Secret Key Generation for Minimally Connected Hypergraphical Sources

TL;DR

This paper characterizes the achievable secret key and discussion rate region for minimally connected hypergraphical sources in multiterminal models, providing explicit formulas and advancing understanding beyond previous models.

Contribution

It offers the first complete single-letter characterization of the secret key and discussion rate region for this class of sources.

Findings

Explicit formula for the maximum secret key rate (constrained secrecy capacity).

Complete characterization of the achievable rate region for minimally connected hypergraphical sources.

Extension beyond the PIN model on a tree.

Abstract

This paper investigates the secret key generation in the multiterminal source model, where users observing correlated sources discuss interactively under limited rates to agree on a secret key. We focus on a class of sources representable by minimally connected hypergraphs. For such sources, we give a single-letter explicit characterization of the region of achievable secret key rate and public discussion rate tuple. This is the first result that completely characterizes the achievable rate region for a multiterminal source model, which is beyond the PIN model on a tree. We also obtain an explicit formula for the maximum achievable secret key rate, called the constrained secrecy capacity, as a function of the total discussion rate.