  This paper studies the private key generation of a cooperative
pairwise-independent network (PIN) with M+2 terminals (Alice, Bob and M
relays), M >= 2. In this PIN, the correlated sources observed by every pair of
terminals are independent of those sources observed by any other pair of
terminal. All the terminals can communicate with each other over a public
channel which is also observed by Eve noiselessly. The objective is to generate
a private key between Alice and Bob under the help of the M relays; such a
private key needs to be protected not only from Eve but also from individual
relays simultaneously. The private key capacity of this PIN model is
established, whose lower bound is obtained by proposing a novel random binning
(RB) based key generation algorithm, and the upper bound is obtained based on
the construction of M enhanced source models. The two bounds are shown to be
exactly the same. Then, we consider a cooperative wireless network and use the
estimates of fading channels to generate private keys. It has been shown that
the proposed RB-based algorithm can achieve a multiplexing gain M-1, an
improvement in comparison with the existing XOR- based algorithm whose
achievable multiplexing gain is about [M]/2.
