Secure Capacity Region for Erasure Broadcast Channels with Feedback

TL;DR

This paper characterizes the maximum secure transmission rates for private messages over erasure broadcast channels with feedback, ensuring unconditional security and robustness against misbehavior.

Contribution

It provides a complete characterization of the secure capacity region and introduces a simple, robust protocol for achieving any rate within this region.

Findings

Largest secure transmission rates are characterized for erasure broadcast channels.

A simple protocol achieves any rate within the secure capacity region.

Protocol is robust to misbehaving users.

Abstract

We formulate and study a cryptographic problem relevant to wireless: a sender, Alice, wants to transmit private messages to two receivers, Bob and Calvin, using unreliable wireless broadcast transmissions and short public feedback from Bob and Calvin. We ask, at what rates can we broadcast the private messages if we also provide (information-theoretic) unconditional security guarantees that Bob and Calvin do not learn each-other's message? We characterize the largest transmission rates to the two receivers, for any protocol that provides unconditional security guarantees. We design a protocol that operates at any rate-pair within the above region, uses very simple interactions and operations, and is robust to misbehaving users.