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Let $\mathbb{F}_q$ be a finite field of characteristic $p$. In this paper weprove that the $c$-Boomerang Uniformity, $c \neq 0$, for all permutationmonomials $x^d$, 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 classof Generalized Triangular Dynamical Systems, a polynomial-based approach todescribe cryptographic permutations, including the well-knownSubstitution-Permutation Network.

A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials