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Chinese Physics

A (2, 3) quantum threshold scheme based on Greenberger–Horne–Zeilinger state

Yuan Li, Zeng Gui-Hua

Published Oct 1, 2007• 9 citations
Publisher

Abstract

In this paper, by using properties of quantum controlled-not manipulation and entanglement states, we have designed a novel (2, 3) quantum threshold scheme based on the Greenberger—Horne—Zeilinger (GHZ) state. The proposed scheme involves two phases, i.e. a secret sharing phase and a secret phase. Detailed proofs show that the proposed scheme is of unconditional security. Since the secret is shared among three participants, the proposed scheme may be applied to quantum key distribution and secret sharing.

DOI
10.1088/1009-1963/16/10/008

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In this paper, by using properties of quantum controlled-not manipulation and entanglement states, we have designed a novel (2, 3) quantum threshold scheme based on the Greenberger—Horne—Zeilinger (GHZ) state. The proposed scheme involves two phases, i.e. a secret sharing phase and a secret phase. Detailed proofs show that the proposed scheme is of unconditional security. Since the secret is shared among three participants, the proposed scheme may be applied to quantum key distribution and secret sharing.
Abstract Based on the d-dimensional Greenberger–Horne–Zeilinger (GHZ) state, this paper proposes a novel multi-party quantum secret sharing scheme with the characteristics of identity authentication and dual-threshold. In the scheme, the dealer first constructs an asymmetric binary polynomial and decomposes it into two unary polynomials, then divides the participants into two groups, and generates secret shares and corresponding polynomial pairs for each participant. The dealer prepares a three-qudit GHZ state and uses two of them to perform dual-line transmission between the two groups of participants. The participants perform specific unitary transformations on the transmitted particles. Finally, the recovery agent collects and measures the information particles to recover the secret. The scheme uses a hash function and a session key to detect fraudulent behavior and identify specific participants to achieve identity authentication. Security analysis shows that the scheme can effectively resist intercept-resend attacks, entangle-measure attacks, dishonest participant attacks and Trojan horse attacks.
In this paper, we present an (n, n) threshold quantum secret sharing scheme of secure direct communication using Greenberger-Horne-Zeilinger state. The present scheme is efficient in that all the Greenberger-Horne-Zeilinger states used in the quantum secret sharing scheme are used to generate shared secret messages except those chosen for checking eavesdropper. In our scheme, the measuring basis of communication parties is invariable and the classical information used to check eavesdropping needs only the results of measurements of the communication parties. Another nice feature of our scheme is that the sender transmit her secret messages to the receivers directly and the receivers recover the sender's secret by combining their results, different from the QSS scheme whose object is essentially to allow a sender to establish a shared key with the receivers. This feature of our scheme is similar to that of quantum secret direct communication.
A novel approach to quantum cryptography to be called NQKD, networking quantum key distribution, has been developed for secure quantum communication schemes on the basis of the complementary relations of entanglement Greenberger–Horne–Zeilinger (GHZ) triplet states. One scheme distributes the private key among legal participants in a probabilistic manner, while another transmits the deterministic message with some certainty. Some decoy photons are employed for preventing a potential eavesdropper from attacking quantum channels. The present schemes are efficient as there exists an elegant method for key distributions. The security of the proposed schemes is exactly guaranteed by the entanglement of the GHZ quantum system, which is illustrated in security analysis.
Quantum secret sharing (QSS) is a crucial quantum cryptographic method that provides unconditional secu-rity through the principles of quantum mechanics and enables practical applications in information security and distributed computing. Many QSS protocols have been proposed based on various quantum properties and operations. In this study, we propose a new and efficient multiparty quantum secret sharing protocol that utilizes entanglement swapping with the Greenberger-Horne-Zeilinger (GHZ) state and introduces a novel structure to efficiently and securely distribute and recover secrets. Due to entanglement swapping, participants can entangle systems without directly interacting with each other, enhancing practical usage. Through GHZ entanglement swapping, initial particle states cannot be directly inferred. The proposed QSS protocol leverages this property to encode information among participants. To decode the secret, participants only require measuring particles on a GHZ basis to get the corresponding information without performing operations. Through security analysis, it is shown that any eavesdropper or dishonest participant will be detected. Efficiency analysis indicates that the proposed protocol substantially reduces costs and significantly enhances efficiency. As the number of participants increases, the resource consumption of the proposed protocol becomes much lower than that of other QSS protocols. In summary, the proposed protocol efficiently achieves unconditional security in QSS, ensuring the secure transmission and sharing of quantum information.
Abstract At present, most quantum secret sharing (QSS) protocols are more or less designed with the incorporation of classical secret sharing schemes. With the increasing maturity of quantum technology, QSS protocols based on pure quantum mechanics are becoming more important. Classical secret sharing schemes cannot achieve absolute security, and their involvement can compromise the security of QSS protocols. This paper proposes a QSS scheme based on Greenberger–Horn–Zeilinger (GHZ) basis measurement and quantum entanglement exchange. In this protocol, the secret sender stores the secret information using Pauli operations. Participants obtain their shares by measuring the product state sequentially. Finally, participants complete the secret reconstruction through quantum entanglement exchange and other related quantum operations. In addition, the particles held by participants in the protocol do not contain any secret information. Each participant’s particles are in a state of maximum entanglement, and no participant can deduce the particle information of other participants through their own particles. At the same time, the protocol is based on pure quantum mechanics and does not involve classical schemes, which avoids the problem of reduced security of the protocol. Security analysis indicates that the protocol is not vulnerable to retransmission interception and collusion attacks. Moreover, it is capable of detecting and terminating the protocol promptly when facing with attacks from dishonest participants.
Abstract Quantum secret sharing (QSS) enables secure secret distribution via quantum mechanics, requiring authorized participants to collaborate for recovery. However, practical scenarios often involve classical users, demand recipient anonymity, and need dynamic participant management—features not simultaneously supported by existing schemes. This work presents a secure dynamic semiquantum anonymous secret sharing (DSQASS) protocol using Greenberger-Horne-Zeilinger-like (GHZ-like) states. The design integrates three practical capabilities: semi-quantum operation for classical participants, dynamic membership updates, and statistical receiver anonymity. Rigorous analysis verifies the protocol’s correctness and resilience against internal and external adversaries. Simulations on a quantum cloud platform confirm its feasibility in hybrid quantum-classical environments.