On construction and (non)existence of $c$-(almost) perfect nonlinear functions

TL;DR

This paper investigates the construction and limitations of functions with low c-differential uniformity, providing characterizations via quadratic polynomials and proving non-existence results for certain classes.

Contribution

It offers a new characterization of c-(almost) perfect nonlinear functions using quadratic polynomials and establishes non-existence results for specific cases.

Findings

Characterization of APcN and PcN functions via quadratic polynomials

Non-existence results for certain c-(almost) perfect nonlinear functions

Insights into the structure of low differential uniformity functions

Abstract

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of APN and PN functions) have been investigated. Here, we provide a characterization of such functions via quadratic polynomials as well as non-existence results.