Private Structured-Subset Retrieval

2026-05-06

AI Summary

This work addresses multi-server private information retrieval (PIR) scenarios where user demands are constrained to a specific structured family of subsets. It introduces, for the first time, a formal model termed “structured subset private retrieval,” which generalizes beyond conventional PIR and multi-message PIR (MPIR) frameworks. By exploiting the prior structural knowledge of the demand sets, the authors propose an efficient protocol based on balanced {0,1}-linear schemes, complemented by dual-bound analysis and optimized construction techniques. The resulting approach achieves higher retrieval rates than MPIR across various structured demand families while substantially reducing the number of subpackets required. Notably, in certain cases, it eliminates the dependency on finite field size constraints, thereby offering both strong privacy guarantees and enhanced computational efficiency.

Abstract

We introduce the \emph{Private Structured-Subset Retrieval (PSSR)} problem, where a user retrieves $D$ messages from a database of $K$ messages replicated across $N$ non-colluding servers, and the demand is restricted to a known structured family of $D$-subsets. This formulation generalizes classical Private Information Retrieval (PIR) and multi-message PIR (MPIR), and captures settings where the demand space is constrained by application-specific structure. Focusing on balanced ${\{0,1\}}$-linear schemes, we derive converse bounds on the maximum retrieval rate and minimum subpacketization level, and develop an optimization-based framework for constructing schemes for general structured demand families. Our results show that, for certain families, the PSSR rate converse bound can exceed the best-known MPIR rate upper bound; when this PSSR bound is achievable, MPIR rate-optimal schemes become suboptimal for those families. By exploiting demand structure, our PSSR schemes achieve higher retrieval rates for many families and never underperform the best-known balanced ${\{0,1\}}$-linear MPIR schemes. Our results also show that demand structure can reduce the required subpacketization even when the optimal rate is unchanged. Our parallel work on contiguous-demand families further illustrates the scope of this framework by yielding rate-optimal schemes with substantially smaller subpacketization and no field-size restrictions, improving upon MPIR-based schemes.

Problem

• Private Information Retrieval
• Structured-Subset Retrieval
• Multi-message PIR
• Demand Structure
• Non-colluding Servers

Innovation

• Private Information Retrieval
• Structured Subset Retrieval
• Subpacketization
• Retrieval Rate
• Optimization-based Scheme