Secret Sharing for n-Colorable Graphs with Application to Public Key Cryptography

TL;DR

This paper introduces a secret sharing scheme for n-colorable graphs, enabling secure distribution of graph colorings, and applies it to enhance public key cryptography within the Polly Cracker system.

Contribution

It presents a novel secret sharing method for graph colorings with known structure and demonstrates its application to public key cryptography.

Findings

Effective sharing of n-coloring secrets for graphs with known structure.

Application of the scheme to secure private keys in Polly Cracker.

Enhanced security in public key cryptosystems using graph-based secret sharing.

Abstract

At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors assigned to vertices form the number with entries from Zn. A secret sharing scheme (SSS) for the graph coloring is proposed. The proposed method is applied to the public-key cryptosystem called "Polly Cracker". In this case the graph structure is a public key, while proper 3-colouring of the graph is a private key. We show how to share the private key. Sharing particular n-coloring (color-to-vertex assignment) for the known-structure graph is presented next.