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Reachability, which indicates whether a person is reachable from another person through a sequence of location-based contacts, is of importance in many domains, such as public health. Nowadays, large amounts of location data are collected by various Location-Based Services (LBS), which helps to improve the accuracy of reachability queries. Meanwhile, as many LBS systems are deployed on cloud platforms, users have huge concerns about the leakage of their location data. In this paper, we consider how to implement privacy-preserving reachability queries over private location data. We first propose SecReach, a system which can process secure reachability queries by applying Bloom filters and Homomorphic Encryption. Based on the main idea of SecReach, we propose a more efficient system, FastReach, that significantly reduces the computation costs by using Single Instruction Multiple Data operations …