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

Pengzhen Ke, Liang Feng Zhang, Huaxiong Wang, Li-Ping Wang

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.

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

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.

Paper Structure

This paper contains 18 sections, 13 theorems, 17 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Technique Overview
  5. Preliminaries
  6. Information-Theoretic Distributed Point Function
  7. Information-Theoretic Error-Detecting Private Information Retrieval
  8. Information-Theoretic Authenticated Private Information Retrieval
  9. Efficient itED-PIR Scheme
  10. The Construction
  11. Analysis
  12. Discussion
  13. Advantages compared with itAPIR
  14. Resilience Against Cyberattacks
  15. Limitations
  16. ...and 3 more sections

Key Result

Theorem 1

The $\ell$-server itED-PIR scheme $\Gamma$ in Fig. fig:construction constructed by itDPF shceme $\Pi$ is correct (Definition def:edpir-correctness) if the scheme $\Pi$ is correct (Definition def:itdpf-correctness). $\blacktriangleleft$$\blacktriangleleft$

Figures (4)

  • Figure 1: The verification experiment $\mathsf{EXP}^{\rm Ver}_{\mathcal{A}, \Gamma}(n, {\bf x}, \alpha, V)$.
  • Figure 2: $\ell$-Server APIR Scheme Over ED-PIR Model with DPF Output Group $\mathbb{G} = (\mathbb{Z}_p$,+)
  • Figure 3: $\ell$-Server itED-PIR scheme $\Gamma = (\mathsf{Que},\mathsf{Ans},\mathsf{Rec})$ for $t$-private itDPF $\Pi$ with output group $\mathbb{G} = (\mathbb{Z}_{p^{\tau}},+)$. This base construction targets binary databases ($1$-bit data entry) and is generalized to databases with $m$-bit data entry for arbitrary $m$ in Appendix \ref{['sec:mbit']}.
  • Figure 4: $\ell$-Server itED-PIR scheme $\Gamma'$ for $t$-private itDPF $\Pi$ with output group $\mathbb{G} = (\mathbb{Z}_{p^{\tau}},+)$. This construction targets $m$-bit data entry for arbitrary $m$.

Theorems & Definitions (35)

  • Definition 1: itDPF gilboa2014distributedboyle2016functionboyle2023informationli2025efficient
  • Definition 2: itDPF Correctness
  • Definition 3: itDPF Perfect $t$-Privacy
  • Definition 4: itDPF Statistical $t$-Privacy
  • Remark 1
  • Definition 5: itED-PIR ke2022twoke2023privateli2025efficientcolombo2023authenticated
  • Remark 2
  • Definition 6: itED-PIR Correctness
  • Definition 7: itED-PIR Perfect $t$-Privacy
  • Definition 8: itED-PIR Statistical $t$-Privacy
  • ...and 25 more