The Private Key Capacity of a Cooperative Pairwise-Independent Network

TL;DR

This paper determines the private key capacity in a cooperative pairwise-independent network with multiple relays, introducing a novel random binning algorithm that outperforms existing XOR-based methods in multiplexing gain.

Contribution

It establishes the exact private key capacity for the PIN model and proposes a new RB-based key generation algorithm with higher multiplexing gain.

Findings

Exact private key capacity is derived for the PIN model.

The RB-based algorithm achieves a multiplexing gain of M-1.

The proposed method outperforms XOR-based algorithms in wireless networks.

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. 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.