The Capacity of Multi-user Private Information Retrieval for Computationally Limited Databases

TL;DR

This paper introduces a private information retrieval scheme that achieves optimal capacity even with a single database by leveraging computational limitations, expanding PIR applicability beyond multi-database scenarios.

Contribution

The paper proposes a novel PIR scheme that attains the capacity bound in single-database settings by exploiting computational constraints, unlike traditional multi-database approaches.

Findings

Achieves capacity bound with a single database.

Utilizes computational complexity to ensure privacy.

Extends PIR applicability to limited database scenarios.

Abstract

We present a private information retrieval (PIR) scheme that allows a user to retrieve a single message from an arbitrary number of databases by colluding with other users while hiding the desired message index. This scheme is of particular significance when there is only one accessible database -- a special case that turns out to be more challenging for PIR in the multi-database case. The upper bound for privacy-preserving capacity for these scenarios is $C=(1+\frac{1}{S}+\cdots+\frac{1}{S^{K-1}})^{-1}$, where $K$ is the number of messages and $S$ represents the quantity of information sources such as $S=N+U-1$ for $U$ users and $N$ databases. We show that the proposed information retrieval scheme attains the capacity bound even when only one database is present, which differs from most existing works that hinge on the access to multiple databases in order to hide user privacy. Unlike the multi-database case, this scheme capitalizes on the inability for a database to cross-reference queries made by multiple users due to computational complexity.