Group secret key agreement over state-dependent wireless broadcast channels

We consider a group of m trusted nodes that aim to create a shared secret key K, using a state-dependent wireless broadcast channel that exists from one of the honest nodes to the rest of the nodes including a passive eavesdropper Eve. All of the trusted nodes can also discuss over a cost-free and unlimited rate public channel which is also observed 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 as well as in the high-SNR regime for wireless channels with large dynamic range over channel states.