A degree bound for the c-boomerang uniformity of permutation monomials

Abstract

Let Fq be a finite field of characteristic p. In this paper we prove that the c-Boomerang Uniformity, c≠0, for all permutation monomials xd, where d>1 and p∤d, is bounded by d2,c2≠1,d·(d-1),c=-1,d·(d-2),c=1. 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 of Fqn, including the well-known substitution–permutation network.