Code-Based Single-Server Private Information Retrieval: Circumventing the Sub-Query Attack

TL;DR

This work targets private information retrieval from a single server by strengthening a code-based PIR scheme. It identifies and counters the sub-query attack that exploits rank differences by introducing high-weight secret vectors $m_i$ in a modified HHW construction, ensuring submatrix ranks reveal no index information and decoupling leakage from the desired file. The modified scheme preserves retrieval rate, matching the original HHW rate for large numbers of retrieved files, and maintains computational efficiency by operating over small extension fields; it also analyzes security against extended attacks and provides practical guidance on parameter choices. Overall, the approach delivers post-quantum, code-based PIR with privacy guarantees on a single server, while maintaining favorable efficiency and scalability, and points to future work on rate improvements for small file sets and potential new attack vectors.

Abstract

Private information retrieval from a single server is considered, utilizing random linear codes. Presented is a modified version of the first code-based single-server computational PIR scheme proposed by Holzbaur, Hollanti, and Wachter-Zeh in [Holzbaur et al., "Computational Code-Based Single-Server Private Information Retrieval", 2020 IEEE ISIT]. The original scheme was broken in [Bordage et al., "On the privacy of a code-based single-server computational PIR scheme", Cryptogr. Comm., 2021] by an attack arising from highly probable rank differences in sub-matrices of the user's query. Here, this attack is now circumvented by ensuring that the sub-matrices have negligible rank difference. Furthermore, the rank difference cannot be attributed to the desired file index, thereby ensuring the privacy of the scheme. In the case of retrieving multiple files, the rate of the modified scheme is largely unaffected and at par with the original scheme.

Figures (3)

• Figure 1: Illustration of the query matrix $Q^{i}$.
• Figure 2: Illustration of the query matrix $Q^{m_i}$.
• Figure 3: Attack complexity vs. $\mathop{\mathrm{wt}}\nolimits(m_i)$, $m=100$ and $m=10000$.

Theorems & Definitions (12)

• Definition 1
• Theorem 1
• Corollary 1
• Remark 1
• Theorem 2
• Corollary 2
• Remark 2
• Remark 3
• Remark 4
• Remark 5