Wiretap Secret Key Capacity of Tree-PIN

TL;DR

This paper investigates the maximum secret key rate in a multiterminal setting with wiretapped sources modeled by Tree-PINs, providing capacity bounds and conditions for tightness, with implications for wireless networks.

Contribution

It derives the wiretap secret key capacity for Tree-PIN models, establishes bounds, and extends results to related models, highlighting the necessity of public interaction.

Findings

Derived the wiretap secret key capacity of Tree-PIN.

Established bounds on secret key length in finite regimes.

Showed public interaction is necessary for capacity achievement.

Abstract

We consider the problem of multiterminal secret key agreement (SKA) in wiretapped source model where terminals have access to samples of correlated random variables from a publicly known joint probability distribution. The adversary has access to a side information variable, that is correlated with terminals' variables. We focus on a special type of terminal variables in this model, known as Tree-PIN, where the relation between variables of the terminals can be represented by a tree. The study of Tree-PIN source model is of practical importance as it can be realized in wireless network environments. We derive the wiretap secret key capacity of Tree-PIN with independent leakage, and give lower and upper bounds on the maximum achievable secret key length in finite-length regime. We then prove an upper bound and a lower bound for the wiretap secret key capacity of a wiretapped PIN and give two conditions for which these bounds are tight. We also extend our main result to two other related models and prove their corresponding capacities. At the end, we argue how our analysis suggests that public interaction is required for achieving the multiterminal WSK capacity.