Abstract Quantum secret sharing, a pivotal research domain within quantum cryptography, has significant applications across diverse fields such as information security and distributed quantum computing. This paper proposes a d-dimensional hierarchical quantum multi-secret sharing scheme with a general access structure. In the proposed scheme, the distributor constructs a special entangled state by leveraging the secret values at each level and a monotone span program. During the secret reconstruction phase, participants only need to measure the particles in their possession, and authorized participants at each level can recover multiple secrets shared at that level. Additionally, each participant can independently compute and obtain multiple lower-level secrets but cannot access any higher-level secret information. Compared to existing hierarchical quantum secret sharing schemes, the proposed scheme is better suited for specific application scenarios with unique requirements. Furthermore, security analysis demonstrates that the scheme can resist various attacks, such as measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, and collusion attacks.
Abstract Quantum secret sharing, a pivotal research domain within quantum cryptography, has significant applications across diverse fields such as information security and distributed quantum computing. This paper proposes a d-dimensional hierarchical quantum multi-secret sharing scheme with a general access structure. In the proposed scheme, the distributor constructs a special entangled state by leveraging the secret values at each level and a monotone span program. During the secret reconstruction phase, participants only need to measure the particles in their possession, and authorized participants at each level can recover multiple secrets shared at that level. Additionally, each participant can independently compute and obtain multiple lower-level secrets but cannot access any higher-level secret information. Compared to existing hierarchical quantum secret sharing schemes, the proposed scheme is better suited for specific application scenarios with unique requirements. Furthermore, security analysis demonstrates that the scheme can resist various attacks, such as measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, and collusion attacks.
Abstract Quantum secret sharing plays an essential role in quantum cryptography. This paper proposes a dynamic hierarchical quantum multi-secret sharing scheme based on linear homogeneous recurrence (LHR) relations. In the scheme, the distributor aggregates multiple secrets into a single master secret using the Chinese Remainder theorem (CRT), and then implements a special hierarchical structure based on LHR relations, generating corresponding shares for the participants. Participants use the generalized Pauli operators to encode their shares into the quantum state to reconstruct multiple secrets. During the transmission of the quantum state, participants can authenticate each other, thereby enhancing the security of the communication process. Additionally, the proposed scheme is dynamic, allowing for the dynamic update of the participants’ set. Security analysis demonstrates that the scheme can resist measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, forgery attacks, collusion attacks, as well as revoked or downgraded participant attacks.
ABSTRACT Quantum secret sharing aims to securely distribute private information among multiple participants, such that only authorized subsets can collaboratively reconstruct the secret. However, current research remains largely exploratory, and most existing protocols are limited to sharing low‐dimensional quantum states and lack hierarchical capabilities. To overcome these limitations, we propose a novel hierarchical quantum secret sharing protocol with identity authentication. Specifically, we construct ‐dimensional disentangler and isometric transformation operations. These are applied to compress arbitrary ‐dimensional entangled states, with each compression corresponding to one hierarchical level. For a given hierarchical participant structure, the entangled particles of the compressed states are allocated as secret shares among the participants. Authorized participants within the same level collaboratively reconstruct the original quantum state using the conjugate transposes of disentangler operations and isometric transformations. Security analysis confirms the protocols resilience against common attacks, including intercept‐resend, entangle‐measure, and dishonest participant attacks. Compared with existing similar protocols, our scheme demonstrates superior performance in terms of quantum efficiency and other metrics.
Quantum secret sharing is an important branch of quantum cryptography, and secure multi-party quantum key distribution protocols can be constructed using quantum secret sharing. In this paper, we construct a quantum secret sharing scheme built on a constrained (t, n ) threshold access structure, where n is the number of participants and t is the threshold number of participants and the distributor. Participants from two different sets perform the corresponding phase shift operations on two particles in the GHZ state passed to them, and then t−1 participants with the distributor can recover the key, where the participant recovering the key measures the particles received by himself and finally obtains the key through the collaboration of the distributors. Security analysis shows that this protocol can be resistant to direct measurement attacks, interception retransmission attacks, and entanglement measurement attacks. This protocol is more secure, flexible, and efficient compared with similar existing protocols, which can save more quantum resources.
A hierarchical quantum secret sharing scheme is proposed, for which participants are divided into multiple layers. In this scheme, the number of participants and the shared secrets can be different for layers. The shared secret of a layer can only be recovered by the cooperation of all the participants at that layer. Moreover, each participant is able to obtain the shared secrets at lower layers, but not those at higher layers. The design is based on a special high-dimensional entangled state, in which the particles have different dimensions and can be set as subtle values to satisfy the hierarchical requirement. The correctness and security of the proposed scheme are analyzed. As compared to existing quantum secret sharing schemes, it possesses distinct features which are demanded by some specified scenarios.
Abstract Quantum secret sharing (QSS) has significant potential to improve secure communications. However, conventional QSS protocols, typically based on (n, n) or (t, n) threshold structures, require participants to possess symmetric authority, which is often impractical. To address scenarios with participants holding asymmetric privileges, we propose an innovative QSS scheme that realizes a hypergraph structure. This enables secret recovery only for authorized sets with the appropriate privileges. In detail, a specialized hypergraph structure is investigated to construct d-dimensional multipartite entangled states. Using these states, we develop an authenticated QSS protocol that enables secret recovery by authorized sets. Security analysis confirms the protocol’s resilience against common attacks, including intercept-resend, entangle-measure, dishonest participant and Trojan horse attacks. We further characterize the distinct impacts of dit-flip, phase-flip, dit-phase-flip, and depolarizing noise channels on quantum state transmission within the protocol. This characterization demonstrates that dynamically adapting error probability threshold according to prevailing noise conditions is essential to maintain security. Compared with existing protocols, our scheme improves quantum efficiency and reduces the number of unitary operations, which enhances its experimental feasibility.
In this paper, a pair of quantum states are constructed based on an orthogonal array and further generalized to multi-body quantum systems. Subsequently, a novel physical process is designed, which is aimed at effectively masking quantum states within multipartite quantum systems. According to this masker, a new authenticable quantum secret sharing scheme is proposed, which can realize a class of special access structures. In the distribution phase, an unknown quantum state is shared safely among multiple participants, and this secret quantum state is embedded into a multi-particle entangled state using the masking approach. In the reconstruction phase, a series of precisely designed measurements and corresponding unitary operations are performed by the participants in the authorized set to restore the original information quantum state. To ensure the security of the scheme, the security analysis of five major types of quantum attacks is conducted. Finally, when compared with other quantum secret sharing schemes based on entangled states, the proposed scheme is found to be not only more flexible but also easier to implement based on existing quantum computing cloud platforms.