We present a private information retrieval (PIR) scheme that allows a user to retrieve a single message from an arbitrary number of databases by colluding with other users while hiding the desired message index. This scheme is of particular significance when there is only one accessible database -- a special case that turns out to be more challenging for PIR in the multi-database case. The upper bound for privacy-preserving capacity for these scenarios is $C=(1+\frac{1}{S}+\cdots+\frac{1}{S^{K-1}})^{-1}$, where $K$ is the number of messages and $S$ represents the quantity of information sources such as $S=N+U-1$ for $U$ users and $N$ databases. We show that the proposed information retrieval scheme attains the capacity bound even when only one database is present, which differs from most existing works that hinge on the access to multiple databases in order to hide user privacy. Unlike the multi-database case, this scheme capitalizes on the inability for a database to cross-reference queries made by multiple users due to computational complexity.

中文翻译：

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计算受限数据库的多用户隐私信息检索能力

我们提出了一种私人信息检索 (PIR) 方案，该方案允许用户通过与其他用户勾结同时隐藏所需的消息索引，从任意数量的数据库中检索单个消息。当只有一个可访问的数据库时，这种方案特别重要——这是一种特殊情况，在多数据库情况下对 PIR 更具挑战性。这些场景的隐私保护能力上限是 $C=(1+\frac{1}{S}+\cdots+\frac{1}{S^{K-1}})^{-1}$ ，其中 $K$ 是消息的数量，$S$ 代表信息源的数量，例如 $U$ 用户和 $N$ 数据库的 $S=N+U-1$。我们表明，即使只有一个数据库，所提出的信息检索方案也能达到容量限制，这与大多数现有作品不同，这些作品依赖于访问多个数据库以隐藏用户隐私。与多数据库情况不同，该方案利用了数据库由于计算复杂性而无法交叉引用多个用户进行的查询的情况。