PHRkNN: Efficient and Privacy-Preserving Reverse kNN Query Over High-Dimensional Data in Cloud

Big data and bursting cloud computing technologies have facilitated an increasing trend of outsourcing data-driven services to the cloud, where the reverse kNN (RkNN) query is a popularly outsourced query service. The RkNN query aims to retrieve objects having the query object as kNN and widely applied in the product recommendation. Considering privacy concerns, the outsourced query services are demanded to protect data privacy, and consequently a series of privacy-preserving query solutions have been put forth. Nevertheless, RkNN query over high-dimensional data has not been studied to date. In this work, we design the first efficient and privacy-preserving RkNN query scheme over encrypted high-dimensional data, named PHRkNN. Specifically, we first introduce a pivot filter condition for the RkNN query and utilize it to deliberately design a pivot filter R-tree (PFR-tree) to organize the high-dimensional dataset such that the RkNN query has sublinear query efficiency. Then, we propose our PHRkNN scheme by designing some homomorphic encryption based private algorithms and applying them to privately achieve PFR-tree based RkNN query. After that, we propose an oblivious PHRkNN scheme on the basis of the PHRkNN scheme by designing a private random tree permutation (PRTP) algorithm to protect the access pattern privacy. The security of our PHRkNN scheme and oblivious PHRkNN scheme is proved by the simulation-based security analysis. The performance is verified through computational costs and communication overheads evaluation.