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International Journal of Quantum Information

Notes on two multiparty quantum secret sharing schemes

Gan Gao

Published Apr 1, 2018• 4 citations
Publisher

Abstract

In the paper [H. Abulkasim et al., Int. J. Quantum Inform. 15 (2017) 1750023], Abulkasim et al. proposed a quantum secret sharing scheme based on Bell states. We study the security of the multiparty case in the proposed scheme and detect that it is not secure. In the paper [Y. Du and W. Bao, Opt. Commun. 308 (2013) 159], Du and Bao listed Gao’s scheme and gave a attack strategy on the listed scheme. We point out that their listing scheme is not the genuine Gao’s scheme and their research method is not advisable.

DOI
10.1142/s0219749918500302

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In the paper [H. Abulkasim et al., Int. J. Quantum Inform. 15 (2017) 1750023], Abulkasim et al. proposed a quantum secret sharing scheme based on Bell states. We study the security of the multiparty case in the proposed scheme and detect that it is not secure. In the paper [Y. Du and W. Bao, Opt. Commun. 308 (2013) 159], Du and Bao listed Gao’s scheme and gave a attack strategy on the listed scheme. We point out that their listing scheme is not the genuine Gao’s scheme and their research method is not advisable.
Recently, Gao et al.'s [ Commun. Theor. Phys. 52 (2009) 421 ] multiparty quantum secret sharing (MQSS) protocol with two-photon three-dimensional Bell states was enhanced by Hwang et al. [ Commun. Theor. Phys. 56 (2011) 79 ]. The improved protocol removes some unnecessary unitary operations, devices, and transmissions by the technique of decoy single photons and careful modification. However, in this paper, we investigate the security of the improved protocol and find it is insecure. The eavesdropper can steal all Alice's secret information. Furthermore, a feasible modification to remedy the security loophole is put forward. Our improved protocol provides a basic method to modify a kind of MQSS protocols which cannot resist the collusion attack.
Recently, Yan and Gao [Phys. Rev. A 72, 012304 (2005)] presented a quantum secret sharing protocol which allows a secret message to be shared between two groups of parties (mmm parties in group 1 and nnn parties in group 2). Their protocol is claimed to be secure that, except with the cooperation of the entire group 1 or group 2, no subgroup of either group 1 or group 2 can extract the secret message. However, this study points out that the mthm\text{th}mth party (the last party to process the quantum state) of group 1 can maliciously replace the secret message with an arbitrary message without the detection of the other parties.
Recently, Yan and Gao proposed a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons (Phys. Rev. A \textbf{72}, 012304 (2005)). We find that it is secure if the quantum signal transmitted is only a single photon but insecure with a multi-photon signal as some agents can get the information about the others' message if they attack the communication with a Trojan horse. However, security against this attack can be attained with a simple modification.