论文标题
低$ c $ -differenten和$ c $ -boomerang互换功能的均匀性
Low $c$-differential and $c$-boomerang uniformity of the swapped inverse function
论文作者
论文摘要
已知以多种方式修改二进制逆函数，例如交换两个输出点会产生$ 4 $不同的统一置换函数。最近，在\ cite {li19}中表明，此交换版本的逆函数具有Boomerang均匀性$ 10 $，如果$ n \ equiv 0 \ equiv 0 \ pmod 6 $，$ 8 $，如果$ n \ equiv 3 \ pmod 6 $ 6 $，则6，如果$ n \ not \ equiv 0 \ equiv 0 \ equiv 0 \ pmod \ pmod 3 $ 3 $。根据我们在\ cite {efrst20}和$ c $ -BOOMERANG均匀性中定义的$ c $ - 数字概念，\ cite {s20}在本文中，我们表征了$ c $ -differtial and $ c $ c $ -c $ -c $ -boomerang均匀性的$（0,1）$ - $ 2 $ $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $： $ c $ - 不同的均匀性在上限为〜$ 4 $，$ c $ -boomerang均匀性均为〜$ 5 $，两个界限都以〜$ n \ geq 4 $的价格获得。
Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a $4$-differential uniform permutation function. Recently, in \cite{Li19} it was shown that this swapped version of the inverse function has boomerang uniformity exactly $10$, if $n\equiv 0\pmod 6$, $8$, if $n\equiv 3\pmod 6$, and 6, if $n\not\equiv 0\pmod 3$. Based upon the $c$-differential notion we defined in \cite{EFRST20} and $c$-boomerang uniformity from \cite{S20}, in this paper we characterize the $c$-differential and $c$-boomerang uniformity for the $(0,1)$-swapped inverse function in characteristic~$2$: we show that for all~$c\neq 1$, the $c$-differential uniformity is upper bounded by~$4$ and the $c$-boomerang uniformity by~$5$ with both bounds being attained for~$n\geq 4$.
