paper

Two Classes of Power Mappings with Boomerang Uniformity 2

arXiv:2203.00485

Abstract

Let $q$ be an odd prime power. Let $F_{1} (x) = x^{d_{1}}$ and $F_{2} (x) = x^{d_{2}}$ be power mappings over $GF (q^{2})$ , where $d_{1} = q - 1$ and $d_{2} = d_{1} + \frac{q ^{2} - 1}{2} = \frac{( q - 1 ) ( q + 3 )}{2}$ . In this paper, we study the the boomerang uniformity of $F_{1}$ and $F_{2}$ via their differential properties. It is shown that, the boomerang uniformity of $F_{i}$ ( $i = 1, 2$ ) is 2 with some conditions on $q$ .

11 pages