The Role of Reusable and Single-Use Side Information in Private Information Retrieval

TL;DR

This paper studies a new private information retrieval problem involving reusable and single-use side information, characterizes its capacity in certain cases, and reveals how side information privacy affects download costs.

Contribution

It introduces the PIR-RSSI problem, analyzes its capacity for specific parameters, and clarifies the impact of side information privacy on retrieval efficiency.

Findings

Capacity characterized for specific parameter cases.

Single-use side information reduces download cost only if kept private.

Reusable side information does not reduce download cost for large message sets.

Abstract

This paper introduces the problem of Private Information Retrieval with Reusable and Single-use Side Information (PIR-RSSI). In this problem, one or more remote servers store identical copies of a set of $K$ messages, and there is a user that initially knows $M$ of these messages, and wants to privately retrieve one other message from the set of $K$ messages. The objective is to design a retrieval scheme in which the user downloads the minimum amount of information from the server(s) while the identity of the message wanted by the user and the identities of an $M_1$-subset of the $M$ messages known by the user (referred to as reusable side information) are protected, but the identities of the remaining $M_2=M-M_1$ messages known by the user (referred to as single-use side information) do not need to be protected. The PIR-RSSI problem reduces to the classical Private Information Retrieval (PIR) problem when ${M_1=M_2=0}$, and reduces to the problem of PIR with Private Side Information or PIR with Side Information when ${M_1\geq 1,M_2=0}$ or ${M_1=0,M_2\geq 1}$, respectively. In this work, we focus on the single-server setting of the PIR-RSSI problem. We characterize the capacity of this setting for the cases of ${M_1=1,M_2\geq 1}$ and ${M_1\geq 1,M_2=1}$, where the capacity is defined as the maximum achievable download rate over all PIR-RSSI schemes. Our results show that for sufficiently small values of $K$, the single-use side information messages can help in reducing the download cost only if they are kept private; and for larger values of $K$, the reusable side information messages cannot help in reducing the download cost.