Efficient Conjunctive Geometric Range Query over Encrypted Spatial Data with Learned Index

With the increasing popularity of geo-positioning technologies and mobile Internet, spatial data query services have attracted extensive attention. To protect the confidentiality of sensitive information outsourced to cloud servers, much efforts have been devoted to designing geometric range query schemes over encrypted spatial data without affecting availability. However, existing works focus on the privacy-preserving schemes with traditional tree indexes, causing more computing and storage issues. In this paper, we propose an efficient conjunctive geometric range query scheme over encrypted spatial data with a learned index. In particular, we design a new privacy-preserving learned index for spatial data to reduce the search space and storage overhead. The main idea is to add noise disturbance to the objective function instead of directly adding it to output results, reducing the leakage of private information and ensuring the correctness of output results. Moreover, we propose a spatial segmentation algorithm to avoid accessing a large number of unnecessary Z codes in the query process. The formal security analysis shows that our scheme ensures index data security and query privacy. Simulation results show that the query efficiency is improved while the storage overhead is significantly reduced compared with the state-of-the-art schemes.