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As a special type of big data, the big graph has wide applications. The remote data integrity checking (RDIC) scheme enables public clouds to efficiently convince the clients that their graph data are stored properly, without the need of retrieving the actual data contents. The existing schemes support verifiable update often by adopting the authentication data structures (ADSs), e.g., Merkel hash tree (MHT). The main obstacle for applying the existing RDIC schemes to big graphs is due to the lack of support for verifiable sub-graph operations with high efficiency. In this paper, we propose a new RDIC scheme for big graphs, called GVD-RDIC, to support public auditing and verifiable dynamic graph updates with high efficiency. We have designed novel ADS based on the graph Voronoi diagram (GVD) and enhanced MHT to address the integrity of graph structure and verifiable sub-graph updates. In addition, our ADS can be applied to any type of graphs. Moreover, our GVD-RDIC scheme adopts a new construction for the homomorphic authenticator to enable index verifications for public auditors. A server response constructed with unchallenged block will be rejected. The proposed scheme is proven secure under a random oracle model. Both the theoretical analysis and the simulation results show that our scheme is practicable for real-world big graphs.

Secure Dynamic Big Graph Data: Scalable, Low-Cost Remote Data Integrity Checking