EPPQ: Efficient and Privacy-Preserving $k$NN Query Processing for Outsourced High-Dimensional Data

Extensive schemes have been conducted on the development of efficient and privacy-preserving $k$NN query algorithms in data outsourcing scenarios. However, existing researches primarily address low-dimensional data, posing scalability challenges in higher dimensions. To tackle this issue, we propose an efficient and privacy-preserving $k$NN query scheme for outsourced high-dimensional data (EPPQ), emphasizing the complete lifecycle from secure dimensionality reduction of high-dimensional data to secure $k$NN query on the reduced-dimensional data. Specifically, in the secure dimensionality reduction phase: on the one hand, EPPQ integrates principal component analysis (PCA) for dimensionality reduction to minimize computational overhead. On the other hand, to address privacy concerns during the process of PCA, by incorporating differential privacy (DP), we propose the Privacy-Preserving Data Dimensionality Reduction Algorithm based on PCA (PDDRP). In the secure $k$NN query phase: for one thing, EPPQ facilitates the index of the reduced-dimensional data by k-d tree. To enhance index efficiency, we innovatively propose plaintexts-based distance calculation definitions (PDC definitions) and construct an efficient variant of k-d tree (Ek-d tree), for the first time. For another, the Paillier homomorphic encryption (PHE) technique is leveraged to safeguard privacy when outsourcing Ek-d tree to untrusted cloud servers. Additionally, for ciphertexts-based distance calculations and comparisons, we design the Secure Precomputed Distance protocol (SPCD) and Secure Comparison protocol (SCOM). Finally, we creatively present the Privacy-Preserving $k$NN Query Algorithm based on Ek-d tree (PKQKT) for efficient and secure $k$NN query. Comprehensive security analysis demonstrates that the EPPQ scheme meets the required security properties under the honest-but-curious model. Extensive experiments confirms that EPPQ achieves high computational efficiency and query accuracy.