Private Information Retrieval Through Wiretap Channel II: Privacy Meets Security

TL;DR

This paper characterizes the capacity of private information retrieval over wiretap channels with security constraints, proposing a scheme that combines privacy, security, and asymmetric traffic considerations, with matching bounds for small message counts.

Contribution

It extends PIR capacity analysis to include security against eavesdroppers and asymmetric traffic, providing a new achievable scheme and matching bounds for specific cases.

Findings

Capacity bounds are derived for PIR-WTC-II.

Achievability scheme encodes secret keys with MDS codes.

Bounds match for M=2 and M=3 messages.

Abstract

We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single message (file) privately out of $M$ messages, which are stored in $N$ replicated and non-communicating databases. An external eavesdropper observes a fraction $\mu_n$ (of its choice) of the traffic exchanged between the $n$th database and the user. In addition to the privacy constraint, the databases should encode the returned answer strings such that the eavesdropper learns absolutely nothing about the \emph{contents} of the databases. We aim at characterizing the capacity of the PIR-WTC-II under the combined privacy and security constraints. We obtain a general upper bound for the problem in the form of a max-min optimization problem, which extends the converse proof of the PIR problem under asymmetric traffic constraints. We propose an achievability scheme that satisfies the security constraint by encoding a secret key, which is generated securely at each database, into an artificial noise vector using an MDS code. The user and the databases operate at one of the corner points of the achievable scheme for the PIR under asymmetric traffic constraints such that the retrieval rate is maximized under the imposed security constraint. The upper bound and the lower bound match for the case of $M=2$ and $M=3$ messages, for any $N$, and any $\boldsymbol{\mu}=(\mu_1, \cdots, \mu_N)$.