来自黑盒密码学的带预处理的私有信息检索的下界
Lower Bounds for PIR with Preprocessing from Blackbox Cryptography
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中文总结 AI 辅助
研究带预处理的单服务器私有信息检索的限制，给出计算下界，证明客户端存储s位时，k = Ω(s)个查询的在线摊销计算为Ω(n/s)，还给出通信下界及匹配构造，排除双高效PIR，体现了对该领域的重要贡献。
中文摘要 AI 辅助
我们研究了带预处理的单服务器私有信息检索（PIR）的限制。先前工作表明，具有亚线性通信的单服务器PIR每个查询需要线性数量的（公钥）服务器操作。近期的突破性工作通过利用预处理构建具有亚线性查询计算的单服务器PIR来规避这些下界。我们的工作给出了任何带预处理的单服务器PIR的计算下界，该PIR对任何密码学进行黑盒使用。对于客户端存储关于n位数据库的s位的任何客户端预处理方案，我们证明在k = Ω(s)个查询中在线摊销计算必须是Ω(n/s)。更详细地说，我们证明它们必须具有Ω(n/s)的摊销在线通信，或者服务器必须执行Ω(n/s)次加密操作。我们的下界是最优的，因为存在满足上述要求之一同时优于另一个的带客户端预处理的PIR。此外，我们的下界还排除了具有亚线性查询计算的来自黑盒密码学的双高效PIR的存在。我们的证明框架还支持三类轻度受限的单服务器PIR的Ω(n/s)通信下界。我们还证明了随机预言模型中带客户端预处理的对称私有信息检索（SPIR）的下界，并提出了一种在查询期间仅使用单向函数的带客户端预处理的匹配SPIR构造。
英文摘要
Single-server private information retrieval (PIR) schemes are known to require linear query time. Recent works circumvent these classical lower bounds by leveraging preprocessing to answer queries in sublinear time. We prove computation lower bounds for PIR with preprocessing schemes making blackbox usage of any cryptography (such as random oracles or virtual blackbox obfuscation). If the client stores $s$ bits about an $n$-bit database, then answering $k = Ω(s)$ queries requires either $Ω(n/s)$ amortized online communication or $Ω(n/s)$ amortized server cryptographic operations. This is tight, as known constructions match either bound while outperforming the other. Our lower bound is unconditional and allows arbitrary query protocols, weakened privacy, and server-side database encodings (including doubly efficient PIR) whenever the encoding is independent of the blackbox cryptography. Previous bounds were only known conditionally and for restricted classes of preprocessing, e.g., under non-encoding assumptions. Our framework also yields $Ω(n/s)$ communication lower bounds for schemes with $o(n/s)$ server cryptographic operations, communication-determined server cryptography, or perfect privacy in the idealized model. Finally, we prove lower bounds for symmetric PIR with client preprocessing in the random oracle model and give a matching construction using only one-way functions in the online phase.
发表机构
- Stevens Institute of Technology（史蒂文斯理工学院）
- Università di Salerno（萨莱诺大学）
- Google（谷歌）
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