FancyPIR: Stateless Batch Private Information Retrieval With Communication-Computation Trade-Offs

Abstract

Existing Private Information Retrieval (PIR) protocols perform reasonably well in practice. However, the communication overhead remains a significant obstacle for large-scale applications. A natural approach is to amortize the communication overhead by querying multiple entries simultaneously. Recent research has explored Batch PIR (Multi-query PIR) protocols that optimize asymptotic complexity in single-server scenarios. This paper presents $\text {FancyPIR}$, a stateless batch PIR solution that attempts to trade off communication against computation without depending on the preprocessing hint. $\text {FancyPIR}$ aims to reduce the communication overhead while managing the computational cost. To this end, $\text {FancyPIR}$ employs two major strategies: first, $\text {FancyPIR}$ reduces the number of rotations in the initialization (offline) phase and the number of multiplication operations in the server response (online) phase, which decreases the computational burden; second, $\text {FancyPIR}$ packs multiple queries and merges responses using the vectorized homomorphic encryption during the online phase, significantly reducing the communication overhead. Specifically, for retrieving a batch of 256 entries from a database containing $2^{20}$ entries (each 256 Bytes in size), $\text {FancyPIR}$ achieves a communication overhead reduction of 8.4$\sim 104\times$ compared to state-of-the-art solutions (presented in IEEE S&P ’18 et al.), along with an improvement in initialization setup time by 1.9$\sim 3\times$. Considering communication and computation, $\text {FancyPIR}$ reduces server monetary costs by 8.5$\sim 59\times$ for different database sizes.