Boomerang uniformity of power permutations and algebraic curves over F2n

Mesnager S., ÖZBUDAK F.

Advances in Geometry, cilt.23, sa.1, ss.107-134, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1515/advgeom-2022-0026
  • Dergi Adı: Advances in Geometry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.107-134
  • Anahtar Kelimeler: algebraic curve, algebraic function field, Boomerang uniformity, differential uniformity
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 2022 Walter de Gruyter GmbH, Berlin/Boston 2022.We obtain the Boomerang Connectivity Table of power permutations F(x)=x2m-1 of F2n with m ∈ {3, n-1/2, n+1/2, n-2}. In particular, we obtain the Boomerang uniformity and the Boomerang uniformity set of F(x) at b∈F2n\F2. Moreover we determine the complete Boomerang distribution spectrum of F(x) using the number of rational points of certain concrete algebraic curves over F2n. We also determine the distribution spectra of Boomerang uniformities explicitly.