The Capacity of Single-Server Weakly-Private Information Retrieval

Paper in proceeding, 2020

Weakly-private information retrieval (WPIR) is a variant of the private information retrieval problem in which a user wants to efficiently retrieve a file stored across a set of servers while tolerating some information leakage on the identity of the requested file to the servers. In this paper, we consider WPIR from a single-server database where the information leakage is measured in terms of the mutual information (MI) or maximal leakage (MaxL) privacy metrics. In particular, we establish a connection between the WPIR problem and rate-distortion theory, and fully characterize the optimal tradeoff between the download cost and the allowed information leakage under the MI and MaxL metrics, settling the single-server WPIR capacity.