Private Information Retrieval Through Wiretap Channel II: Privacy Meets Security
Karim Banawan, Sennur Ulukus

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 messages, which are stored in replicated and non-communicating databases. An external eavesdropper observes a fraction (of its choice) of the traffic exchanged between the 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…
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