Model {#subsec:Model}
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The channel model has three terminals — a sender, a receiver and an eavesdropper. The sender communicates with the other two terminals over a discrete-memoryless-channel controlled by a random state parameter. The transition probability of the channel is $p_{\rvyr, \rvye|\rvx,\rvs}(\cdot)$ where $\rvx$ denotes the channel input symbol, whereas $\rvyr$ and $\rvye$ denote the channel output symbols at the receiver and the eavesdropper respectively. The symbol $\rvs$ denotes a state variable that controls the channel transition probability. We assume that it is independent and identically distributed (i.i.d.) from a distribution $p_{\rvs}(\cdot)$ in each channel use. Further, the entire sequence $\rvs^n$ is known to the sender before the communication begins.

As explained in section \[subsec:ExtendedModel\] the model generalizes easily to take into account correlated side information sequence at each of the receivers.

![Wiretap channel controlled by a state parameter. The channel transition probability $p_{y_r,y_e|x,s}$ is controlled by a state parameter $\rvs$. The entire source sequence $\rvs^n$ is known to the sender but not to the receiver or the eavesdropper. The sender and receiver generate a secret key ${\mathsf{\kappa}}$ at the end of the transmission.[]{data-label="fig:wiretap"}](state2)

Secret-Key Capacity {#subsec:SecKeyCap}
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A length $n$ encoder is defined as follows. The sender samples 