| Summary: | Due to the rapid development of social networks, bio-informatics, internet-of-things etc., subgraph matching query can be found in various applications. Meanwhile, the increasing popularity of storing graph data in the cloud drives demands for graph query processing on a remote cloud server. However, the query results in this scenario may not be guaranteed to be correct, especially when the cloud service provider (CSP) is malicious or compromised by some adversaries, for example, a CSP might omit some edges of the graph so that its search cost would be substantially reduced. Besides, various software bugs and unintended errors are also inevitable. All current generic verifiable computation (VC) schemes applied in this scenario are not only too impractical to be implemented but also need a lot of space to locally store their auxiliary data. To that end, we have put forth both public and designated verification schemes which focus on subgraph matching problems for outsourced graph data. They utilize a modified cryptographic primitive called accumulator to realize fast verification and low local storage overhead. In addition to the two main constructions, we have proposed an optimization to make the scheme more applicable, namely, supporting dynamic updates of the graph. At last, rigorous security proofs and efficiency analysis are given, which justify that our proposed schemes are secure and efficient, satisfying the requirements of general verifiable computation protocols.
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