Achieving Practical and Privacy-Preserving kNN Query Over Encrypted Data
Yandong Zheng, Rongxing Lu, Songnian Zhang, Jun Shao, Hui Zhu
Abstract
As one of the most popular queries in big data era, the <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> nearest neighbors ( <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 plays a significant role in various applications, such as medical diagnosis, signal processing, and recommendation systems. Meanwhile, driven by the advancement of the cloud service, an emerging trend among applications is to outsource the dataset and the corresponding <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 services to the cloud. However, as the cloud is not fully trusted, those applications will face vital privacy concerns, and thus they usually encrypt data before outsourcing them to the cloud. Because encrypted data are outsourced to cloud, the <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 over encrypted data has become increasingly attractive, and many solutions have been put forth in recent years. However, existing solutions cannot fully satisfy the objects of returning exact query results, protecting database privacy and query privacy, achieving high query efficiency, and imposing low computational costs at the user side. To address these issues, in this paper, we propose a new practical 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. Specifically, we first refine the general security requirements for the matrix encryption by systematically analyzing existing algorithms. Then, we design a novel asymmetric matrix encryption (AME) to securely achieve Euclidean distance computation and two distances comparison in a single-party and non-interactive way. Then, based on the AME scheme, we propose a 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, in which a max-heap of size <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> is used to accelerate query efficiency. Detailed security analysis shows that our proposed scheme is really privacy-preserving. In addition, extensive performance evaluations are conducted, and the results demonstrate that our proposed scheme is also highly efficient.