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Advanced Quantum Technologies

Improvements on Efficient Controlled Semi‐Quantum Secret Sharing With Entangled States

Cai Zhang, Ruiqing Zhang, Run-hua Tang, Zhiwei Sun

Published Mar 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Semi‐quantum secret sharing represents a significant area in quantum cryptography, offering the advantage of not requiring all participants to be fully quantum‐capable. Recently, Houshmand et al. (Opt. Quant. Electron. 2024, 56(5), 759) proposed a controlled semi‐quantum secret sharing protocol based on entangled states and claimed it was secure. However, the results of our analysis indicate that its security check is flawed and that the secret can be recovered if collaborates with any single other classical user. Accordingly, we propose an improved protocol that rectifies the flaws and resists not only the aforementioned attack, but also attacks initiated by up to dishonest users. In addition, our analysis of an existing denial‐of‐service attack shows that this attack cannot induce classical users to recover incorrect secrets. Consequently, no security check is necessary for this attack.

DOI
10.1002/qute.202500820

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ABSTRACT Semi‐quantum secret sharing represents a significant area in quantum cryptography, offering the advantage of not requiring all participants to be fully quantum‐capable. Recently, Houshmand et al. (Opt. Quant. Electron. 2024, 56(5), 759) proposed a controlled semi‐quantum secret sharing protocol based on entangled states and claimed it was secure. However, the results of our analysis indicate that its security check is flawed and that the secret can be recovered if collaborates with any single other classical user. Accordingly, we propose an improved protocol that rectifies the flaws and resists not only the aforementioned attack, but also attacks initiated by up to dishonest users. In addition, our analysis of an existing denial‐of‐service attack shows that this attack cannot induce classical users to recover incorrect secrets. Consequently, no security check is necessary for this attack.
Quantum secret sharing is a basic quantum cryptographic primitive, which plays an important role in robust key management and secure multiparty computation etc. In this work, we give a cryptanalysis of efficient controlled semi-quantum secret sharing protocol with entangled states proposed recently, which shows that the controller can recover the secret if he cooperates with any one participant. Furthermore, an external opponent can make participants recover a false secret without being detected by a special denial-of-service attack. Therefore, this protocol does not satisfy the security requirement that any unauthorized set can gain access to no information on the secret and cannot guarantee its correctness.
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.
Abstract Quantum secret sharing (QSS) can address the increasing threat of computing power. While semi-QSS protocols alleviate participants’ reliance on quantum devices, ensuring security and lowering the participation difficulty. In this paper, we propose a semi-QSS protocol based on four quantum entangled states within a four-dimensional quantum system. It generates a four-dimensional four-quantum entangled state through a dealer, requiring full quantum capability for the dealer and only partial quantum capability for the participants. Participants perform random operations on the received qubits, and eavesdropping detection is based on these random operations. Then the dealer can choose the correct measurement basis based on the receiver’s specific operations. The security and quantum efficiency of protocol depend on the ratio of information to decoy particles inserted by the dealer. Furthermore, the security analysis shows that the protocol is resistant to common quantum attacks.
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.
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.