Paper 2024/2012 Original: eprint.iacr.org/2024/2012 ↗

GraSS: Graph-based Similarity Search on Encrypted Query

Abstract

Similarity search, i.e., retrieving vectors in a database that are similar to a query, is the backbone of many applications. Especially, graph-based methods show state-of-the-art performance. For sensitive applications, it is critical to ensure the privacy of the query and the dataset. In this work, we introduce GraSS, a secure protocol between client (query owner) and server (dataset owner) for graph-based similarity search based on fully homomorphic encryption (FHE). Both the client-input privacy against the server and the server-input privacy against the client are achievable based on underlying security assumptions on FHE. We first propose an FHE-friendly graph structure with a novel index encoding method that makes our protocol highly scalable in terms of data size, reducing the computational complexity of neighborhood retrieval process from $O(n^2)$ to $\tilde{O}(n)$ for the total number of nodes $n$. We also propose several core FHE algorithms to perform graph operations under the new graph structure. Finally, we introduce GraSS, an end-to-end solution of secure graph-based similarity search based on FHE. To the best of our knowledge, it is the first FHE-based solution for secure graph-based database search. We implemented GraSS with an open-source FHE library and estimated the performance on a million-scale dataset. GraSS identifies (approximate) top-16 in about $83$ hours achieving search accuracy of $0.918$, making it over $28\times$ faster than the previous best-known FHE-based solution.