Secrecy capacities for multiterminal channel models

We derive single-letter characterizations of (strong) secrecy capacities for models in which a "helper" terminal is connected to an arbitrary number of "user" terminals by a discrete memoryless channel (DMC). The helper terminal governs the input of the DMC, over which it transmits to the user terminals that observe the corresponding outputs; transmissions over the DMC are secure. Additionally, following each transmission over the DMC, unrestricted and interactive public communication is permitted between all the terminals. A subset of the user terminals, and possibly the helper terminal, generate secrecy with the remaining user terminals acting as abettors. We distinguish between the cases in which the helper terminal may, or may not, randomize. Two kinds of secrecy capacity are considered, depending on the extent of an eavesdropper\´s knowledge: secret key (SK) and private key (PK) capacity. These secrecy capacities are shown to be achievable with noninteractive communication between the terminals and with no public transmission from the helper terminal. When the helper terminal is forbidden to randomize, the needed transmission over the DMC entails only that of a constant sequence. It is also shown that additional randomization at the user terminals does not serve to enhance the secrecy capacities