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With the pervasiveness of mobile devices and the development of wireless communication technique, location-based services (LBSs) have made our life more convenient, and the polygons spatial query, which can provide more flexible LBS, has attracted considerable interest recently. However, the flourish of polygons spatial query still faces many challenges including the query information privacy. In this paper, we present an efficient and privacy-preserving polygons spatial query framework for location-based services, called Polaris. With Polaris, the LBS provider (LP) outsources the encrypted LBS data to cloud server (CS), and the registered user can query any polygon range to get accurate LBS results without divulging his/her query information to the LP and CS. Specifically, an efficient special polygons spatial query (SPSQ) algorithm over ciphertext is constructed, based on an improved homomorphic …