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