Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol

TL;DR

This paper analyzes the security of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol against participant attacks, revealing its vulnerabilities and providing a method to identify potential security breaches.

Contribution

It introduces a general method to analyze participant attacks in quantum secret-sharing protocols, specifically demonstrating the insecurity of the HBB protocol and constructing explicit attack schemes.

Findings

HBB protocol is insecure against dishonest participants

A method to determine when a participant can gain all information without errors

Explicit attack schemes are constructed based on the analysis

Abstract

The participant attack is the most serious threat for quantum secret-sharing protocols. We present a method to analyze the security of quantum secret-sharing protocols against this kind of attack taking the scheme of Hillery, Buzek, and Berthiaume (HBB) [Phys. Rev. A 59 1829 (1999)] as an example. By distinguishing between two mixed states, we derive the necessary and sufficient conditions under which a dishonest participant can attain all the information without introducing any error, which shows that the HBB protocol is insecure against dishonest participants. It is easy to verify that the attack scheme of Karlsson, Koashi, and Imoto [Phys. Rev. A 59, 162 (1999)] is a special example of our results. To demonstrate our results further, we construct an explicit attack scheme according to the necessary and sufficient conditions. Our work completes the security analysis of the HBB protocol, and the method presented may be useful for the analysis of other similar protocols.