are new. Among RDPPs on Fq with q < 200, with only one exception, all belong to the RDPP families established in this paper.

Original languageEnglish (US)
Pages (from-to)748-773
Number of pages26
JournalFinite Fields and their Applications
Volume15
Issue number6
DOIs
StatePublished - Dec 2009

Keywords

  • Almost perfect nonlinear function
  • Dickson polynomial
  • Finite field
  • Reversed Dickson polynomial

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