Group secret key agreement over state-dependent wireless broadcast channels

TL;DR

This paper develops an information-theoretic protocol for secure group key agreement over state-dependent wireless broadcast channels, optimizing power allocation and achieving optimality in high-SNR regimes.

Contribution

It introduces a new secret key agreement protocol for state-dependent wireless channels, including a multi-layer wiretap coding scheme and an optimal power allocation method.

Findings

Protocol is optimal for linear deterministic channels.

Achievability scheme works for Gaussian channels with high SNR.

Dynamic programming finds optimal power allocation.

Abstract

We consider a group of $m$ trusted and authenticated nodes that aim to create a shared secret key $K$ over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.