Boomerang uniformity of power permutations and algebraic curves over F2n

Mesnager S., ÖZBUDAK F.

Advances in Geometry, vol.23, no.1, pp.107-134, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1515/advgeom-2022-0026
  • Journal Name: Advances in Geometry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.107-134
  • Keywords: algebraic curve, algebraic function field, Boomerang uniformity, differential uniformity
  • Middle East Technical University Affiliated: Yes

Abstract

© 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.