bound to Theorem \[thm:lbNoDisc\] the following result provides an upper bound to the secret-key capacity that is amenable to numerical evaluation.

The secret-key capacity is upper bounded by $C \le R^+$, where $$\label{eq:upperBoundNoDisc} R^+ = \min_{p_{\rvyr,\rvye|\rvx,\rvs} \in
\cP}\max_{p_{\rvx|\rvs}} I(\rvx,\rvs;\rvyr|\rvye),$$ where $\cP$ denotes all the joint distributions $p^\star_{\rvyr,\rvye|\rvx,\rvs}$ that have the same marginal distribution as the original channel. \[thm:ubNoDisc\]

The intuition behind the upper bound is as follows. We create a degraded channel by revealing the output of the eavesdropper to the legitimate receiver. We further assume a channel with two inputs $(\rvx^n,\rvs^n)$ i.e., the state sequence $\rvs^n$ is not arbitrary, but rather a part of the input codeword with distribution $p_{\rvs}$. The secrecy capacity of the resulting wiretap channel is then given by $I(\rvx,\rvs;\rvyr|\rvye)$.

Note that the problem of secret-key agreement is different from the secret-message transmission problem considered in [@mitrapant:06; @chenVinck:06; @LiuChen:07]. This is because the secret-key can be an arbitrary function of the state sequence (known only to the transmitter) whereas the secret-message needs to be independent function of the state sequence. For comparison, the best known lower bound on the secret-message transmission problem is stated below.

[@mitrapant:06; @chenVinck:06; @LiuChen:07] An achievable secret message rate for the wiretap 