Digital signature schemes are a foundational building block enabling integrity and non-repudiation. We propose a graph signature scheme and corresponding proofs that allow a prover (1) to obtain a signature on a committed graph and (2) to subsequently prove to a verifier knowledge of such a graph signature. The graph signature scheme and proofs are a building block for certification systems that need to establish graph properties in zero-knowledge, as encountered in cloud security assurance or provenance. We extend the Camenisch-Lysyanskaya (CL) signature scheme to graphs and enable efficient zero-knowledge proofs of knowledge on graph signatures, notably supporting complex statements on graph elements. Our method is based on honest-verifier Σ-proofs and the strong RSA assumption. In addition, we explore the capabilities of graph signatures by establishing a proof system on graph 3-colorability (G3C). As G3C is NP-complete, we conclude that there exist Camenisch-Lysyanskaya proof systems for statements of NP languages.
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