a random variables $\rvm_\rvx$ from the conditional distribution $p_{\rvm_\rvx|\rvs^n}(\cdot|s^n)$. The encoding function produces a channel input sequence $$\rvx^n = f_n(\rvm_\rvx, \rvs^n) \label{eq:def:Enc}$$ and transmits it over $n$ uses of the channel. At time $i$ the symbol $\rvx_i$ is transmitted and the legitimate receiver and the eavesdropper observe output symbols $\rvy_{ri}$ and $\rvy_{ei}$ respectively, sampled from the conditional distribution $p_{\rvyr,\rvye|\rvx,\rvs}(\cdot)$. The sender and receiver compute secret keys $${\mathsf{\kappa}}= g_n(\rvm_\rvx,\rvs^n), \qquad \rvl = h_n(\rvyr^n).\label{eq:def:Dec}$$ A rate $R$ is achievable if there exists a sequence of encoding functions such that for some sequence $\eps_n$ that vanishes as $n\rightarrow\infty$, we have that $\Pr({\mathsf{\kappa}}\neq\rvl) \le \eps_n$ and $$\label{eq:rate}\frac{1}{n}H({\mathsf{\kappa}}) \ge R - \eps_n,$$ and $$\label{eq:secNoInterac} \frac{1}{n}I({\mathsf{\kappa}};\rvye^n) \le \eps_n.$$ The largest achievable rate is the secret-key capacity.

Extended Model {#subsec:ExtendedModel}
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In our proposed model we are assuming the state variable is only known to the transmitter and not to the receiving terminals. A more general model involves a state variable that can be decomposed into $\rvs = ({\mathsf{s}_{t}}, {\mathsf{s}_{r}}, {\mathsf{s}_{e}}, \rvs_0)$ where the sequence ${\mathsf{s}_{t}}^n$ is revealed noncausally to the sender whereas ${\mathsf{s}_{r}}^n$ and ${\mathsf{s}_{e}}^n$ are revealed to the legitimate receiver and the eavesdropper respectively while $\rvs_0^n$ is not revealed to any of the terminals. It 