Billion-Scale Nearest-Neighbor Search under Fully Homomorphic Encryption on a Single GPU, Balancing Leakage and Cost
We build a system that answers"which database vectors are most similar to my query?"without the server ever seeing the query. The query is encrypted with fully homomorphic en- cryption (FHE); the server does all its scoring on ciphertexts and returns encrypted results that only the client can read. The challenge is speed: at a billion vectors, scoring every row under encryption is far too slow, so we combine two ideas - rank reduction (shrink each vector's dimen- sion) and a hierarchy (route to a small candidate set instead of scanning everything) - executed under encryption on a single GPU. We evaluate on three corpora at very different scales: a face corpus of 222 049 centroids clustered from ~10 M face images (512-dim), DataComp-1B (1.39 x 10^9 vectors, 512-dim CLIP), and Deep1B (10^9 vectors, 96-dim). On DataComp-1B we reach a recall@10 of 0.90 against the single labeled answer, or 0.95 when a near-duplicate im- age in the top-10 also counts as correct (the data is web-scraped and full of duplicates), at ~6 s per encrypted query on a GPU; a lighter configuration reaches 0.78/0.83 at ~1.8 s. These are warm (deployable) server-side latencies - client decryption and network transfer are excluded. On Deep1B we reach recall@10 0.90 under all-levels FHE (0.9045 measured over 2000 FHE queries, matching the 0.906 plaintext routing - the 96 ->128 zero-pad is exact, correlation 1.0) at 2.3 s warm per query. We describe the full client-server protocol in enough detail to repro- duce it, and report accuracy and latency for every configuration. We also measure what this speed costs: the hierarchy's access pattern leaks the database geometry (an observer recovers 72% of the coarse-cell neighbor graph from access patterns alone), and we show that seeded (fixed-group) padding cuts this leak by ~35x (to ~2%), where naive padding is defeated by a repeated-query attack.