VeriKNN: A verifiable and efficient secure k-NN query scheme via homomorphic encryption in dual-cloud environments

With the widespread adoption of cloud computing, data privacy protection has become a critical issue, especially for encrypted retrieval tasks in cloud environments. This paper proposes VeriKNN, a secure, efficient, and verifiable $k$-nearest neighbor (kNN) query scheme based on homomorphic encryption. The scheme introduces a verification mechanism that specifically ensures communication integrity between servers under an honest-but-curious threat model. VeriKNN first constructs a Voronoi diagram and partitions it into encrypted grids for coarse filtering. Then, it builds a multi-layer index of neighboring cells to enable fine-grained search. To address the challenges of computational efficiency and security, we propose a novel set of secure protocols specifically designed for dual-cloud collaboration, significantly improving retrieval performance. Extensive experiments demonstrate that VeriKNN outperforms the state-of-the-art SVK scheme by up to 3000 times in speed across various dataset sizes and $k$-values, and is applicable not only to two-dimensional data but also to high-dimensional data. Compared to the HFkNN scheme, VeriKNN achieves a slight reduction in accuracy but offers a 500-fold increase in speed, with the performance gap widening as dataset size increases, highlighting its superior scalability and efficiency.