Abstract: 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. In the PIN, the pairwise source observed by every pair of terminals is independent of those sources observed by any other pairs. Secrecy is required from an eavesdropper that has access to the public inter-terminal communication. All the terminals can communicate with each other over a public channel which is also observed by Eve noiselessly. the PK needs to be protected not only from Eve but also from the two relays. 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. PK generation algorithms are extended to a cooperative wireless network, where the correlated source observations are obtained from estimating wireless channels during a training phase. 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 ?M?/2.
Keywords: PIN model, Private key capacity, Multiplexing gain, co-operative PIN model, index security.