Efficient Zero-Knowledge Proofs of Graph Signature for Connectivity and Isolation Using Bilinear-Map Accumulator

To prove the graph relations such as the connectivity and the isolation for a certified graph, the system of graph signature and proofs have been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues a prover the signature. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size of each element. Furthermore, the proof size and the verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.