反函数在$EA$ -等价下的$c$ -微分性
The $c$-differential behavior of the inverse function under the $EA$-equivalence
摘要：
虽然经典的微分均匀性（$c=1$）在CCZ-等价下是不变的，但新定义的$c$ -微分均匀性的\cite{EFRST20}概念在EA或CCZ-等价下一般不是不变的，如在\cite{SPRS20}中观察到的。在本文中，我们发现了一个有趣的行为的反函数，即，添加一些适当的线性单项式增加$c$ -微分均匀性显着，一些$c$。例如，添加线性化单式$x^{p^d}$，其中$d$是$n$的最大非平凡因子，将所提到的$c$ -微分均匀性从~ $2$或$3$（对于$c\neq 0$）增加到$\geq p^{d}+2$，其在$\F_{2^8}$上的AES反函数的情况下是~ $18$的有效值。
英文摘要：
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~$18$.
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