A new construction of differentially 4-uniform permutations over $F_{2^{2k}}$

TL;DR

This paper introduces a novel construction of differentially 4-uniform permutations over finite fields of characteristic two, enhancing cryptographic S-box design with functions that are CCZ-inequivalent, highly nonlinear, and of optimal algebraic degree.

Contribution

It provides a new method to construct differentially 4-uniform permutations that are CCZ-inequivalent to known functions, with optimal algebraic degree and high nonlinearity.

Findings

Generated many new CCZ-inequivalent functions

Functions have optimal algebraic degree

Functions exhibit high nonlinearity

Abstract

Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this paper, we present a new construction of differentially 4-uniformity permutations over even characteristic finite fields and obtain many new CCZ-inequivalent functions. All the functions are switching neighbors in the narrow sense of the multiplicative inverse function and have the optimal algebraic degree and high nonlinearity.