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Opaque Cheat Attack on Quantum Secret Sharing Schemes Based on Entanglement

Fu‐Guo Deng, Xihan Li, Hong-Yu Zhou

Published May 2, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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.
Security of the three-party 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 attack scheme is presented for the dishonest agent to eavesdrop the message obtained by the other agent freely, which reveals that these QSS schemes are insecure for transmission efficiencies lower than 50%, especially when they are used to share an unknown quantum state. Finally, we present a general way to improve the security of QSS schemes for sharing not only a private key but also an unknown quantum state.
Quantum communication protocols can be designed to detect eavesdropping attacks, something that classical technologies are unable to do since classical information can be replicated in a non-destructive manner. Eavesdropping detection is, therefore, a standard feature in all the proposed quantum secret sharing (QSS) protocols. However, detection is often done by a statistical analysis of the outcome of multiple decoy rounds, and this causes a significant communication overhead. In our quest for a QSS protocol that works even in one round, we came across a one-shot secret-sharing framework proposed by Hsu (Phys. Rev. A 2003). The scheme was designed to work over public channels without requiring multiple rounds to detect eavesdropping but it lacked a thorough security analysis. In this work we present a complete characterisation of the correctness and security properties of this framework. Our characterisation allowed us to improve the original protocol to be more resistant towards eavesdropping. However, we prove a couple of impossibility results, including one that dictates that complete security against an eavesdropper is not possible in this framework. Thus, it is not possible to design a perfect QSS using this framework.
Multi-party quantum secret sharing scheme with high efficient based on entanglement states is proposed and analyzed. A three-party which is presented shares a sequence of joint key bits. In this scheme, a general proof of the security against eavesdropping for three-party quantum secret sharing based on entanglement swapping is provided. The scheme which is showed is secure against a dishonest participant's intercept-and-resend attack and eavesdropper's entangle auxiliary-particles attack. In case of eavesdropping attacks with full information again, the detection bit needs to be transmitted except those for detection, the total efficiency of the scheme approaches to 100%. The protocol can be generalized to N-party system by using N-partite entanglement states.
This paper proposes a protocol for multi-party quantum secret sharing utilizing four non-orthogonal two-particle entangled states following some ideas in the schemes proposed by Liu et al . ( 2006 Chin. Phys. Lett. 23 3148 ) and Zhang et al . ( 2009 Chin. Phys. B 18 2149 ) respectively. The theoretical efficiency for qubits of the new protocol is improved from 50% to approaching 100%. All the entangled states can be used for generating the private key except those used for the eavesdropping check. The validity of a probable attack called opaque cheat attack to this kind of protocols is considered in the paper for the first time.