On the Secrecy Capacity of 1-2-1 Atomic Networks

TL;DR

This paper investigates the maximum secure communication rate in a specialized noiseless network model inspired by mmWave technology, providing new bounds that sometimes exactly determine the secrecy capacity.

Contribution

It introduces novel upper and lower bounds on the secrecy capacity of 1-2-1 atomic networks, improving upon existing bounds in certain regimes.

Findings

Derived tighter bounds on secrecy capacity.

Identified regimes where bounds match, characterizing capacity.

Enhanced understanding of secure communication in directed networks.

Abstract

We consider the problem of secure communication over a noiseless 1-2-1 network, an abstract model introduced to capture the directivity characteristic of mmWave communications. We focus on structured networks, which we refer to as 1-2-1 atomic networks. Broadly speaking, these are characterized by a source, a destination, and three layers of intermediate nodes with sparse connections. The goal is for the source to securely communicate to the destination in the presence of an eavesdropper with unbounded computation capabilities, but limited network presence. We derive novel upper and lower bounds on the secrecy capacity of 1-2-1 atomic networks. These bounds are shown to be tighter than existing bounds in some regimes. Moreover, in such regimes, the bounds match and hence, they characterize the secrecy capacity of 1-2-1 atomic networks.