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

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, Bužek and Berthiaume 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.