Secret Key Establishment over a Pair of Independent Broadcast Channels

This paper considers the problem of information-theoretic Secret Key Establishment (SKE) in the presence of a passive adversary, Eve, when Alice and Bob are connected by a pair of independent discrete memoryless broadcast channels in opposite directions. We refer to this setup as 2DMBC. We define the secret-key capacity in the 2DMBC setup and prove lower and upper bounds on this capacity. The lower bound is achieved by a two-round SKE protocol that uses a two-level coding construction. We show that the lower and the upper bounds coincide in the case of degraded DMBCs.