Secret key sharing in a new source model: Rate regions

A source model for secret key generation between terminals is considered. Two users, namely users 1 and 2, at one side communicate with another user, namely user 3, at the other side via public channels where three users can observe i.i.d outputs of correlated sources. Each of users 1 and 2 intends to share a secret key with user 3 where user 1 acts as a wiretapper for user 2 and vice versa. In this model, two situations are considered: communication from users 1 and 2 to user 3 (forward key strategy) and from user 3 to users 1 and 2 (backward key strategy). This model is motivated by wireless communications when considering user 3 as a base station and users 1 and 2 as network users. In this paper, for both forward and backward key strategies, inner and outer bounds of secret key capacity regions are derived. In special attitudes where one of users 1 and 2 are only interested in wiretapping and not key sharing, our results agree with that of Ahlswede and Csiszar. Also, we investigate some special cases in which inner bound coincides on outer bound and secret key capacity region is deduced.