Secret Sharing from Correlated Gaussian Random Variables and Public Communication

TL;DR

This paper characterizes the fundamental trade-off between secret sharing rate and public communication rate in a Gaussian setting, allowing secure secret distribution without perfect channels.

Contribution

It provides a closed-form solution for the secret-public communication trade-off in Gaussian correlated variables with public communication.

Findings

Derived a closed-form expression for the secret-public rate trade-off.

Showed that secure secret sharing can be achieved without perfect channels.

Established the fundamental limits of Gaussian-based secret sharing with public communication.

Abstract

In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.