Wally: Batched Private Nearest Neighbor Search at Scale

We present Wally, a batched private nearest-neighbor search protocol that uses differential privacy to break the linear computation barrier of fully-oblivious schemes. In Tiptoe, the server must process the entire database per query to hide the access pattern, resulting in low throughput (909 QPS) and high communication (17.4 MB) on a 3.2M-entry database. Sublinear alternatives like Pacmann require 614 MB of client storage and an offline streaming phase. Wally's key insight is that fully-oblivious schemes are prohibitively expensive at scale, but the same scale also provides an opportunity. Large-scale systems naturally have many concurrent clients. Wally batches queries from non-coordinating clients, each independently adding fake queries to hide which clusters it accesses. The fake query counts follow a negative binomial distribution, which is non-negative and infinitely divisible, allowing independent sampling without coordination. Clients send queries at random times through an existing anonymization service, avoiding a centralized shuffler. The server sees only an anonymized, noisy stream of cluster accesses that is provably (epsilon, delta)-differentially private, computing over only the relevant clusters. The client encrypts its query under SHE so the server returns only encrypted similarity scores. On a 3.2M-entry database with 500K-query batches, Wally achieves 7-29x higher throughput and 6.7-31x lower communication than Tiptoe, and 15,000x lower client storage than Pacmann, with strong (epsilon=0.1, delta=2^{-26})-DP and comparable accuracy. We also propose optimizations to SHE and keyword PIR yielding 2-3x improvements in PIR and 20-25% in BFV operations, and release an open-source BFV library in Swift.