Tight Analysis of a One-Shot Quantum Secret Sharing Scheme

TL;DR

This paper thoroughly analyzes a one-shot quantum secret sharing scheme, improving its security features, but also establishing fundamental limitations on achieving complete security within this framework.

Contribution

The authors provide a comprehensive security and correctness analysis of Hsu's one-shot QSS scheme and demonstrate inherent impossibility results for perfect security.

Findings

Improved resistance to eavesdropping in the protocol

Complete security against eavesdroppers is impossible in this framework

The protocol can be made more secure but cannot achieve perfect security

Abstract

Quantum communication protocols can be designed to detect eavesdropping attacks, something that classical technologies are unable to do since classical information can be replicated in a non-destructive manner. Eavesdropping detection is, therefore, a standard feature in all the proposed quantum secret sharing (QSS) protocols. However, detection is often done by a statistical analysis of the outcome of multiple decoy rounds, and this causes a significant communication overhead. In our quest for a QSS protocol that works even in one round, we came across a one-shot secret-sharing framework proposed by Hsu (Phys. Rev. A 2003). The scheme was designed to work over public channels without requiring multiple rounds to detect eavesdropping but it lacked a thorough security analysis. In this work we present a complete characterisation of the correctness and security properties of this framework. Our characterisation allowed us to improve the original protocol to be more resistant towards eavesdropping. However, we prove a couple of impossibility results, including one that dictates that complete security against an eavesdropper is not possible in this framework. Thus, it is not possible to design a perfect QSS using this framework.