Millions of users use location-based applications (LBAs) to share their positions with friends, request information from points of interest finders, or get notifications from event finders, etc. Such LBAs are typically based on location servers (LSs) managing mobile object positions in a scalable fashion. However, storing precise user positions on LSs raises privacy concerns, in particular, if LS providers are non-trusted. To solve this problem, we present PShare-BSP, a novel approach for the secure management of private user positions on non-trusted LSs. PShare-BSP splits up precise user positions into position shares and distributes them to different LSs of different providers. Thus, a compromised provider only reveals user positions with degraded precision. Nevertheless, LBAs can combine several shares from different LSs to increase their precision.

PShare-BSP improves on our previous position sharing approaches: It uses a deterministic share generation approach based on binary space partitioning to avoid probabilistic attacks based, for instance, on Monte Carlo simulations. Moreover, it significantly decreases the computational complexity and increases the efficiency by reducing the update costs for succeeding position updates.