Most of our lives are conducted in the cyberspace. The human notion of
privacy translates into a cyber notion of privacy on many functions that take
place in the cyberspace. This article focuses on three such functions: how to
privately retrieve information from cyberspace (privacy in information
retrieval), how to privately leverage large-scale distributed/parallel
processing (privacy in distributed computing), and how to learn/train machine
learning models from private data spread across multiple users (privacy in
distributed (federated) learning). The article motivates each privacy setting,
describes the problem formulation, summarizes breakthrough results in the
history of each problem, and gives recent results and discusses some of the
major ideas that emerged in each field. In addition, the cross-cutting
techniques and interconnections between the three topics are discussed along
with a set of open problems and challenges.

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