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

TL;DR

This paper introduces a ring-based ED-PIR scheme using prime-power-order DPFs, significantly reducing key sizes and communication overhead, thus enhancing efficiency and practicality for large-scale, high-security applications.

Contribution

It proposes a novel ring-based ED-PIR scheme utilizing prime-power DPFs, overcoming finite field limitations and reducing communication overhead without sacrificing privacy.

Findings

Reduces key size growth compared to prime-field schemes.

Halves query communication overhead with single DPF key.

Enables efficient, high-security private data retrieval in distributed systems.

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.