论文标题
$ 0 $ -apn电源功能的新结果超过$ \ mathbb {f} _ {2^n} $
New results of $0$-APN power functions over $\mathbb{F}_{2^n}$
论文作者
论文摘要
部分APN功能吸引了研究人员最近的特别兴趣。它在研究APN功能中起着重要作用。在本文中，基于多变量方法和结果消除，我们在$ \ mathbb {f} _ {2^n} $上提出了几个新的无限类别的$ 0 $ -APN POWER功能。此外，完全表征了两个无限类别的$ 0 $ -apn POWER函数$ x^d $ $ x^d $ of $ x^d $ a {f} _ {2^n} $，其中$（2^k-1）d \ equiv 2^m-1〜（{\ rm mod} \ rm mod} \ 2^n-1）对于某些正整数$ n，m，k $的mod} \ 2^n-1）$。这些无限类别的$ 0 $ -APN功率功能可以解释表$ 1 $ in \ cite {bkrs2020}的表$ 1 $的一些示例。
Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite classes of $0$-APN power functions over $\mathbb{F}_{2^n}$. Furthermore, two infinite classes of $0$-APN power functions $x^d$ over $\mathbb{F}_{2^n}$ are characterized completely where $(2^k-1)d\equiv 2^m-1~({\rm mod}\ 2^n-1)$ or $(2^k+1)d\equiv 2^m+1~({\rm mod}\ 2^n-1)$ for some positive integers $n, m, k$. These infinite classes of $0$-APN power functions can explain some examples of exponents of Table $1$ in \cite{BKRS2020}.
