Low c-Differential Uniformity of the Swapped Inverse Function in Odd Characteristic

TL;DR

This paper investigates the $c$-differential uniformity of swapped inverse functions over finite fields of odd characteristic, showing they generally have low uniformity, which is significant for cryptographic function design.

Contribution

It provides the first analysis of the $c$-differential uniformity of swapped inverse functions in odd characteristic, establishing an upper bound of 6.

Findings

Swapped inverse functions have $c$-differential uniformity at most 6.

Most swapped inverse functions in odd characteristic are low $c$-differential uniformity functions.

Exceptional cases with higher uniformity are identified.

Abstract

The study of Boolean functions with low $c$-differential uniformity has become recently an important topic of research. However, in odd characteristic case, there are not many results on the ($c$-)differential uniformity of functions that are not power functions. In this paper, we investigate the $c$-differential uniformity of the swapped inverse functions in odd characteristic, and show that their $c$-differential uniformities are at most 6 except for some special case.