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Location-based service (LBS) is booming up in recent years with the rapid growth of mobile devices and the emerging of cloud computing paradigm. Among the challenges to establish LBS, the user privacy issue becomes the most important concern. A successful privacy-preserving LBS must be secure and provide accurate query [e.g., -nearest neighbor (NN)] results. In this work, we propose a private circular query protocol (PCQP) to deal with the privacy and the accuracy issues of privacy-preserving LBS. The protocol consists of a space filling curve and a public-key homomorphic cryptosystem. First, we connect the points of interest (POIs) on a map to form a circular structure with the aid of a Moore curve. And then the homomorphism of Paillier cryptosystem is used to perform secret circular shifts of POI-related information (POI-info), stored on the server side. Since the POI-info after shifting and the amount of shifts are encrypted, LBS providers (e.g., servers) have no knowledge about the user's location during the query process. The protocol can resist correlation attack and support a multiuser scenario as long as the predescribed secret circular shift is performed before each query; in other words, the robustness of the proposed protocol is the same as that of a one-time pad encryption scheme. As a result, the security level of the proposed protocol is close to perfect secrecy without the aid of a trusted third party and simulation results show that the k-NN query accuracy rate of the proposed protocol is higher than 90% even when is large.