Multiple key generation with restricted public discussion structure

In this paper, the problem of simultaneously generating multiple keys in a model where the key generating parties have restricted access to public discussions is considered. The model consists of four terminals, i.e., Alice, Bob, Carol and Eve. Alice and Bob are connected via a noiseless channel while Bob connects with Carol and Eve via a wiretap channel. There is no direct link connecting Alice with Carol or Eve, and hence Carol and Eve cannot directly access the discussion between Alice and Bob. Alice wishes to share a secret key with Carol while Bob wishes to share another independent secret key with Carol. Under this model, inner and outer bounds on the secret-key capacity region are provided. It is shown that the two bounds match when a certain Markov chain relationship holds.