REEXAMINING THE SECURITY OF THE RECONSTRUCTION PHASE OF THE HILLERY-BUZĚK-BERTHIAUME QUANTUM SECRET-SHARING PROTOCOL

Abstract

The participant attack is the most serious threat for quantum secret-sharing protocols. However, it is only during the transmission of quantum information carriers that attention is paid to this kind of attack in the existing quantum secret-sharing protocols. The security considerations of the secret reconstruction phase of quantum secret-sharing protocols against this kind of attack are neglected. We demonstrate our viewpoint by taking the scheme of Hillery, Buzěk, and Berthiaume (HBB) [Phys. Rev. A59 (1999) 18–29] as an example. By telling a lie in the reconstruction phase, a dishonest participant can easily attain the entire secret key instead of eavesdropping during the transmission awkwardly, whereas the honest one cannot judge whether the dishonest one tells the truth and the obtained secret random key is identical to what the secret distributor owns because of lack of verification mechanism in the HBB protocol. It is not difficult to find that almost all the quantum secret-sharing protocols have such disadvantages. Our viewpoint presented may be useful for the design of other similar protocols.