On Simultaneously Generating Multiple Keys in a Joint Source-Channel Model

In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties (i.e., Alice, Bob, and Carol) and an eavesdropper (Eve), where Alice and Bob wish to agree with Carol on independent secret keys, both of which should be kept secret from Eve. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a full characterization of the secret-key capacity region is provided for the case in which Eve has no side information. This result shows that there exists a tradeoff between the individual secret-key rates. Then, this result is generalized to the case in which Eve has side information, and the corresponding secret-key capacity region is fully characterized.