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arXiv · 2307.12621

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

Matthias Johann Steiner
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Abstract

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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Matthias Johann Steiner. 2023-07-24. A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials. https://doi.org/10.1007/s00200-024-00670-6

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