Efficient DPF-based Error-Detecting Information-Theoretic Private Information Retrieval Over Rings

2026-03-31

AI Summary

This work proposes the first information-theoretically secure error-detecting private information retrieval (itED-PIR) scheme based on prime-power rings, addressing the limitations of existing finite-field-based authenticated PIR schemes that rely on prime-order distributed point functions (DPFs). These prior approaches suffer from large key sizes and high communication overhead, hindering practical deployment in information-theoretic security settings and large-scale scenarios. By constructing an information-theoretic DPF (itDPF) over prime-power rings, the proposed scheme circumvents the constraints of finite fields and substantially reduces key size. Furthermore, a single-itDPF key mechanism is introduced, which simultaneously ensures privacy, verifiability, and a 50% reduction in query communication cost. This framework offers an efficient and practical foundation for lightweight, high-security PIR resilient against malicious adversaries.

Abstract

Authenticated private information retrieval (APIR) is the state-of-the-art error-detecting private information retrieval (ED-PIR), using Distributed Point Functions (DPFs) for subpolynomial complexity and privacy. However, its finite field structure restricts it to prime-order DPFs, leading to prohibitively large key sizes under information-theoretic settings, while its dual-DPF-key design introduces unnecessary communication overhead, limiting its practicality for large-scale deployments. This paper proposes a novel ring-based information-theoretic ED-PIR (itED-PIR) scheme that overcomes these limitations by leveraging prime-power-order information-theoretic DPFs (itDPFs). Built over a prime-power ring, the proposed scheme breaks APIR's field-induced constraint to enable more efficient DPF utilization, significantly reducing key size growth and rendering the scheme feasible for high-security scenarios. Additionally, a single-itDPF-key design halves query-side communication overhead by eliminating APIR's redundant dual-key setup, without compromising privacy or verifiability. Beyond immediate efficiency gains, this work establishes a lightweight, flexible framework for constructing DPF-based malicious-resilient private information retrieval, opening new avenues for privacy-preserving data retrieval in distributed storage systems and post-quantum privacy protocols.

Problem

• Private Information Retrieval
• Distributed Point Functions
• Information-Theoretic Security
• Error Detection
• Ring-based Cryptography

Innovation

• ring-based itED-PIR
• prime-power-order itDPFs
• single-itDPF-key design
• information-theoretic privacy
• error-detecting PIR