Boomerang uniformity of power permutations and algebraic curves over 픽2n.

We obtain the Boomerang Connectivity Table of power permutations F (x) = x 2 m − 1 of F 2 n 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 ∈ F 2 n ∖ F 2. Moreover we determine the complete Boomerang distribution spectrum of F(x) using the number of rational points of certain concrete algebraic curves over F 2 n . We also determine the distribution spectra of Boomerang uniformities explicitly. [ABSTRACT FROM AUTHOR]