Coding for Positive Rate in the Source Model Key Agreement Problem

TL;DR

This paper introduces a new coding scheme for the source model key agreement problem, relating it to hypothesis testing and Re9nyi divergence, improving bounds on secret-key capacity, especially for binary sources.

Contribution

It develops a novel coding scheme based on hypothesis testing, providing a sufficient condition for positive SK rate and improving capacity bounds for erasure models.

Findings

New coding scheme relates key agreement to hypothesis testing.

Improved upper bounds on Eve's erasure probabilities for zero SK capacity.

Bound is tight for binary sources, extending previous results.

Abstract

A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of R\'enyi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information, and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables, which is of independent interest.