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 its boomerang uniformity over the finite field $\F_{2^n}$ is $2$ and $4$, when $n\equiv 0(\mathrm{mod}4)$ and $n\equiv 2(\mathrm{mod}4)$, respectively. As a consequence, we show that for this class of power maps, the differential uniformity is strictly greater than its boomerang uniformity.

11 pages

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