Towards Secure Approximate <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math> </inline-formula>-Nearest Neighbor Query Over Encrypted High-Dimensional Data

Abstract

As many services have been subcontracted to the cloud, data in such services (i.e., management applications, signal processing, and so on) are stored on cloud in encrypted form for protecting user private information. In many emerging data and signal processing applications, approximate k-nearest neighbor (ANN) query is a prerequisite component for massive high-dimensional data (such as time series, biometric, signal, multimedia data, and so on). Unfortunately, existing secure ANN (SANN) methods encounter the limitation of dimensionality. To further resolve ANN query over high-dimensionally encrypted data, in this paper, we propose an effective SANN model in Euclidean space. In overview, a secure greedy partition method is carefully designed by applying locality sensitive hashing coding and an optimized linear order. Based on that, a novel partition-based SANN ( $\text {SANN}_{\text {P}}$ ) and a multi-division version $\text {mSANN}_{\text {P}}$ resolve SANN query by sequentially scanning a candidate set, which is produced by matching a cloak query with a map index. Our proposed solutions guarantee security and accuracy simultaneously, and reduce communication cost significantly. Meanwhile, the greedy partition method is proved to be indistinguishable secure under chosen-plaintext attack , which is the foundation of security for the proposed solutions. Through extensive experimental studies on four data sets, the proposed mechanisms outperform the state-of-the-art approaches and provide effective and tradeoff between result accuracy and communication cost.