Private Data Transfer over a Broadcast Channel

TL;DR

This paper investigates the problem of private data transfer over a broadcast channel, establishing optimal rates for two-file databases and providing bounds for larger databases under privacy constraints.

Contribution

It introduces a new model combining a binary erasure broadcast channel with public discussion, deriving the optimal transfer rate for two files and bounds for larger databases.

Findings

Optimal rate for two-file database transfer.

Upper and lower bounds for larger databases.

Impossibility of privacy with only private randomness and noiseless links.

Abstract

We study the following private data transfer problem: Alice has a database of files. Bob and Cathy want to access a file each from this database (which may or may not be the same file), but each of them wants to ensure that their choices of file do not get revealed even if Alice colludes with the other user. Alice, on the other hand, wants to make sure that each of Bob and Cathy does not learn any more information from the database than the files they demand (the identities of which will be unknown to her). Moreover, they should not learn any information about the other files even if they collude. It turns out that it is impossible to accomplish this if Alice, Bob, and Cathy have access only to private randomness and noiseless communication links. We consider this problem when a binary erasure broadcast channel with independent erasures is available from Alice to Bob and Cathy in addition to a noiseless public discussion channel. We study the file-length-per-broadcast-channel-use rate in the honest-but-curious model. We focus on the case when the database consists of two files, and obtain the optimal rate. We then extend to the case of larger databases, and give upper and lower bounds on the optimal rate.