New Results on Secret Key Establishment over a Pair of Broadcast Channels

Abstract: The problem of Secret Key Establishment (SKE) over a pair of independent Discrete Memoryless Broadcast Channels (DMBCs) has already been studied in \cite{Ah10}, where we provided lower and upper bounds on the secret-key capacity. In this paper, we study the above setup under each of the following two cases: (1) the DMBCs have secrecy potential, and (2) the DMBCs are stochastically degraded with independent channels. In the former case, we propose a simple SKE protocol based on a novel technique, called Interactive Channel Coding (ICC), and prove that it achieves the lower bound. In the latter case, we give a simplified expression for the lower bound and prove a single-letter capacity formula under the condition that one of the legitimate parties sends only i.i.d. variables.