Quantum secret sharing plays a crucial role in quantum cryptography. The two main trends in quantum secret sharing are to address the problem of scheme failure due to participant spoofing and to improve the efficiency of quantum secret sharing. This paper focuses on the quantum secret sharing scheme with general access structure due to its flexibility. We design a special entangled state by resorting to Monotone Span Program (MSP). Based on the special 2-dimensional entangled state, an efficient and verifiable general quantum secret sharing (GQSS) scheme is proposed. In the GQSS scheme, the authorized participants only provide the X-basis measurement results of particles to recover and verify the shared secret, which makes that our scheme have lower communication consumption and quantum computational complexity. The analysis shows that the proposed scheme is simpler and more practical compared with related quantum secret sharing schemes.
Quantum secret sharing plays a crucial role in quantum cryptography. The two main trends in quantum secret sharing are to address the problem of scheme failure due to participant spoofing and to improve the efficiency of quantum secret sharing. This paper focuses on the quantum secret sharing scheme with general access structure due to its flexibility. We design a special entangled state by resorting to Monotone Span Program (MSP). Based on the special 2-dimensional entangled state, an efficient and verifiable general quantum secret sharing (GQSS) scheme is proposed. In the GQSS scheme, the authorized participants only provide the X-basis measurement results of particles to recover and verify the shared secret, which makes that our scheme have lower communication consumption and quantum computational complexity. The analysis shows that the proposed scheme is simpler and more practical compared with related quantum secret sharing schemes.
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 a crucial role in quantum cryptography. In this paper, an efficient and novel weighted threshold quantum secret sharing scheme with changeable participant weights is firstly proposed based on the monotone span program(MSP) and linear secret sharing(LSS) scheme. First, in the secret reconstruction phase, participants only need to perform simple measurement operations on the particles to successfully recover and verify the secret. Additionally, throughout the entire scheme, participants are not required to perform any quantum operations, significantly enhancing the efficiency of the scheme. Secondly, without altering the secret shares of all participants, our scheme firstly enables dynamic changes in participant weights without the need for re-execution, which improves the practicality of the scheme. Security analysis shows that our scheme is resistant to a series of typical attacks. Compared with the existing schemes, our scheme is more efficient and practical.
Abstract How to efficiently share secrets among multiple participants is a very important problem in key management. In this paper, we propose a multi-secret sharing scheme based on the Greenberger Horne Zeilinger (GHZ) state. First, the distributor uses monotone span program to encode the secrets and generate the corresponding secret shares to send to the participants. Then, each participant uses the generalized Pauli operator to embed its own secret share into the transmitted particle. The participant who wants to get the secrets can get multiple secrets at the same time by performing a GHZ-state joint measurement. Furthermore, since this scheme is based on a monotone span program, its access structure is more general than the access structure (t, n) threshold. Compared with other schemes, our proposed scheme is more efficient, less computational cost.
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.
Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.
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.