  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.
