On the Source Model Key Agreement Problem

TL;DR

This paper investigates the source model key agreement problem for binary variables, focusing on conditions where the key capacity bound simplifies, and explores the XOR case to understand the limits of achievable key rates.

Contribution

It provides conditions under which the key capacity upper bound simplifies to mutual information and discusses the XOR case to challenge existing bounds.

Findings

Upper bound reduces to I(X;Y) under certain conditions

XOR case demonstrates the bound may not be achievable

Proposes ideas for new upper bounds on key capacity

Abstract

We consider the source model key agreement problem involving two legitimate parties and an eavesdropper who observe n i.i.d. samples of X, Y, and Z, respectively. In this paper, we focus on one of the simplest instances where the key capacity remains open, specifically when X and Y are binary random variables and Z is a function of the pair (X, Y). The best-known upper bound on the key capacity is characterized by an inf-max optimization problem that generally lacks a closed-form solution. We provide general conditions under which the upper bound reduces to I(X;Y). As an example, we consider the XOR setting in which X and Y are binary, and Z is the XOR of X and Y. The upper bound reduces to I(X;Y) for this source. Next, we conjecture that the rate I(X;Y) is not achievable for the XOR source and provide some ideas that might be useful for developing a new upper bound on the source model problem.