We study a class of private information retrieval (PIR) methods that we call one-shot schemes. The intuition behind one-shot schemes is the following. The user’s query is regarded as a dot product of a query vector and the message vector (database) stored at multiple servers. Privacy, in an information theoretic sense, is then achieved by encrypting the query vector using a secure linear code, such as secret sharing. Several PIR schemes in the literature, in addition to novel ones constructed here, fall into this class. One-shot schemes provide an insightful link between PIR and data security against eavesdropping. However, their download rate is not optimal, i.e., they do not achieve the PIR capacity. Our main contribution is two transformations of one-shot schemes, which we call refining and lifting. We show that refining and lifting one-shot schemes gives capacity-achieving schemes for the cases when the PIR capacity is known. In the other cases, when the PIR capacity is still unknown, refining and lifting one-shot schemes gives, for most parameters, the best download rate so far.

中文翻译：

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One-Shot PIR：细化和提升

我们研究了一类称为一次性方案的私有信息检索 (PIR) 方法。一次性方案背后的直觉如下。用户的查询被认为是一个查询向量和存储在多个服务器上的消息向量（数据库）的点积。然后，在信息理论意义上，隐私是通过使用安全线性代码（例如秘密共享）加密查询向量来实现的。除了这里构建的新颖方案外，文献中的几个 PIR 方案都属于这一类。一次性方案在 PIR 和数据安全防窃听之间提供了深刻的联系。但是，它们的下载速率不是最佳的，即它们没有达到 PIR 容量。我们的主要贡献是一次性方案的两个转换，我们称之为精炼和提升。我们表明，在 PIR 容量已知的情况下，改进和提升一次性方案可提供容量实现方案。在其他情况下，当 PIR 容量仍然未知时，改进和提升一次性方案为大多数参数提供了迄今为止最好的下载速率。