The Capacity of Single-Server Weakly-Private Information Retrieval

A private information retrieval (PIR) protocol guar- antees that a user can privately retrieve files stored in a database without revealing any information about the identity of the requested file. Existing information-theoretic PIR proto- cols ensure perfect privacy, i.e., zero information leakage to the servers storing the database, but at the cost of high download. In this work, we present weakly-private information retrieval (WPIR) schemes that trade off perfect privacy to improve the download cost when the database is stored on a single server. We study the tradeoff between the download cost and information leakage in terms of mutual information (MI) and maximal leak- age (MaxL) privacy metrics. By relating the WPIR problem to rate-distortion theory, the download-leakage function, which is defined as the minimum required download cost of all single- server WPIR schemes for a given level of information leakage and a fixed file size, is introduced. By characterizing the download- leakage function for the MI and MaxL metrics, the capacity of single-server WPIR is fully described