Pliable Private Information Retrieval

TL;DR

This paper introduces pliable private information retrieval (PPIR), allowing users to retrieve any message from a subset of classes without revealing class identities, and shows that PPIR can achieve the same capacity as classical PIR under certain conditions.

Contribution

The paper formulates the PPIR problem, derives capacity bounds, and demonstrates that PPIR can match classical PIR capacity, highlighting a privacy-rate trade-off.

Findings

PPIR capacity matches classical PIR capacity for noncolluding databases.

Pliability enables privacy for classes rather than individual messages.

Trade-off between privacy and download rate is achieved through pliability.

Abstract

We formulate a new variant of the private information retrieval (PIR) problem where the user is pliable, i.e., interested in any message from a desired subset of the available dataset, denoted as pliable private information retrieval (PPIR). We consider a setup where a dataset consisting of $f$ messages is replicated in $n$ noncolluding databases and classified into $\Gamma$ classes. For this setup, the user wishes to retrieve any $\lambda\geq 1$ messages from multiple desired classes, i.e., $\eta\geq 1$, while revealing no information about the identity of the desired classes to the databases. We term this problem multi-message PPIR (M-PPIR) and introduce the single-message PPIR (PPIR) problem as an elementary special case of M-PPIR. We first derive converse bounds on the M-PPIR rate, which is defined as the ratio of the desired amount of information and the total amount of downloaded information, followed by the corresponding achievable schemes. As a result, we show that the PPIR capacity, i.e., the maximum achievable PPIR rate, for $n$ noncolluding databases matches the capacity of PIR with $n$ databases and $\Gamma$ messages. Thus, enabling flexibility, i.e., pliability, where privacy is only guaranteed for classes, but not for messages as in classical PIR, allows to trade-off privacy versus download rate. A similar insight is shown to hold for the general case of M-PPIR.