Complete characterization of a class of permutation trinomials in characteristic five

Grassl M., ÖZBUDAK F., ÖZKAYA B., Temür B. G.

Cryptography and Communications, vol.16, no.4, pp.825-841, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.1007/s12095-024-00705-2
  • Journal Name: Cryptography and Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.825-841
  • Keywords: 11T71, 12E10, Absolutely irreducible, Finite fields, MSC 11T06, Permutation polynomials
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form f(x)=x4q+1+λ1x5q+λ2xq+4 over the finite field F5k, which are not quasi-multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on λ1,λ2∈F5k so that f(x) is a permutation monomial, binomial, or trinomial of F52k.