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

Extensive schemes have been conducted on the development of efficient and privacy-preserving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN query scheme for outsourced high-dimensional data (EPPQ), emphasizing the complete lifecycle from secure dimensionality reduction of high-dimensional data to secure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN query on the reduced-dimensional data. Specifically, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in the secure dimensionality reduction phase</i>: 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). <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In the secure <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN query phase</i>: 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN Query Algorithm based on Ek-d tree (PKQKT) for efficient and secure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN query. Comprehensive security analysis demonstrates that the EPPQ scheme meets the required security properties under the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">honest-but-curious</i> model. Extensive experiments confirms that EPPQ achieves high computational efficiency and query accuracy.