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International Journal of Quantum Information

EFFICIENT KEY CONSTRUCTION ON SEMI-QUANTUM SECRET SHARING PROTOCOLS

Chun‐Wei Yang, Tzonelih Hwang

Published Aug 1, 2013• 62 citations
Publisher

Abstract

Semi-quantum secret sharings (SQSSs), as they are of now, require all the agents choose to measure the received qubits to produce the shared secret key. As a result, to share an n-bit secret key in an (m + 1)-party SQSS, the number of quanta required to transmit is n × 2m, which increases exponentially with the number of agents (i.e. m). This study proposes a new idea on the construction of the secret key for the existing SQSS such that only 2nm qubits are required to produce an n-bit secret key in the (m + 1)-party SQSS.

DOI
10.1142/s0219749913500524

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Semi-quantum secret sharings (SQSSs), as they are of now, require all the agents choose to measure the received qubits to produce the shared secret key. As a result, to share an n-bit secret key in an (m + 1)-party SQSS, the number of quanta required to transmit is n × 2m, which increases exponentially with the number of agents (i.e. m). This study proposes a new idea on the construction of the secret key for the existing SQSS such that only 2nm qubits are required to produce an n-bit secret key in the (m + 1)-party SQSS.
This study proposes a multiparty single-photon semi-quantum secret sharing (SQSS) protocol to simultaneously improve quantum bit (qubit) efficiency and practical feasibility. Existing quantum secret sharing protocols typically assume that all participants possess full quantum capabilities, which limits their deployment in real-world environments. To address this issue, the proposed protocol was designed using a semi-quantum model, allowing N agents with limited quantum capabilities to participate in the secret-sharing process. In terms of efficiency, the proposed protocol employs single photons as quantum resources and is analyzed under a unified definition of qubit efficiency. The results show that the qubit efficiency of the proposed protocol reaches 12N\frac{1}{2N}2N1​ , which is comparable to the best recent quantum secret sharing protocols and outperforms most existing SQSS methods. Unlike certain protocols in which qubit efficiency decreases exponentially with the number of participants, the quantum resource consumption of the proposed protocol increases linearly with the number of agents. Consequently, its qubit efficiency decreases proportionally to 1N\frac{1}{N}N1​ , rather than exponentially, providing better scalability as the number of agents increases. In terms of security, the protocol is analyzed against several attack models, including intercept-resend, entangle-and-measure, collective, and collusion attacks. The analysis shows that an adversary cannot obtain useful information without detection under these attacks, demonstrating the robustness of the proposed protocol.
The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational (ZZZ) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.
A semi-quantum secret sharing (SQSS) scheme based on Bell states is proposed in this paper. The sender who can perform any relevant quantum operations uses Bell states to share the secret keys with her participants that are limited to perform classical operations on the transmitted qubits. It is found that our scheme is easy to generalize from three parties to multiparty and more efficient than the previous schemes [Q. Li, W. H. Chan and D. Y. Long, Phys. Rev. A 82 (2010) 022303; L. Z. Li, D. W. Qiu and P. Mateus, J. Phys. A: Math. Theor. 26 (2013) 045304; C. Xie, L. Z. Li and D. W. Qiu, Int. J. Theor. Phys. 54 (2015) 3819].
Abstract Semi-quantum secret sharing (SQSS) is an important branch of semi-quantum cryptography, and differs from quantum secret sharing (QSS) in that not all parties are required to possess quantum capabilities. All previous SQSS protocols have three common features: (i) they adopt product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a tree-type way; and (iii) they require the classical parties to possess the measurement capability. In this paper, two circular SQSS protocols with single particles are suggested, where the first one requires the classical parties to possess the measurement capability while the second one does not have this requirement. Compared with the previous SQSS protocols, the proposed SQSS protocols have some distinct features: (i) they adopt single particles rather than product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a circular way; and (iii) the second protocol releases the classical parties from the measurement capability. The proposed SQSS protocols are robust against some famous attacks from an eavesdropper, such as the measure-resend attack, the intercept-resend attack and the entangle-measure attack, and are feasible with present quantum technologies in reality .
Semi-quantum secret sharing (SQSS) is a branch of quantum cryptography which only requires the dealer to have quantum capabilities, reducing the difficulty of protocol implementation. However, the efficiency of the SQSS protocol still needs to be further studied. In this paper, we propose a semi-quantum secret sharing protocol, whose efficiency can approach 100% as the length of message increases. The protocol is based on single particles to reduce the difficulty of resource preparation. Particle reordering, a simple but effective operation, is used in the protocol to improve efficiency and ensure security. Furthermore, our protocol can share specific secrets while most SQSS protocols could not. We also prove that the protocol is secure against common attacks.
Quantum secret sharing protocol, which lets a master share a secret with his/her agents and the agents can recover the master’s secret when they collaborate, is an important research issue in the quantum information field. In order to make the quantum protocol more practical, the concept of semi-quantum protocol is advanced by Boyer et al. Based on this concept, many semi-quantum secret sharing protocols have been proposed. The various entanglement states (including Bell state, GHZ state and so on) were used to be the quantum resources in these SQSS protocols, except for W-state which is the other multi-qubit entanglement state and different from GHZ states. Therefore, this study wants to use the entanglement property of W-state to propose the first three-party SQSS protocol and analyze the proposed protocol is free from the well-known attacks.