Timely Private Information Retrieval

TL;DR

This paper introduces the concept of timely private information retrieval (PIR) using the age of information metric, characterizing the optimal tradeoff between retrieval rate and timeliness for multiple servers and messages.

Contribution

It formulates the timely PIR problem as an AoI minimization under PIR constraints and explicitly characterizes the optimal tradeoff for the case of two servers and three messages.

Findings

Optimal tradeoff between PIR rate and AoI for N=2, M=3.

Reduction of timely PIR to AoI minimization under asymmetric traffic.

Structural insights for general N and M cases.

Abstract

We introduce the problem of \emph{timely} private information retrieval (PIR) from $N$ non-colluding and replicated servers. In this problem, a user desires to retrieve a message out of $M$ messages from the servers, whose contents are continuously updating. The retrieval process should be executed in a timely manner such that no information is leaked about the identity of the message. To assess the timeliness, we use the \emph{age of information} (AoI) metric. Interestingly, the timely PIR problem reduces to an AoI minimization subject to PIR constraints under \emph{asymmetric traffic}. We explicitly characterize the optimal tradeoff between the PIR rate and the AoI metric (peak AoI or average AoI) for the case of $N=2$, $M=3$. Further, we provide some structural insights on the general problem with arbitrary $N$, $M$.