A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials. (arXiv:2307.12621v2 [math.NT] UPDATED)

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.

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