Threshold spatial keyword ciphertext retrieval with enhanced privacy

With the rapid development of geolocation technology and the explosive growth of data volumes, massive spatial data has been migrated to cloud storage and processing, which effectively alleviates the pressure on local storage and computing resources but also gives rise to non-negligible security challenges. Currently, most research focuses on encrypting a single attribute (spatial or keyword) of spatial keyword data, making it difficult to directly address complex geo-keyword range query requirements. Moreover, most existing solutions use Asymmetric Scalar Product Encryption (ASPE) to encrypt data, but ASPE has been proven insecure against known plaintext attacks. In light of this, we propose an Enhanced Threshold Spatial Keyword Ciphertext Query (ETSKQ) scheme based on Enhanced ASPE (EASPE). Specifically, this scheme first converts spatial coordinates using Gray codes and achieves efficient compression with wildcard techniques. Then, it designs an extension method based on random numbers and Bloom filters to expand the Gray codes, enhancing the flexibility and query efficiency of the data structure. In terms of keyword processing, thresholds are introduced to encode the keyword set into vectors, and a quadtree index is constructed to support fast and accurate range queries. Meanwhile, this paper abandons the traditional ASPE encryption method and adopts EASPE technology instead, ensuring that the data remains indistinguishable even under chosen plaintext attacks (IND-CPA). Extensive experiments have demonstrated the practical effectiveness of our scheme.