On weakly APN functions and 4-bit S-Boxes

TL;DR

This paper investigates the conditions under which 4-bit S-Boxes are weakly APN, providing theoretical criteria and leveraging classification results for comprehensive analysis.

Contribution

It offers new theoretical criteria for identifying weakly APN 4-bit S-Boxes, supported by computer-aided proofs based on existing classifications.

Findings

Derived necessary and sufficient conditions for weakly APN 4-bit S-Boxes

Enhanced understanding of S-Box security properties

Utilized classification to strengthen theoretical results

Abstract

S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently by De Canni\'ere and Leander-Poschmann, we can strengthen our results with a computer-aided proof.