论文标题
两类具有Boomerang均匀性的功率映射2
Two Classes of Power Mappings with Boomerang Uniformity 2
论文作者
论文摘要
让$ Q $成为奇怪的素数。令$ f_1（x）= x^{d_1} $和$ f_2（x）= x^{d_2} $ be power mappings $ \ mathrm {gf}（q^2）$，其中$ d_1 = q-1 = q-1 $和$ d_2 = d_1+\ frac {q^2-1} {2} = \ frac {（q-1）（q+3）} {2} $。在本文中，我们通过其不同属性研究了$ f_1 $和$ f_2 $的回旋镖均匀性。结果表明，$ f_i $（$ i = 1,2 $）的回旋镖均匀性为2，在$ q $上有一些条件。
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 $\mathrm{GF}(q^2)$, 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 $q$.
