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Modern Physics Letters A

Multiparty semi-quantum secret sharing protocol based on single photon sequence and permutation

Xiangjun Xin, Fan He, Chaoyang Li, Fagen Li

Published Jun 14, 2024• 8 citations
Publisher

Abstract

Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent’s secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack.

DOI
10.1142/s0217732324500846

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Modern Physics Letters A•Feb 11, 2026•1 citation
Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent’s secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack.
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.
Most (k, n) threshold quantum secret sharing protocols are fully quantum. The message receivers must be equipped with complex quantum devices so as to prepare various quantum resources and perform complex quantum operations, which may affect the practice of these protocols. On the other hand, the qubit efficiency of most (k, n) threshold quantum secret sharing protocols is not more than 1/2. To simplify the (k, n) threshold quantum secret sharing protocol and improve its practice and qubit efficiency, a new (k, n) threshold secret sharing protocol with semi-quantum properties is proposed. In this protocol, the dealer prepares decoy particles and sends them to the receivers. The receivers insert particles carrying secret information along with Z-basis decoy particles into the received particle sequence to generate mixed-particle sequences, which are returned to the dealer. The dealer measures the received particle sequences to check for eavesdropping and establishes shared secret keys with the receivers. With the shared secret keys, the dealer distributes the secret pieces among the receivers using Shamir’s secret sharing scheme. Multiple secret messages can be recovered by k or more receivers. The qubit efficiency of our protocol is k/n. For an (n, n) threshold protocol, the qubit efficiency would be 100%. The proposed scheme is based on single particles without using any entangled system. Therefore, its quantum resources are relatively easy to prepare. Receivers must only prepare simple Z-basis qubits. Its semi-quantum properties enhance practice implementation. The proposed protocol has robust security against various types of attacks, including eavesdropping, internal, and collusion attacks. Furthermore, it can resist the unitary attack, which is seldom analyzed in other protocols.
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.
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.
Typical multiparty semi-quantum secret sharing (MSQSS) protocols require the dealer to possess full quantum capabilities, while the classical users usually need to perform three operations. To address this practical limitation, this paper introduces a new mediated MSQSS protocol that enables Alice, a classical user, to share a secret with [Formula: see text] classical Bobs, with the assistance of an untrusted third party (TP) who may attempt any possible attack to steal Alice’s secret. Furthermore, the classical participants require only two capabilities instead of three, namely: (a) performing measurements in the [Formula: see text] basis; and (b) reordering qubits. The proposed scheme offers significant advantages over existing mediated QSS protocols: (1) It is the first mediated SQSS protocol to adopt single qubits, instead of entangled states, as the quantum resource, which makes it more practical and easier to implement; (2) It achieves higher qubit efficiency. Security analysis also demonstrates that the protocol is secure against well-known attacks.