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

07/24/2023

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by   Matthias Johann Steiner, et al.

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Let 𝔽_q be a finite field of characteristic p. In this paper we prove that the c-Boomerang Uniformity, c ≠ 0, for all permutation monomials x^d, where d > 1 and p ∤ 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.