Semantic search systems map data to a high-dimensional vector space and support retrieval of similar data via approximate nearest neighbor search. When the system is hosted by an untrusted cloud provider, there is no privacy for the data or the query. Our goal is to design a system with three properties: privacy, accuracy, and efficiency. Existing works adopt either homomorphic encryption (HE), oblivious RAM (ORAM), or a differential privacy (DP) approach. They fall short of achieving all three properties. In this paper, we present MESS, a system that realizes our goal. It maps the original vectors into binary codes, applies locality-sensitive hashing (LSH) and randomized response, and constructs a multi-graph Hierarchical Navigable Small World (HNSW) index over the perturbed codes. MESS ensures data, query, and access pattern privacy. It also ensures search pattern privacy via a two-phase query perturbation mechanism. The multi-graph index mitigates the impact of perturbation on result quality, thereby achieving accuracy. MESS is efficient because search is performed directly over perturbed codes, without the overhead of homomorphic encryption or ORAM. We give formal analysis of the system's privacy and extensive evaluation of its performance. The results show that MESS achieves up to 15.08\times lower latency than state-of-the-art baselines.

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