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.

翻译：私人信息检索是一种隐私保护设置，允许用户从存储于数据库系统中的一组消息中下载所需消息，且不向数据库泄露所需消息的索引。私人信息检索最初在计算隐私保证下提出，近期被重新构建以提供信息论保证，从而形成"信息论隐私"。随后，在基础私人信息检索问题的众多重要变体中，研究者们既关注了基本性能极限，也探讨了可实现方案。近期，私人信息检索的概念扩展层出不穷，包括私人集合交集、私人集合并集和私人读写更新等。这些扩展主要旨在解决分布式学习应用中因机器学习对用户私人数据的广泛依赖而产生的隐私问题。本文首先通过示例介绍基础私人信息检索，并简要描述其直接变体；随后详细讨论私人信息检索的概念扩展，同时探讨潜在研究方向。