Approximate and exact hybrid algorithms for private nearest-neighbor queries with database protection

Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O(|D|) in the worst case). PIR, on the other hand, reduces this bound to $O(\sqrt{|D|})$, but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead.