# Two Classes of Power Mappings with Boomerang Uniformity 2

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+q^2-1/2=(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.

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