## 1 Introduction
[19] proposed a new efficient and privacy-preserving LBS query scheme in the outsourced cloud; [PERSON] et al. [20] developed the collaborative trajectory privacy-preserving scheme for the trajectory privacy of continuous queries. However, with vast LBS requests generated everyday, the transmission of the extraordinarily huge volume data to the cloud has resulted in unbearable transmission latency, which will degrade the quality of service to end users, especially mobile users [9; 21; 22]. As a result, privacy-preserving LBS query schemes designed for cloud computing may not satisfy the low-latency. Hence, the content of fog computing has been introduced to make up the disadvantage of the centralized processing in the cloud [1]. As far as we know, existing schemes in fog computing mainly concentrated on location privacy in wireless sensor networks [23] or real-time navigation of vehicular ad hoc networks [24]. Nevertheless, few fog computing-based schemes considered the privacy issue in the LBS query. Moreover, almost all state-of-the-art LBS query schemes only take the location matching into consideration without considering content matching, and thus this is not fine-grained. For instance, when a mobile user wants to query a hospital within 500 m, the returned results in existing schemes are all the LBS data meeting the spatial range (within 500 m). That is, in addition to the hospital, the result may include a restaurant, a park, or a small and so on. In fact, these results are not necessary for LBS users, and it will lead to additional communication and computational costs, e.g., users have to decrypt all the returned ciphertexts to find the point of interest. To not only ensure the privacy-preserving and low-latency, but also achieve the fine-grained query result, in this paper, we propose a fine-grained and privacy-preserving query scheme for fog computing-enhanced location-based service (FGPQ). The contributions of this paper are threefold as follows. * First, we present our FGPQ scheme, which is characterized by employing the bilinear pairing [25] and the asymmetric scalar-product preserving encryption (ASPE) [26] to realize the LBS searching. In addition to satisfying the given spatial range, the searching result satisfies the given searching content, which is not considered in many up-to-date schemes. * Secondly, we give detailed privacy analysis to show that our proposed FGPQ indeed achieves the privacy preservation of both the LBS provider and mobile users. Finally, we theoretically analyze the computational and communication overheads, and run extensive experiments to demonstrate that our FGPQ scheme is more efficient than the EPLQ scheme [18] and EPQ scheme [19]. In addition, the latency analysis shows that our FGPQ scheme is really low-latency, which is suitable for the real-time LBS query. The remainder of this paper is organized as follows. In Section 2, we introduce our system model and design goals. Then, we describe some preliminaries in Section 3. In Section 4, we present our FGPQ scheme, followed by privacy analysis and performance analysis in Section 5 and Section 6, respectively. Finally, we draw our conclusions in Section 7.