Single-Server Client Preprocessing PIR with Tight Space-Time Trade-Off

This paper partly solves the open problem of tight trade-off of client storage and server time in the client preprocessing setting of private information retrieval (PIR). In the client preprocessing setting of PIR, the client is allowed to store some hints generated from the database in a preprocessing phase and use the hints to assist online queries. We construct a new single-server client preprocessing PIR scheme. For a database with $n$ entries of size $w$, our protocol uses $S=O((n/T) \cdot (\log n + w))$ bits of client storage and $T$ amortized server probes over $n/T$ queries, where $T$ is a tunable online time parameter. Our scheme matches (up to constant factors) a $ST = \Omega(nw)$ lower bound generalized from a recent work by Yeo (EUROCRYPT 2023) and a communication barrier generalized from Ishai, Shi, and Wichs (CRYPTO 2024).

From a technical standpoint, we present a novel organization of hints where each PIR query consumes a hint, and entries in the consumed hint are relocated to other hints. We then present a new data structure to track the hint relocations and use small-domain pseudorandom permutations to make the hint storage sublinear while maintaining efficient lookups in the hints.