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 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, 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.
Quantum secret sharing holds a significant place in quantum cryptography. In this paper, a (w, t, n)-weighted threshold dynamic quantum secret sharing scheme with cheating identification is constructed based on the CRT for a polynomial ring. In our scheme, on the premise of not altering the private shares of the old participants, the dynamic update of the participants can be realized without other participants’ help, and the shared secret will not be changed. During the secret reconstruction phase, via executing the quantum state digital signature, the proposed scheme not only can timely detect the existence of the cheating behavior, but also once exists, definitely can identify one cheater and eliminate him from the system, making the scheme more secure. Moreover, our scheme enables secret sharing among participants with different authorities, which enhances the practicability of the scheme. Finally, the security analysis shows our scheme not only is resistant to a range of typical external attacks but can detect forgery, collusion, denial and dishonest revoked 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.
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 Based on the d-dimensional Greenberger–Horne–Zeilinger (GHZ) state, this paper proposes a novel multi-party quantum secret sharing scheme with the characteristics of identity authentication and dual-threshold. In the scheme, the dealer first constructs an asymmetric binary polynomial and decomposes it into two unary polynomials, then divides the participants into two groups, and generates secret shares and corresponding polynomial pairs for each participant. The dealer prepares a three-qudit GHZ state and uses two of them to perform dual-line transmission between the two groups of participants. The participants perform specific unitary transformations on the transmitted particles. Finally, the recovery agent collects and measures the information particles to recover the secret. The scheme uses a hash function and a session key to detect fraudulent behavior and identify specific participants to achieve identity authentication. Security analysis shows that the scheme can effectively resist intercept-resend attacks, entangle-measure attacks, dishonest participant attacks and Trojan horse attacks.