The sender-excited secret key agreement model: Capacity theorems

We consider the fundamental limits of the secret key generation problem when the sources are excited by the sender. In many practical communication settings, the channel may be influenced by the parties involved. Similar to recent works on probing capacity and channels with action-dependent states, our system model captures such a scenario. We derive single-letter expressions for the secret key capacity. Our coding strategy involves wiretap channel coding and a key generation scheme. By assuming that the eavesdropper receives a degraded version of the legitimate receiver´s observation, we also obtain a capacity result that does not involve any auxiliary random variables. Finally, by studying two examples, we show that there is a fundamental tradeoff in between the amount of common randomness (i.e., the secret key rate) and the wiretap secrecy rate.