  Csiszar and Narayan[3] defined the notion of secret key capacity for multiple
terminals, characterized it as a linear program with Slepian-Wolf constraints
of the related source coding problem of communication for omniscience, and
upper bounded it by some information divergence expression from the joint to
the product distribution of the private observations. This paper proves that
the bound is tight for the important case when all users are active, using the
polymatroidal structure[6] underlying the source coding problem. When some
users are not active, the bound may not be tight. This paper gives a
counter-example in which 3 out of the 6 terminals are active.
