Common randomness and secret key generation with a helper

Summary form only given. We consider the generation of common randomness (CR), secret or not secret, by two user terminals with aid from a “helper” terminal. Each terminal observes a different component of a discrete memoryless multiple source. The helper aids the users by transmitting information to them over a noiseless public channel subject to a rate constraint. Furthermore, one of the users is allowed to transmit to the other user over a public channel under a similar rate constraint. We study the maximum rate of the CR which can be thus generated, and also under additional secrecy conditions when it must be concealed from an eavesdropper and from a wiretapper. Single-letter capacity formulae are obtained for several special cases of interest. Connections are shown between CR capacity and identification capacity in specific situations