  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 a public channel 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 (the forward key strategy) and from user 3 to users 1 and 2
(the backward key strategy). In both situations, the goal is sharing a secret
key between user 1 and user 3 while leaking no effective information about that
key to user 2, and simultaneously, sharing another secret key between user 2
and user 3 while leaking no effective information about the latter key to user
1. 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
the forward and backward key strategies, inner and outer bounds of secret key
capacity regions are derived. In special situations where one of users 1 and 2
is 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
the inner bound coincides with the outer bound and secret key capacity region
is deduced.
