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Modern Physics Letters B

A novel semi-quantum secret sharing scheme based on Bell states

Aihan Yin, Zefan Wang, Fangbo Fu

Published May 10, 2017• 22 citations
Publisher

Abstract

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].

DOI
10.1142/s0217984917501500

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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].
A recent paper proposed a semi-quantum secret sharing (SQSS) scheme based on Bell states [A. Yin et al., Mod. Phys. Lett. B. https://doi.org/10.1142/S0217984917501500 ]. This protocol was presumed that only the sender has the quantum power and all participants perform classical operations. However, we find this protocol is not that secure as it is expected. We can utilize the intercept-resend method to attack this scheme. Then, we give an improvement strategy based on semi-quantum key distribution, which ensures that the new scheme resists the attack we have proposed.
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.
Recently, Younes et al. proposed an efficient multi-party semi-quantum secret sharing (SQSS) scheme that generalizes Tian et al.'s three-party protocol \cite{Tian2021} to accommodate multiple participants. This scheme retains the original advantages, such as high qubit efficiency and allowing the secret dealer, Alice, to control the message content. However, He et al. \cite{He2024} identified a vulnerability in Tian et al.'s protocol to the double CNOT attack (DCNA), which also affects the generalized scheme. In response, He et al. proposed an improved protocol to address this issue. Despite these improvements, their protocol is limited to two participants and remains a primarily two-way communication scheme, which does not fully prevent the Trojan horse attack without expensive quantum devices such as photon number splitters (PNS) and wavelength filters (WF). To address these issues, this paper develops a novel multi-party SQSS scheme using the quantum property between Bell states and the Hadamard operation to detect eavesdroppers. This new scheme is secure against the DCNA, intercept-resend attack, and collective attack. It employs a fully one-way communication scheme, entirely preventing the Trojan horse attack without costly quantum devices, aligning with the semi-quantum environment's original intent. This new protocol also offers better qubit efficiency and allows Alice to share specific secrets.
Semi-quantum cryptography communication stipulates that the quantum user has complete quantum capabilities, and the classical user has limited quantum capabilities, only being able to perform the following operations: (1) measuring and preparing qubits with a Z basis and (2) returning qubits without any processing. Secret sharing requires participants to work together to obtain complete secret information, which ensures the security of the secret information. In the semi-quantum secret sharing (SQSS) protocol, the quantum user Alice divides the secret information into two parts and gives them to two classical participants. Only when they cooperate can they obtain Alice's original secret information. The quantum states with multiple degrees of freedom (DoFs) are defined as hyper-entangled states. Based on the hyper-entangled single-photon states, an efficient SQSS protocol is proposed. The security analysis proves that the protocol can effectively resist well-known attacks. Compared with the existing protocols, this protocol uses hyper-entangled states to expand the channel capacity. The transmission efficiency is 100% higher than that of single-degree-of-freedom (DoF) single-photon states, providing an innovative scheme for the design of the SQSS protocol in quantum communication networks. This research also provides a theoretical basis for the practical application of semi-quantum cryptography communication.
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.
Abstract Semi-quantum secret sharing (SQSS) is a branch of quantum cryptography, with the advantage of fewer quantum resources. In this paper, we present a SQSS protocol based on hybrid single particle and GHZ-type states. Our protocol adopts circular transport structure to share secret information between classical and quantum parties, employing the entanglement correlation and uncertainty of GHZ-type states to guarantee the security of the transmission. Security analysis indicates that the proposed SQSS protocol enables resilience against various potential attacks such as measure-resend, entangle-measure, internal, and Trojan attacks. Furthermore, our protocol is easy to generalize to multi-party scenarios without increasing the complexity of state preparation. Compared with some typical SQSS protocols, our protocol has higher qubit efficiency without the need for entanglement swapping operations. The proposed SQSS protocol has the potential for broader applications in practical scenarios.