Towards Multi-User, Secure, and Verifiable <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN Query in Cloud Database

With the boom in cloud computing, data outsourcing in location-based services is proliferating and has attracted increasing interest from research communities and commercial applications. Nevertheless, since the cloud server is probably both untrusted and malicious, concerns about data security and result integrity have become on the rise sharply. In addition, in the single-user situation assumed by most existing works, query users can capture query content from each other even though the queries are encrypted, which may incur the leakage of query privacy. Unfortunately, there exists little work that can commendably assure data security and result integrity in the multi-user setting. To this end, in this article, we study the problem of multi-user, secure, and verifiable <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="cui-ieq2-3237879.gif"/></alternatives></inline-formula> nearest neighbor query (<bold>MSV <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="cui-ieq3-3237879.gif"/></alternatives></inline-formula> NN</bold>). To support MSV <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="cui-ieq4-3237879.gif"/></alternatives></inline-formula> NN, we first propose a novel unified structure, called verifiable and secure index (VSI). Based on this, we devise a series of secure protocols to facilitate query processing and develop a compact verification strategy. Given an MSV <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="cui-ieq5-3237879.gif"/></alternatives></inline-formula> NN query, our proposed solution can not merely answer the query efficiently while can guarantee: 1) preserving <italic>data privacy</italic>, <italic>query privacy</italic>, <italic>result privacy</italic>, and <italic>access patterns privacy</italic>; 2) authenticating the <italic>correctness</italic> and <italic>completeness</italic> of the results; 3) supporting <italic>multi-user</italic> with different keys. Finally, the formal security analysis and complexity analysis are theoretically proven and the performance and feasibility of our proposed approach are empirically evaluated and demonstrated.