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.
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.
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 (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.
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 walks, as the quantum mechanical counterpart of classical random walks, is an advanced tool for constructing quantum algorithms. Quantum secret sharing protocols based on quantum walks reduce the demand for entangled state preparation and simplify the complexity of quantum operations. However, existing quantum secret sharing protocols based on quantum walks have relatively limited functionality. This paper proposes a hierarchical quantum secret sharing protocol based on two-direction quantum walks on a circle and linear homogeneous recurrence relations. In this protocol, the secret distributor first verifies the participants’ identities simultaneously using a symmetric bivariate polynomial, then uses two-particle product states to carry secrets and encrypts them using evolution operators and global shifting operators. Finally, participants who satisfy the hierarchical access structure can simultaneously reconstruct their private classical sequence and quantum state sequence. Correctness analyses demonstrate that qualified participants can accurately obtain and reconstruct the secret information. In terms of security, the protocol can resist both external and internal attacks simultaneously. Lastly, efficiency analysis and comparisons demonstrate that the protocol outperforms other quantum secret sharing protocols based on quantum walks and holds an efficiency advantage.
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.
Abstract Quantum secret sharing plays a key role as a foundational method for disseminating a secret to all participants in quantum cryptography. Group authentication plays a significant role in safeguarding information, as it confirms the identity of communication parties. This paper presents a d−level (t,m) threshold quantum secret-sharing scheme combined with group authentication. Group members can simultaneously authenticate their identities through group authentication. Leveraging the Lagrange interpolation polynomial, the group authentication method disperses multiple secret shares to group members and later allows joint verification of some or all members. According to our analysis, the complexities of our group authentication scheme are much lower than those found in widely recognized existing group authentication methods. This algorithm allows each participant to keep their secret shares secure and undisclosed. By avoiding transmission of these shares, external eavesdroppers are unable to obtain any secret information. This protocol offers security, efficiency, and practicality. Security analysis reveals its ability to resist intercept-resend attacks, entangle-measure attacks, collusion attacks, and forgery attacks. The proposed scheme ensures both confidentiality and integrity.