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The private key capacity of a cooperative pairwise-independent network

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This paper studies the private key generation of a cooperative pairwise-independent network (PIN) with M + 2 terminals, where Alice and Bob wish to generate a private key under the help of the M relays, M ≥ 2; such a private key needs to be protected not only from Eve but also from individual relays simultaneously. In this PIN, the correlated source observed by every pair of terminals is independent of those sources observed by any other pair of terminals. All the terminals can communicate with each other over a public channel which is also observed by Eve noiselessly. 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. Compared to the existing XOR-based algorithm whose achievable multiplexing gain is ⌊M/2⌋, the proposed RB-based algorithm is demonstrated to achieve the optimal multiplexing gain M - 1.