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

TL;DR

This paper investigates secret key establishment over pairs of broadcast channels, proposing new protocols and capacity formulas for cases with secrecy potential and degraded channels, advancing understanding of secure communication limits.

Contribution

It introduces a novel Interactive Channel Coding technique and derives simplified capacity expressions for specific channel conditions.

Findings

The ICC-based protocol achieves the lower bound in channels with secrecy potential.

A simplified lower bound expression is provided for stochastically degraded channels.

A single-letter capacity formula is proven when one party transmits only i.i.d. variables.

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.