Secret Key Agreement over a Pair of Independent Broadcast Channels

This paper considers the problem of information-theoretic Secret Key Agreement (SKA) when Alice and Bob are connected by a pair of independent discrete memoryless broadcast channels in opposite directions, which we call a 2DMBC. We define the secrecy capacity of 2DMBC's (or briefly the two-way secrecy capacity). We focus on the two-way secrecy capacity when at most two rounds of communication are permitted and provide a lower bound on this capacity by giving a two-round SKA protocol based on a two-level coding structure. In addition, we revise the results of SKA over three existing setups and derive the three corresponding lower bounds for the two-way secrecy capacity. Having compared these three lower bounds with ours, we show that our lower bound is tighter in two cases and equals the third. We also introduce a novel interactive channel coding (ICC) technique that can be used, as a part, to achieve the above lower bound while having a simpler construction. We prove an upper bound on the two-way secrecy capacity and show that the lower and the upper bounds coincide in the case of degraded DMBC's. Our results have both theoretical and practical significance. We discuss our results and future work.