Simultaneously generating multiple keys in a four-terminal network

A source model including four terminals is considered, where three simultaneously generating three types of keys are intended. Terminals 1, 2 and 3 wish to share a common key, the secret key, which should be kept secret from terminal 4 and simultaneously terminals 1 and 2 intend to share a private key with terminal 3, which should be kept secret from each other. Also, all the keys should be concealed from terminal 4 (the external wiretapper). The authors assume that all terminals including the external wiretapper have access to distinct correlated i.i.d. sources; there is also a noiseless public channel with unlimited capacity among the terminals. The authors have investigated the model on two scenarios of key sharing depending on the direction of the public channel. Rate regions of the keys are derived. It is shown that in some special cases the inner and outer bounds of the capacity regions coincide and the capacity regions are derived.