Monitoring location updates from mobile users has important applications in many areas, ranging from public safety and national security to social networks and advertising. However, sensitive information can be derived from movement patterns, thus protecting the privacy of mobile users is a major concern. Users may only be willing to disclose their locations when some condition is met, for instance in proximity of a disaster area or an event of interest. Currently, such functionality can be achieved using searchable encryption. Such cryptographic primitives provide provable guarantees for privacy, and allow decryption only when the location satisfies some predicate. Nevertheless, they rely on expensive pairing-based cryptography (PBC), of which direct application to the domain of location updates leads to impractical solutions. We propose secure and efficient techniques for private processing of location updates that complement the use of PBC and lead to significant gains in performance by reducing the amount of required pairing operations. We implement two optimizations that further improve performance: materialization of results to expensive mathematical operations, and parallelization. We also propose an heuristic that brings down the computational overhead through enlarging an alert zone by a small factor (given as system parameter), therefore trading off a small and controlled amount of privacy for significant performance gains. Extensive experimental results show that the proposed techniques significantly improve performance compared to the baseline, and reduce the searchable encryption overhead to a level that is practical in a computing environment with reasonable resources, such as the cloud.