## 2 Related Work
### Privacy-Preserving Location-Based Query  
Although location-based services enhance daily convenience, they introduce significant challenges related to customer privacy and the protection of location data. Consequently, researchers have proposed many privacy-preserving location query schemes [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15] in industry and academia. These schemes can be roughly categorized into the following two categories: non-cryptographic schemes and cryptographic schemes. Some schemes [2; 3; 4; 5; 6; 7] utilize non-cryptographic methods to protect the privacy of location data. [PERSON] et al. [2] employed anonymization techniques to protect the privacy of the location of the mobile user. [PERSON] et al. [3] proposed location privacy protection for smartphones (LPPS), which is a privacy-preserving top-k query. LPPS operates without relying on a trusted third party (TTP) and does not necessitate changes to the business model of location-based service (LBS) servers. [PERSON] et al. [4] proposed a strategy that combines a caching mechanism with K-anonymity, which not only meets users' demands for accessing required services at the lowest cost but also safeguards users' location privacy. [PERSON] et al. [5] filtered out potential bogus data based on three criteria: time accessibility, direction similarity, and in-degree/out-degree. As a result, the remaining data helps to protect the privacy of the actual location information. However, these schemes suffer from lower privacy and returned results are not accurate enough. [PERSON] et al. [6] proposed a novel query for spatial databases, known as the RNH query, which identifies neighborhoods where a specified query facility is the nearest facility among others in the dataset. In summary, most of these schemes rely on anonymization techniques or pseudo data to provide only a weak level of privacy protection. Other schemes [8; 9; 10; 11; 12; 13; 14; 15] aim to use various cryptographic methods to protect the privacy of location data, such as homomorphic encryption (HE), differential privacy (DP), and order-preserving encryption (OPE). [PERSON] et al. [8] proposed a novel privacy-preserving reverse nearest neighbor (PPRNN) scheme in a static setting based on structured encryption (SE) and the proposed reference-locked order-preserving encryption (RL-OPE), referred to as sPPRNN. [PERSON] et al. [9] proposed a privacy-preserving scheme that enables data owners to respond to location-based queries without sharing their data with other businesses and without accessing sensitive information, such as the customer lists of the businesses submitting the queries. [PERSON] et al. [10] proposed a privacy-preserving optimal location query scheme (PPOLQ) that supports multiple condition filters and queries across multiple data providers in outsourced environments. [PERSON] et al. [11] proposed a privacy-preserving spatiotemporal keyword search framework for encrypted location-based service (LBS) data, utilizing attribute-based encryption, linear encryption, and Rivest-Shamir-Adleman (RSA) encryption. This framework enables mobile users to submit LBS queries that incorporate spatial ranges, time intervals, and Boolean keyword expressions, providing accurate and authorized search results by matching these query conditions, along with the corresponding access policies. [PERSON] et al. [12] proposed a novel oblivious location-based k-nearest neighbor (KNN) query scheme, ensuring that the cloud cannot link two queries, even if they are initiated by query users from the same location. [PERSON] et al. [13] proposed a privacy-preserving framework, which supports multi-location queries with fine-grained access control and allows searching based on location attributes. [PERSON] et al. [14] proposed a privacy-preserving indoor localization scheme that utilizes received signal strength measurements, employing Paillier encryption and garbled circuits to ensure data privacy. [PERSON] et al.