论文标题
$ c $差异行为在$ ea $等值下
The $c$-differential behavior of the inverse function under the $EA$-equivalence
论文作者
论文摘要
虽然在CCZ等效性下，经典的差异均匀性（$ c = 1 $）是不变的，但新定义的\ cite {efrst20}的概念$ c $ - 差异均匀性的概念，通常在\ cite {sprs {sprs20}中观察到的EA或CCZ-等效性并不是不变的。在本文中，我们发现逆函数的一种有趣的行为，即，对于某些〜$ c $而言，添加一些适当的线性化单体可显着增加$ c $不同的均匀性。例如，添加线性化的$ x^{p^d} $，其中$ d $是$ n $的最大非平凡的分隔线，将上述$ c $ -c $ -differential均匀性从〜$ 2 $或$ 3 $（$ c \ c \ c \ neq 0 $）增加到$ \ geq p^p^d $ $ \ f_ {2^8} $是〜$ 18 $的显着值。
While the classical differential uniformity ($c=1$) is invariant under the CCZ-equivalence, the newly defined \cite{EFRST20} concept of $c$-differential uniformity, in general is not invariant under EA or CCZ-equivalence, as was observed in \cite{SPRS20}. In this paper, we find an intriguing behavior of the inverse function, namely, that adding some appropriate linearized monomials increases the $c$-differential uniformity significantly, for some~$c$. For example, adding the linearized monomial $x^{p^d}$, where $d$ is the largest nontrivial divisor of $n$, increases the mentioned $c$-differential uniformity from~$2$ or $3$ (for $c\neq 0$) to $\geq p^{d}+2$, which in the case of AES' inverse function on $\F_{2^8}$ is a significant value of~$18$.
