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International Journal of Quantum Information

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

Yu‐Guang Yang, Weifeng Cao, Qiaoyan Wen

Published Oct 1, 2009• 0 citations
Publisher

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.

DOI
10.1142/s0219749909005882

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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.
We present a fake-signal-and-cheating attack strategy for the dishonest agent in quantum secret sharing (QSS) to steal the information of the other agents' fully and freely. It is found that almost all the QSS protocols existing, such as the two famous QSS protocols, the Hillery-Buzˇ\check{z}zˇek-Berthiaume [Phys. Rev. A \textbf{59}, 1829 (1999)] and the Karlsson-Koashi-Imoto [Phys. Rev. A \textbf{59}, 162 (1999)], can be eavesdropped freely if the process for the eavesdropping check is accomplished with the cooperation of the dishonest agent. He can sends a fake signal to the other agents after intercepting the original photons and storing them. His action can be hidden with entanglement swapping and cheating when the photons are chosen as the samples for checking eavesdropping. Finally, we present a possible improvement of these QSS protocols' security with decoy photons.
In this article we present a general security strategy for quantum secret sharing (QSS) protocols based on the scheme presented by Hillery, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, and Berthiaume (HBB) [Phys. Rev. A 59, 1829 (1999)]. We focus on a generalization of the HBB protocol to nnn communication parties thus including nnn-partite Greenberger-Horne-Zeilinger states. We show that the multipartite version of the HBB scheme is insecure in certain settings and impractical when going to large nnn. To provide security for such QSS schemes in general we use the framework presented by some of the authors [M. Huber, F. Mintert, A. Gabriel, B. C. Hiesmayr, Phys. Rev. Lett. 104, 210501 (2010)] to detect certain genuine nnn-partite entanglement between the communication parties. In particular, we present a simple inequality which tests the security.
Recently, Yang et al. proposed a kind of quantum cryptographic schemes based on secret sharing. The main idea is drawn from the case, where any n participants who share a secret K can co-operate as K does. This process can be applied to encryption, authentication, signature and so on. Unfortunately, since there is no identity authentication of the share’s holder, these schemes inherit the limitation of secret sharing in practice. If some participants do not follow the protocol, the protocol would be a failure at last. Moreover, these schemes encounter another serious attack. Any two participants can co-operate to defeat the schemes by sending different shares to the parties unknown to the distributor of the secret K, such that these parties can execute the protocol as well. The attack proves that it is not enough for quantum cryptographic schemes that only the secret key is secure.
Security of the one-way quantum secret sharing (QSS) schemes based on entanglement and a collective eavesdropping check is analyzed in the case of considerable quantum channel losses. An opaque cheat attack scheme is presented for the dishonest agent, which reveals that these QSS schemes are completely insecure for transmission efficiencies lower than 50%. That is, the dishonest agent can eavesdrop fully and freely in almost all the one-way QSS schemes based on entanglement if the quantum channel induces 50% losses, including the two pioneer works, the Hillery-Bu\v{z}ek-Berthiaume scheme and the Karlsson-Koashi-Imoto scheme. Finally, we present two ways for possible improvement of these schemes.