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

Fuente: arXiv
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Main Author: Steiner, Matthias Johann
Format: Preprint
Published: 2023
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author Steiner, Matthias Johann
author_facet Steiner, Matthias Johann
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_12621
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials
Steiner, Matthias Johann
Number Theory
Cryptography and Security
Information Theory
Algebraic Geometry
11T06, 14G50, 14H50, 94A60
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.
title A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials
topic Number Theory
Cryptography and Security
Information Theory
Algebraic Geometry
11T06, 14G50, 14H50, 94A60
url https://arxiv.org/abs/2307.12621