Secret Communication over Broadcast Erasure Channels with State-feedback

TL;DR

This paper characterizes the capacity of secure broadcast erasure channels with state-feedback, proposing efficient two-phase schemes for secret key generation and message encryption, ensuring security against eavesdroppers and dishonest receivers.

Contribution

It provides the first capacity characterization for secure communication over broadcast erasure channels with state-feedback, using linear two-phase schemes for secret key creation and message encryption.

Findings

Capacity achieved with two-phase schemes: key creation and message encryption.

The required secret key size is smaller than the message size and matches the eavesdropper's joint information.

Dishonest feedback does not reduce the honest receivers' achievable rate.

Abstract

We consider a 1-to-$K$ communication scenario, where a source transmits private messages to $K$ receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-$K$ communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all cases where we have an exact characterization, we can achieve the capacity by using linear complexity two-phase schemes: in the first phase we create appropriate secret keys, and in the second phase we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the non-secure communication problem.