Boomerang uniformity of a class of power maps

Abstract

We consider the boomerang uniformity of an infinite class of (locally-APN) power maps and show that their boomerang uniformity over the finite field F2n is 2 and 4, when n≡0(mod4) and n≡2(mod4), respectively. As a consequence, we show that for this class of power maps, the differential uniformity is strictly greater than their boomerang uniformity. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.