Efficient Secure k-Nearest Neighbours over Encrypted Data

Enterprise customers of cloud services are wary of outsourcing sensitive user and business data due to inherent security and privacy concerns. In this context, storing and computing directly on encrypted data is an attractive solution, especially against insider attacks. Homomorphic encryption, the keystone enabling technology is unfortunately prohibitively expensive. In this paper, we focus on finding k-Nearest Neighbours (k-NN) directly on encrypted data, a basic data-mining and machine learning algorithm. The goal is to compute the nearest neighbours to a given query, and present exact results to the clients, without the cloud learning anything about the data, query, results, or the access and search patterns. We describe a novel protocol in the two-party cloud setting, using an underlying somewhat homomorphic encryption scheme. In comparison to the state-of-the-art protocol in this setting, we provide asymptotically faster performance, without sacrificing any security guarantees. We implemented our protocol to demonstrate that it is efficient and practical on large and relevant real-world datasets and study how it scales well across different parameters on simulated data.