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International Journal of Quantum Information

A NOTE ON SOME QUANTUM SECRET SHARING SCHEMES

Zhengjun Cao, Olivier Markowitch

Published Apr 1, 2010• 1 citation
Publisher

Abstract

We remark that the schemes [S. Gaertner, C. Kurtsiefer, M. Bourennane and H. Weinfurter, Phys. Rev. Lett.98 (2007) 020503; H. Takesue and K. Inoue, Phys. Rev. A74 (2006) 012315; L. Hsu and C. Li, Phys. Rev. A71 (2005) 022321; F. Yan and T. Gao, Phys. Rev. A72 (2005) 012304; L. Xiao, G. Long, F. Deng and J. Pan, Phys. Rev. A69 (2004) 052307; M. Hillery, V. Bužek and A. Berthiaume, Phys. Rev. A59 (1999) 1829] are not secret sharing schemes as claimed.

DOI
10.1142/s0219749910006150

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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, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, 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.

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Comment on “High-dimensional deterministic multiparty quantum secret sharing without unitary operations”

Ming‐Ming Wang, Xiu‐Bo Chen, Yixian Yang

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We remark that the schemes [S. Gaertner, C. Kurtsiefer, M. Bourennane and H. Weinfurter, Phys. Rev. Lett.98 (2007) 020503; H. Takesue and K. Inoue, Phys. Rev. A74 (2006) 012315; L. Hsu and C. Li, Phys. Rev. A71 (2005) 022321; F. Yan and T. Gao, Phys. Rev. A72 (2005) 012304; L. Xiao, G. Long, F. Deng and J. Pan, Phys. Rev. A69 (2004) 052307; M. Hillery, V. Bužek and A. Berthiaume, Phys. Rev. A59 (1999) 1829] are not secret sharing schemes as claimed.
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.
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, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, 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.