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, $c \neq 0$, 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.12621
- arXiv:
- arXiv:2307.12621
- Bibcode:
- 2023arXiv230712621S
- Keywords:
-
- Mathematics - Number Theory;
- Computer Science - Cryptography and Security;
- Computer Science - Information Theory;
- Mathematics - Algebraic Geometry;
- 11T06;
- 14G50;
- 14H50;
- 94A60