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.Comment: Revtex, 7 pages, 3 figures; Introduction modifie
