A class of permutations on \({\mathbb {Z}}_{p}\) with differential uniformity at most 3

The article delves into the construction and properties of a class of permutations with differential uniformity at most 3, a key metric in cryptographic security. It builds upon previous research by Drakakis et al. and others, providing exhaustive results for primes less than or equal to 7 and mathematical proofs for larger primes. The study focuses on the sets and their elements, offering a detailed analysis of their cardinality and relationships. The paper introduces several theorems and propositions that characterize these permutations and their differential uniformity, contributing valuable insights to the field of cryptography.