The secret key capacity for multiple terminals

We consider the problem of characterizing the secret key (SK)-capacity [Maurer 1993, Ahlswede-Csiszar 1993, Csiszar-Narayan 2000] for an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unconstrained public communication allowed between these terminals. Our main contribution is the determination of SK-capacity for an arbitrary subset of terminals with the remaining terminals serving as "helpers," when an eavesdropper observes the communication between the terminals but does not have access to any other information. We also determine the private key (PK)-capacity when the eavesdropper additionally wiretaps some of the helper terminals from which too the key must then be concealed.