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arXiv:quant-ph/0405179 · Physical Review A

Efficient multiparty quantum-secret-sharing schemes

Xiao Li, Gui Lu Long, Fu‐Guo Deng, Jian-Wei Pan

Published May 11, 2004• 838 citations

Abstract

In this work, we generalize the quantum-secret-sharing scheme of Hillery, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, and Berthiaume [Phys. Rev. A 59, 1829 (1999)] into arbitrary multiparties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Berthiaume quantum-secret-sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum-secret-sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis quantum-secret-sharing scheme is developed from the Lo-Chau-Ardehali technique [H. K. Lo, H. F. Chau, and M. Ardehali, e-print quant-ph∕0011056] where all the participants choose their measuring-basis asymmetrically, and the measuring-basis-encrypted quantum-secret-sharing scheme is developed from the Hwang-Koh-Han technique [W. Y. Hwang, I. G. Koh, and Y. D. Han, Phys. Lett. A 244, 489 (1998)] where all participants choose their measuring basis according to a control key. Both schemes are asymptotically $100%$ in efficiency, hence nearly all the Greenberger-Horne-Zeilinger states in a quantum-secret-sharing process are used to generate shared secret information.

DOI: 10.1103/physreva.69.052307

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In this work, we generalize the quantum-secret-sharing scheme of Hillery, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, and Berthiaume [Phys. Rev. A 59, 1829 (1999)] into arbitrary multiparties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Berthiaume quantum-secret-sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum-secret-sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis quantum-secret-sharing scheme is developed from the Lo-Chau-Ardehali technique [H. K. Lo, H. F. Chau, and M. Ardehali, e-print quant-ph∕0011056] where all the participants choose their measuring-basis asymmetrically, and the measuring-basis-encrypted quantum-secret-sharing scheme is developed from the Hwang-Koh-Han technique [W. Y. Hwang, I. G. Koh, and Y. D. Han, Phys. Lett. A 244, 489 (1998)] where all participants choose their measuring basis according to a control key. Both schemes are asymptotically

100%

in efficiency, hence nearly all the Greenberger-Horne-Zeilinger states in a quantum-secret-sharing process are used to generate shared secret information.

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

n

communication parties thus including

n

-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

n

. 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

n

-partite entanglement between the communication parties. In particular, we present a simple inequality which tests the security.

An efficient multiparty quantum secret sharing scheme is proposed with Greenberger–Horne–Zeilinger (GHZ) states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations I , σ z , σ x and i σ y to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total efficiency both approach the maximal values.

The aim of quantum secret sharing, as one of most promising components of quantum cryptograph, is one-to-multiparty secret communication based on the principles of quantum mechanics. In this paper, an efficient multiparty quantum secret sharing protocol in a high-dimensional quantum system using a single qudit is proposed. Each participant's shadow is encoded on a single qudit via a measuring basis encryption method, which avoids the waste of qudits caused by basis reconciliation. Security analysis indicates that the proposed protocol is immune to general attacks, such as the measure-resend attack, entangle-and-measure attack and Trojan horse attack. Compared to former protocols, the proposed protocol only needs to perform the single-qudit measurement operation, and can share the predetermined dits instead of random bits or dits.

Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol.

Abstract In the paper (EPJ Quant. Technol. 10:29, 2023), Kuo et al. proposed a multiparty quantum secret sharing protocol based on a novel structure and single qubits. Owing to the absence of an entanglement state, the proposed protocol is more practical than other quantum secret sharing protocols which use entanglement properties. Therefore, we study the security of the proposed protocol and find there exists a security loophole in the n-party (

n\geq 4

n ≥ 4 ) secret sharing case in it, that is, two dishonest agents can collude to obtain (part of) Alice’s secret without the help of the other agents. In order to overcome the security loophole, we give an improved protocol and make a security analysis for it. By calculating, the qubit efficiency of the three-party case in it is equal to

\frac{1}{8}

1 8 , which is higher than that in Hillery et al.’s protocol (Phys. Rev. A 59:1829, 1999).