We consider the boomerang uniformity of an infinite class of (locally-APN) power maps and show that their boomerang uniformity over the finite field \(\mathbb {F}_{2^n}\) is 2 and 4, when \(n \equiv 0 \pmod 4\) and \(n \equiv 2 \pmod 4\), respectively. As a consequence, we show that for this class of power maps, the differential uniformity is strictly greater than their boomerang uniformity.

中文翻译：

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一类功率图的回旋镖均匀性

我们考虑无限类（局部 APN）功率图的回旋镖均匀性，并表明它们在有限域\(\mathbb {F}_{2^n}\)上的回旋镖均匀性为 2 和 4，当\( n \equiv 0 \pmod 4\)和\(n \equiv 2 \pmod 4\)分别。因此，我们表明，对于此类功率图，差分均匀度严格大于它们的回旋镖均匀度。