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

Abstract

Let ${\mathbb{F}}_q$ be a finite field of characteristic $p$. In this paper we prove that the $c$-Boomerang Uniformity, $c\ne 0$, 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.

References in corpus (1)

• Boomerang uniformity of a class of power maps