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.

翻译：认证私有信息检索（APIR）是当前最先进的检错私有信息检索（ED-PIR）技术，利用分布式点函数（DPF）实现次多项式复杂度和隐私保护。然而，其有限域结构限制只能使用素数阶DPF，导致信息论设置下密钥尺寸过大；同时其双DPF密钥设计引入了不必要的通信开销，限制了在大规模部署中的实用性。本文提出一种新型的基于环的信息论ED-PIR（itED-PIR）方案，通过利用素数幂阶信息论DPF（itDPF）克服了上述限制。该方案构建于素数幂环之上，打破了APIR的域约束，从而实现更高效的DPF利用，显著降低了密钥尺寸增长，使方案在高安全场景下具备可行性。此外，单itDPF密钥设计通过消除APIR中冗余的双密钥设置，将查询端通信开销减半，且不损害隐私性或可验证性。除了直接提升效率外，本工作还为构建基于DPF的抗恶意攻击隐私信息检索建立了轻量级、灵活的框架，为分布式存储系统和后量子隐私协议中的隐私保护数据检索开辟了新途径。