On a class of permutation trinomials over finite fields

Temür B. G., ÖZKAYA B.

Turkish Journal of Mathematics, cilt.48, sa.4, ss.778-792, 2024 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.55730/1300-0098.3540
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.778-792
  • Anahtar Kelimeler: cryptography, finite fields, Hasse-Weil bound, Permutation polynomials
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.