Quantum secret sharing is an encryption technique based on quantum mechanics, which utilizes uncertainty principle to achieve security in transmission. Most protocols focus on the study of quantum (n,n) or (t,n) threshold single secret sharing. In this paper, the first quantum (t,n) threshold multi-secret sharing protocol based on Lagrangian interpolation and cluster states is proposed, which requires onlytinstead ofnparticipants to reconstruct multiple quantum secrets. The protocol exploits the security properties of the cluster state to transmit shared information in two parts, quantum and classical, where the shares remain private after reconstructing quantum secrets. Meanwhile, extending the new measurement basis in cluster states enables participants to transmit quantum information without preparing particles. In the presented protocol, the dealer can be offline after sending secrets. And required quantum operations are all common quantum operations, thus the protocol is practical under the current technical conditions. It is proven to be theoretically secure against external and internal attacks by analyzing the protocol under several common external attacks and internal attacks. In addition, experiments on IMB Q prove that the protocol satisfies correctness and feasibility.
Quantum secret sharing is an encryption technique based on quantum mechanics, which utilizes uncertainty principle to achieve security in transmission. Most protocols focus on the study of quantum (n,n) or (t,n) threshold single secret sharing. In this paper, the first quantum (t,n) threshold multi-secret sharing protocol based on Lagrangian interpolation and cluster states is proposed, which requires onlytinstead ofnparticipants to reconstruct multiple quantum secrets. The protocol exploits the security properties of the cluster state to transmit shared information in two parts, quantum and classical, where the shares remain private after reconstructing quantum secrets. Meanwhile, extending the new measurement basis in cluster states enables participants to transmit quantum information without preparing particles. In the presented protocol, the dealer can be offline after sending secrets. And required quantum operations are all common quantum operations, thus the protocol is practical under the current technical conditions. It is proven to be theoretically secure against external and internal attacks by analyzing the protocol under several common external attacks and internal attacks. In addition, experiments on IMB Q prove that the protocol satisfies correctness and feasibility.
Abstract With the rapid development of quantum computing, traditional encryption methods face growing security threats. Quantum Secret Sharing (QSS) has emerged as a promising solution, using quantum principles to improve communication security and prevent internal and external attacks. This study proposes a new (t, n) Threshold Quantum Secret Sharing (TQSS) protocol based on single-qubit unitary operations and Lagrange interpolation. The protocol allows secret reconstruction without third-party or dealer assistance and remains efficient even when some participants are absent. To address more complex real-world scenarios, we extend our previously proposed (t, n) TQSS protocol into a Conditional Dynamic TQSS (CDTQSS). This approach uses resource-based share splitting to allow new participants to join without requiring the dealer to redistribute information. However, the protocol is ‘conditional’ because existing participants must take on extra responsibility-they must assist in generating shares for new members and also participate in the secret reconstruction process together with them. The protocol maintains strong security, reduces resource consumption, and offers better flexibility, making it well-suited for practical and dynamic quantum communication needs.
Abstract In addition to secret splitting, secret reconstruction is another important component of secret sharing. In this paper, the first quantum secret reconstruction protocol is proposed to protect the reconstruction process. Before the protocol, a classical secret is divided into multiple shares that are distributed to the shareholds, respectively. In the presented protocol, the dealer utilizes the secret to encrypt a privacy quantum state, and sends the encrypted state to a combiner who is chosen by the dealer within the shareholders. With the help of other shareholders, the combiner utilizes the properties of cluster states to recover the privacy quantum state. It is shown that the proposed protocol is secure against several common attacks, including external and internal attacks. Compared with classical secret reconstruction protocols, this protocol not only achieves information‐theoretic security of all shares, but is also more efficient due to the reduced distribution and computation cost. To demonstrate the feasibility of the protocol, a corresponding simulation quantum experiment is conducted on the IBM Q. Furthermore, in conjunction with quantum fingerprinting, it can be directly applied to achieve the task of quantum multiple secrets sharing, since the classical shares can be reused in the proposed protocol.
