On a class of permutation trinomials over finite fields

Temür B. G., ÖZKAYA B.

Turkish Journal of Mathematics, vol.48, no.4, pp.778-792, 2024 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3540
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.778-792
  • Keywords: cryptography, finite fields, Hasse-Weil bound, Permutation polynomials
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we study the permutation properties of the class of trinomials of the form (Formula presented), where λ1, λ2 ∈ \BbbFq and they are not simultaneously zero. We find all necessary and sufficient conditions on λ1 and λ2 such that f(x) permutes \BbbFq2, where q is odd and q = 22k+1, k ∈ \BbbN.