Boomerang uniformity of power permutations and algebraic curves over F2n

Date

2023-01-01

Author

Mesnager, Sihem
Özbudak, Ferruh

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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.

Subject Keywords

algebraic curve, algebraic function field, Boomerang uniformity, differential uniformity

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85146381247&origin=inward
https://hdl.handle.net/11511/102173

Journal

Advances in Geometry

DOI

https://doi.org/10.1515/advgeom-2022-0026

Collections

Department of Mathematics, Article

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Citation Formats

S. Mesnager and F. Özbudak, “Boomerang uniformity of power permutations and algebraic curves over F2n,” Advances in Geometry, vol. 23, no. 1, pp. 107–134, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85146381247&origin=inward.