Private Multi-File Retrieval From Distributed Databases

TL;DR

This paper investigates private multi-file retrieval from distributed databases, establishing capacity bounds, designing optimal schemes for large r, and reducing complexity compared to traditional PIR methods.

Contribution

It introduces the first capacity bounds for PMFR, and proposes a scheme that achieves optimality for r ≥ M/2 with significantly reduced complexity.

Findings

Achieves the capacity bound for r ≥ M/2

Reduces subpackage count from N^M to N^2

Near-optimal solutions for small r

Abstract

Suppose there are $N$ distributed databases each storing a full set of $M$ independent files. A user wants to retrieve $r$ out of the $M$ files without revealing the identity of the $r$ files. When $r=1$ it is the classic problem of private information retrieval (PIR). In this paper we study the problem of private multi-file retrieval (PMFR) which covers the case of general $r$. We first prove an upper bound on the capacity of PMFR schemes which indicates the minimum possible download size per unit of retrieved files. Then we design a general PMFR scheme which happens to attain the upper bound when $r\geq\frac{M}{2}$, thus achieving the optimal communication cost. As $r$ goes down we show the trivial approach of executing $r$ independent PIR instances achieves the near optimal communication cost. Comparing with the capacity-achieving PIR schemes, our PMFR scheme reduces the number of subpackages needed for each file from $N^M$ to $N^2$, which implies a great reduction of implementation complexity.