Key agreement over a 3-receiver broadcast channel

TL;DR

This paper investigates secret key agreement in a complex 3-receiver broadcast channel with state information, deriving bounds on key capacities for different setups involving secrecy and public channels.

Contribution

It introduces new inner and outer bounds on secret and private key capacity regions for state-dependent broadcast channels with multiple receivers.

Findings

Derived bounds on secret key capacity region.

Established capacity region for state-dependent wiretap channel.

Analyzed scenarios with and without public channels.

Abstract

In this paper, we consider the problem of secret key agreement in state-dependent 3-receiver broadcast channels. In the proposed model, there are two legitimate receivers, an eavesdropper and a transmitter where the channel state information is non-causally available at the transmitter. We consider two setups. In the first setup, the transmitter tries to agree on a common key with the legitimate receivers while keeping it concealed from the eavesdropper. Simultaneously, the transmitter agrees on a private key with each of the legitimate receivers that needs to be kept secret from the other legitimate receiver and the eavesdropper. For this setup, we derive inner and outer bounds on the secret key capacity region. In the second setup, we assume that a backward public channel is available among the receivers and the transmitter. Each legitimate receiver wishes to share a private key with the transmitter. For this setup, an inner bound on the private key capacity region is found. Furthermore, the capacity region of the secret key in the state-dependent wiretap channel can be deduced from our inner and outer bounds.