Most (k, n) threshold quantum secret sharing protocols are fully quantum. The message receivers must be equipped with complex quantum devices so as to prepare various quantum resources and perform complex quantum operations, which may affect the practice of these protocols. On the other hand, the qubit efficiency of most (k, n) threshold quantum secret sharing protocols is not more than 1/2. To simplify the (k, n) threshold quantum secret sharing protocol and improve its practice and qubit efficiency, a new (k, n) threshold secret sharing protocol with semi-quantum properties is proposed. In this protocol, the dealer prepares decoy particles and sends them to the receivers. The receivers insert particles carrying secret information along with Z-basis decoy particles into the received particle sequence to generate mixed-particle sequences, which are returned to the dealer. The dealer measures the received particle sequences to check for eavesdropping and establishes shared secret keys with the receivers. With the shared secret keys, the dealer distributes the secret pieces among the receivers using Shamir’s secret sharing scheme. Multiple secret messages can be recovered by k or more receivers. The qubit efficiency of our protocol is k/n. For an (n, n) threshold protocol, the qubit efficiency would be 100%. The proposed scheme is based on single particles without using any entangled system. Therefore, its quantum resources are relatively easy to prepare. Receivers must only prepare simple Z-basis qubits. Its semi-quantum properties enhance practice implementation. The proposed protocol has robust security against various types of attacks, including eavesdropping, internal, and collusion attacks. Furthermore, it can resist the unitary attack, which is seldom analyzed in other protocols.
Abstract The ( t , n ) -threshold schemes offer significant advantages over n , n -threshold schemes due to their flexibility, fault tolerance, and practicality. In this paper, a ( t , n ) -threshold quantum secret-sharing (QSS) and quantum state sharing schemes based on single photons are proposed by incorporating unitary phase shift operations. The proposed scheme employs symmetric bivariate polynomials and utilizes polynomial interpolation for secret sharing. This approach facilitates the secure distribution of classical data and quantum states while maintaining confidentiality and integrity during transmission. Mutual identity authentication between the dealer and participants is ensured, and the accuracy of secret reconstruction is achieved using Lagrange interpolation. The analysis demonstrates that the proposed scheme is resilient against common interception methods, including eavesdropping attacks and participant-driven threats such as entanglement swapping. Additionally, the scheme is characterized by ease of implementation within physical frameworks and adaptability to various applications offering a practical and efficient alternative to existing methods.
Abstract Threshold quantum secret sharing is a cryptography technique for dividing and reconstructing secret information. The dealer shares a secret based on quantum mechanics principles, and a subset of participants cooperate to recover that secret. For example, in k , n quantum threshold scheme and n , n quantum threshold scheme, the former can only reconstruct the secret when at least k shares are collected. The latter requires all n shares to be collected to reconstruct the secret. However, in real scenarios, the priority of participant identities may vary. In order to meet the actual needs of participants with different rights, this paper proposes a w , ω , n quantum secret sharing (QSS) scheme. When the sum of participants’ weights w is greater than or equal to a threshold ω, they can cooperate to reconstruct the secret. In order to achieve this, this paper uses the entangled state of single particles and constructs a verifiable QSS scheme based on the Chinese remainder theorem. Significantly, in case of a dishonest participant, the dealer can delete the participant before recovering the secret to ensure the security of the communication. This scheme is more flexible than other threshold protocols. At the same time, it reduces the communication cost of the participants. In addition, security analysis shows that the scheme resists typical external and internal attacks.
Semi-quantum secret sharing is an important research issue in quantum cryptography. In this paper, we propose a (t, n) threshold semi-quantum secret sharing protocol, which combines the practicality of semi-quantum secret sharing protocols and the flexibility of (t, n) threshold quantum secret sharing protocols. Participants prepare and transmit single particles in a circular way, and then any t out of n participants can recover the secret according to Shamir’s secret sharing scheme. As quantum resources, single particles are easy to prepare. Furthermore, classical participants only need to possess the capability to prepare and insert particles. The security analysis shows our protocol has security against most attacks. Except decoy particles, all particles are useful to carry the secret message, so the efficiency of the proposed protocol can achieve 100%.