PGSim: Efficient and Privacy-Preserving Graph Similarity Query Over Encrypted Data in Cloud

The boom of cloud computing has stimulated the prevalence of outsourced query services, and privacy concerns further motivate extensive studies on privacy-preserving queries in the cloud. Graph similarity query is one critical query type, in which the similarity between two graphs is usually measured by graph edit distance (GED). Although many schemes have been proposed for GED computation/graph similarity query, they do not consider data privacy and are not applicable to the cloud computing scenario. To address this issue, in this paper, we propose the first efficient and privacy-preserving graph similarity query (PGSim) scheme in the filter and verification framework. Specifically, we first identify the pivot filter property of GED and use the property to design a pivot R-tree based filter algorithm, which can efficiently retrieve candidate graphs for graph similarity query. Then, we design a vertex mapping (VM) tree to index all vertex mappings between two graphs and develop a GED query verification algorithm to verify candidate graphs. After that, we design a suite of private algorithms based on a symmetric homomorphic encryption scheme and apply them to propose a pivot R-tree based filter predicate encryption (PRFilter) scheme and a private GED query verification (PGQVerify) algorithm. Based on the PRFilter scheme and the PGQVerify algorithm, we propose our PGSim scheme. Rigorous security analysis shows that our scheme is selectively secure. Performance evaluation also demonstrates the high efficiency of our scheme.