Let $\mathbb{F}_q$ be a finite field of characteristic $p$. In this paper we prove that the $c$-Boomerang Uniformity, $c \neq 0$, for all permutation monomials $x^d$, where $d > 1$ and $p \nmid d$, is bounded by $d^2$. Further, we utilize this bound to estimate the $c$-boomerang uniformity of a large class of Generalized Triangular Dynamical Systems, a polynomial-based approach to describe cryptographic permutations, including the well-known Substitution-Permutation Network.

翻译：设$\mathbb{F}_q$为特征$p$的有限域。本文证明，对于所有满足$d > 1$且$p \nmid d$的置换单项式$x^d$，其非零常数$c$的c-回旋镖均匀性以$d^2$为上界。进一步地，我们利用这一界来估计一大类广义三角动力系统的c-回旋镖均匀性——这是一类基于多项式方法描述密码置换的系统，其中包括著名的代换-置换网络。