Secrecy via sources and channels: A secret key - Secret message rate tradeoff region

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available – correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources. No other resource, in particular, no other channel is available. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution based on a separation architecture and prove its optimality for the parallel channels and sources case when each sub-channel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper). I