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Faster privacy-preserving location proximity schemes for circles and polygons

In the last decade, location information became 
 easily obtainable using off-the-shelf mobile devices. 
 This gave a momentum to developing Location Based Services (LBSs) 
 such as location proximity detection, which can be used to find 
 friends or taxis nearby. LBSs can, however, be easily misused to 
 track users, which draws attention to the need of protecting 
 privacy of these users. 
 In this work, we address this issue by designing, implementing, 
 and evaluating multiple algorithms for Privacy-Preserving 
 Location Proximity (PPLP) that are based on different secure 
 computation protocols. Our PPLP protocols support both circle and 
 polygon range queries and have runtimes from a few to some 
 hundreds of milliseconds and bandwidth requirements from a few 
 hundreds of bytes to one megabyte. Consequently, they are 
 well-suited for different scenarios and offer faster runtimes and 
 savings in bandwidth and computational power as well as security 
 improvements compared to previous PPLP schemes. In addition, the 
 computationally most expensive parts of the PPLP computation can 
 be precomputed in our protocols, such that the input-dependent 
 online phase runs in just a few milliseconds.