论文标题
在功率映射$ x^{p^m+2} $的差分属性上
On the Differential Properties of the Power Mapping $x^{p^m+2}$
论文作者
论文摘要
让$ m $成为一个正整数，而$ p $ a Prime。在本文中，我们调查了$ \ \ mathbb {f} _ {p^n} $的电源映射$ x^{p^m+2} $的差分属性，其中$ n = 2m $ $或$ n = 2M-1 $。对于情况，$ n = 2M $，通过转换$ x^{p^m+2} $的导数方程并研究一些相关方程，我们完全确定了该功率映射的差异频谱。对于$ n = 2M-1 $的情况，可以将衍生方程转换为$ p+3 $的多项式。问题更加困难，我们获得了有关$ x^{p^m+2} $的差分光谱的部分结果。
Let $m$ be a positive integer and $p$ a prime. In this paper, we investigate the differential properties of the power mapping $x^{p^m+2}$ over $\mathbb{F}_{p^n}$, where $n=2m$ or $n=2m-1$. For the case $n=2m$, by transforming the derivative equation of $x^{p^m+2}$ and studying some related equations, we completely determine the differential spectrum of this power mapping. For the case $n=2m-1$, the derivative equation can be transformed to a polynomial of degree $p+3$. The problem is more difficult and we obtain partial results about the differential spectrum of $x^{p^m+2}$.
