Secure mutual proximity zone enclosure evaluation

Mobile users engage in novel and exciting location-based social media applications (e.g., geosocial networks, spatial crowdsourcing) in which they interact with other users sit- uated in their proximity. In several application scenarios, users define their own proximity zones of interest (typically in the form of polygonal regions, such as a collection of city blocks), and want to find other users with whom they are in a mutual enclosure relationship with respect to their respective proximity zones. This boils down to evaluating two point-in-polygon enclosure conditions, which is easy to achieve for revealed user locations and proximity zones. However, users may be reluctant to share their whereabouts with their friends and with social media service providers, as location data can help one infer sensitive details such as an individual's health status, financial situation or lifestyle choices. In this paper, we propose a mechanism that allows users to securely evaluate mutual proximity zone enclosure on encrypted location data. Our solution uses homomor-phic encryption, and supports convex polygonal proximity zones. We provide a security analysis of the proposed solution, we investigate performance optimizations, and we show experimentally that our approach scales well for datasets of millions of users.