Investigations of c-Differential Uniformity of Permutations with Carlitz Rank 3

TL;DR

This paper studies the $c$-differential uniformity of permutations with low Carlitz rank, especially rank 3, demonstrating their potential for cryptographic resistance against differential attacks.

Contribution

It establishes that permutations with low Carlitz rank, particularly rank 3, have low $c$-differential uniformity, advancing understanding of their cryptographic suitability.

Findings

Permutations with low Carlitz rank exhibit low $c$-differential uniformity.

Detailed analysis of Carlitz rank 3 permutations shows favorable cryptographic properties.

Results support using low Carlitz rank permutations in cryptographic functions.

Abstract

The $c$-differential uniformity is recently proposed to reflect resistance against some variants of differential attack. Finding functions with low $c$-differential uniformity is attracting attention from many researchers. For even characteristic, it is known that permutations of low Carlitz rank have good cryptographic parameters, for example, low differential uniformity, high nonlinearity, etc. In this paper we show that permutations with low Carlitz rank have low $c$-differential uniformity. We also investigate $c$-differential uniformity of permutations with Carlitz rank 3 in detail.