Low c-differentially uniform functions via an extension of Dillon's switching method

TL;DR

This paper extends Dillon's switching method to precisely analyze and construct functions with low c-differential uniformity, enhancing cryptographic function design.

Contribution

It generalizes Dillon's switching method for c-differential uniformity, enabling the construction of PcN and APcN functions with improved cryptographic properties.

Findings

Constructed new PcN and APcN functions for all c ≠ 1.

Generalized previous results on c-differential uniformity.

Provided computational examples with low differential uniformity.

Abstract

In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential uniformity in a controllable number of coordinates to render more such functions. We present several applications of the method in constructing PcN and APcN functions with respect to all $c\neq 1$. As a byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, {\em New PcN and APcN functions over finite fields}, Designs Codes Crypt. 89 (2021), 2637--2651]. Computational results rendering functions with low differential uniformity, as well as, other good cryptographic properties are sprinkled throughout the paper.