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

Kamil Kulesza·Zbigniew Kotulski
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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.

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Kamil Kulesza, Zbigniew Kotulski. 2003-10-28. Secret Sharing for n-Colorable Graphs with Application to Public Key Cryptography. https://arxiv.org/abs/cs/0310053

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