On the Optimality of Secret Key Agreement via Omniscience

TL;DR

This paper investigates the conditions under which the omniscience strategy achieves the minimum discussion rate for secret key agreement, providing bounds and identifying cases where it is optimal.

Contribution

It derives single-letter bounds for discussion rate optimality and establishes the optimality of omniscience for hypergraphical sources.

Findings

Omniscience can be discussion-rate optimal under certain conditions.

Single-letter bounds help identify when omniscience achieves secrecy capacity.

Hypergraphical sources are shown to have optimal omniscience strategies.

Abstract

For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower and upper bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources including the hypergraphical sources. Through conjectures and examples, we explore other source models to which our methods do not easily extend.