Successive Secret Key Agreement over Generalized Multiple Access and Broadcast Channels

TL;DR

This paper studies secret key sharing among three users over combined generalized multiple access and broadcast channels, deriving capacity bounds and analyzing special cases with Markov chain conditions.

Contribution

It introduces a new framework for successive secret key agreement over combined channels and derives capacity regions, including special Markov chain cases.

Findings

Inner bound of secret key capacity region derived

Capacity region characterized for Markov chain special case

Binary example illustrates the theoretical results

Abstract

A secret key agreement framework between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. There is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 where the three users receive outputs from the channel. Furthermore, there is a broadcast channel (BC) from user 3 to users 1 and 2. Secret key sharing is intended where GDMMAC and BC can be successively used. In this framework, an inner bound of the secret key capacity region is derived. Moreover, for a special case where the channel inputs and outputs of the GDMAC and the BC form Markov chains in some order, the secret key capacity region is derived. Also the results are discussed through a binary example.