Complete characterization of a class of permutation trinomials in characteristic five

Grassl, Markus; ÖZBUDAK, FERRUH; ÖZKAYA, BUKET; Temür, FERRUH

doi:10.1007/s12095-024-00705-2

Complete characterization of a class of permutation trinomials in characteristic five

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

Cryptography and Communications, cilt.16, sa.4, ss.825-841, 2024 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 16 Sayı: 4
Basım Tarihi: 2024
Doi Numarası: 10.1007/s12095-024-00705-2
Dergi Adı: Cryptography and Communications
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
Sayfa Sayıları: ss.825-841
Anahtar Kelimeler: 11T71, 12E10, Absolutely irreducible, Finite fields, MSC 11T06, Permutation polynomials
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.