Secret Key Generation with One Communicator and a One-Shot Converse via Hypercontractivity

TL;DR

This paper introduces a new multi-party secret key agreement model involving a single communicator, providing a single-letter characterization and a zero-rate one-shot converse, generalizing previous models.

Contribution

It proposes a novel secret key agreement model with a single communicator and derives fundamental limits, including a one-shot converse, extending existing frameworks.

Findings

Single-letter achievable region characterization

Zero-rate one-shot converse for secret key per bit

Generalization of previous key agreement models

Abstract

A new model of multi-party secret key agreement is proposed, in which one terminal called the communicator can transmit public messages to other terminals before all terminals agree on a secret key. A single-letter characterization of the achievable region is derived in the stationary memoryless case. The new model generalizes some other (old and new) models of key agreement. In particular, key generation with an omniscient helper is the special case where the communicator knows all sources, for which we derive a zero-rate one-shot converse for the secret key per bit of communication.