Differentially low uniform permutations from known 4-uniform functions

TL;DR

This paper introduces new methods for constructing permutations with low differential uniformity, specifically 6-uniform functions, by modifying known functions on subfields, enhancing cryptographic resistance.

Contribution

It presents novel piecewise constructions of differentially 6-uniform permutations based on modifications of Gold and Bracken-Leander functions.

Findings

Constructed two new 6-uniform permutation functions

Demonstrated resistance to differential attacks

Extended known functions with low differential uniformity

Abstract

Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken-Leander function on a subfield.