Where are you bob? privacy-preserving proximity testing with a napping party

Location based services (LBS) extensively utilize proximity testing to help people discover nearby friends, devices, and services. Current practices rely on full trust to the service providers: users share their locations with the providers who perform proximity testing on behalf of the users. Unfortunately, location data has been often breached by LBS providers, raising privacy concerns over the current practices. To address these concerns previous research has suggested cryptographic protocols for privacy-preserving location proximity testing. Yet general and precise location proximity testing has been out of reach for the current research. A major roadblock has been the requirement by much of the previous work that for proximity testing between Alice and Bob both must be present online. This requirement is not problematic for one-to-one proximity testing but it does not generalize to one-to-many testing. Indeed, in settings like ridesharing, it is desirable to match against ride preferences of all users, not necessarily ones that are currently online. This paper proposes a novel privacy-preserving proximity testing protocol where, after providing some data about its location, one party can go offline (nap) during the proximity testing execution, without undermining user privacy. We thus break away from the limitation of much of the previous work where the parties must be online and interact directly to each other to retain user privacy. Our basic protocol achieves privacy against semi-honest parties and can be upgraded to full security (against malicious parties) in a straight forward way using advanced cryptographic tools. Finally, we reduce the responding client overhead from quadratic (in the proximity radius parameter) to constant, compared to the previous research. Analysis and performance experiments with an implementation confirm our findings