Private Randomness Agreement and its Application in Quantum Key Distribution Networks

TL;DR

This paper introduces the private randomness agreement problem, a new variation of private message transmission, and presents protocols for solving it efficiently, with applications in quantum key distribution networks.

Contribution

It defines the PRA problem, proves its multi-round solvability, and provides an efficient four-round protocol based on polynomial evaluation.

Findings

PRA cannot be solved in a single round.

A three-round solution exists with exponential cost.

An efficient four-round protocol is proposed.

Abstract

We define a variation on the well-known problem of private message transmission. This new problem called private randomness agreement (PRA) gives two participants access to a public, authenticated channel alongside the main channels, and the 'message' is not fixed a priori. Instead, the participants aim to agree on a random string completely unknown to a computationally unbounded adversary. We define privacy and reliability, and show that PRA cannot be solved in a single round. We then show that it can be solved in three rounds, albeit with exponential cost, and give an efficient four-round protocol based on polynomial evaluation.