On a class of permutation trinomials over finite fields

Authors

BURCU GÜLMEZ TEMÜRFollow
BUKET ÖZKAYAFollow

Author ORCID Identifier

BUKET ÖZKAYA: 0000-0003-2658-5441

BURCU GÜLMEZ TEMÜR: 0000-0002-0435-6894

DOI

10.55730/1300-0098.3540

Abstract

In this paper, we study the permutation properties of the class of trinomials of the form f(x) = x4q+1 +λ1xq+4 +λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficientconditions on λ1 and λ2 such that f(x) permutes Fq2 , where q is odd and q = 22k+1, k ∈ N.

Keywords

cryptography, finite fields, Hasse-Weil bound, Permutation polynomials

First Page

778

Last Page

792

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

GÜLMEZ TEMÜR, BURCU and ÖZKAYA, BUKET (2024) "On a class of permutation trinomials over finite fields," Turkish Journal of Mathematics: Vol. 48: No. 4, Article 11. https://doi.org/10.55730/1300-0098.3540
Available at: https://journals.tubitak.gov.tr/math/vol48/iss4/11