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With the pervasiveness of location-aware mobile terminals and the popularity of social applications, location-based social networking service (LBSNS) has brought great convenience to people's life. Meanwhile, proximity detection, which makes LBSNS more flexible, has aroused widespread concern. However, the prosperity of LBSNS still faces many severe challenges on account of users' location privacy and data security. In this paper, we propose two efficient and privacy-preserving proximity detection schemes, named arbitrary geometric range query for polygons (AGRQ-P) and arbitrary geometric range query for circles (AGRQ-C), for location-based social applications. With proposed schemes, a user can choose any area on the map, and query whether her/his friends are within the region without divulging the query information to both social application servers and other users, meanwhile, the accurate …