论文标题
两个新的双变量APN功能系列
Two new families of bivariate APN functions
论文作者
论文摘要
在这项工作中，我们介绍了两个二次APN功能的新系列。第一个（F1）是通过双原则多项式构建的。这个家族包括Göloǧlu在2022年引入的两个APN家族之一。然后，遵循与li \ emph {等}（2022）中类似的方法，我们通过将某些术语添加到F1中获得了另一个家族（F2）。作为副产品，第二个家庭包括Li \ Emph {等}（2022）引入的两个家庭之一。此外，我们表明，对于$ n = 12 $，从我们的构造中，我们可以获得与$ \ mathbb {f} _ {2^{12}} $上任何其他已知的APN函数相对于任何其他已知的APN函数的apn函数。
In this work, we present two new families of quadratic APN functions. The first one (F1) is constructed via biprojective polynomials. This family includes one of the two APN families introduced by Göloǧlu in 2022. Then, following a similar approach as in Li \emph{et al.} (2022), we give another family (F2) obtained by adding certain terms to F1. As a byproduct, this second family includes one of the two families introduced by Li \emph{et al.} (2022). Moreover, we show that for $n=12$, from our constructions, we can obtain APN functions that are CCZ-inequivalent to any other known APN function over $\mathbb{F}_{2^{12}}$.
