Private information retrieval (PIR) is a privacy setting that allows a user to download a required message from a set of messages stored in a system of databases without revealing the index of the required message to the databases. PIR was introduced under computational privacy guarantees, and is recently re-formulated to provide information-theoretic guarantees, resulting in \emph{information theoretic privacy}. Subsequently, many important variants of the basic PIR problem have been studied focusing on fundamental performance limits as well as achievable schemes. More recently, a variety of conceptual extensions of PIR have been introduced, such as, private set intersection (PSI), private set union (PSU), and private read-update-write (PRUW). Some of these extensions are mainly intended to solve the privacy issues that arise in distributed learning applications due to the extensive dependency of machine learning on users' private data. In this article, we first provide an introduction to basic PIR with examples, followed by a brief description of its immediate variants. We then provide a detailed discussion on the conceptual extensions of PIR, along with potential research directions.

中文翻译：

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私人信息检索及其应用：简介、未解决的问题、未来的方向

私人信息检索 (PIR) 是一种隐私设置，它允许用户从存储在数据库系统中的一组消息中下载所需的消息，而无需向数据库透露所需消息的索引。PIR 是在计算隐私保证下引入的，最近重新制定以提供信息理论保证，从而产生 \emph{信息理论隐私}。随后，研究了基本 PIR 问题的许多重要变体，重点关注基本性能限制和可实现的方案。最近，引入了 PIR 的各种概念扩展，例如私有集交集 (PSI)、私有集并集 (PSU) 和私有读-更新-写 (PRUW)。其中一些扩展主要是为了解决由于机器学习对用户隐私数据的广泛依赖而在分布式学习应用中出现的隐私问题。在本文中，我们首先通过示例介绍基本 PIR，然后简要描述其直接变体。然后，我们详细讨论了 PIR 的概念扩展，以及潜在的研究方向。