  Location-based alerts have gained increasing popularity in recent years,
whether in the context of healthcare (e.g., COVID-19 contact tracing),
marketing (e.g., location-based advertising), or public safety. However,
serious privacy concerns arise when location data are used in clear in the
process. Several solutions employ Searchable Encryption (SE) to achieve secure
alerts directly on encrypted locations. While doing so preserves privacy, the
performance overhead incurred is high. We focus on a prominent SE technique in
the public-key setting -- Hidden Vector Encryption (HVE), and propose a graph
embedding technique to encode location data in a way that significantly boosts
the performance of processing on ciphertexts. We show that finding the optimal
encoding is NP-hard, and provide several heuristics that are fast and obtain
significant performance gains. Furthermore, we investigate the more challenging
case of dynamic alert zones, where the area of interest changes over time. Our
extensive experimental evaluation shows that our solutions can significantly
improve computational overhead compared to existing baselines.
