Verifiable secret sharing schemes are important in cloud computing environments. Thus a key can be distributed over many servers by threshold secret sharing mechanism. The key is then reconstructed when needed. Secret sharing has also been suggested for sensor networks where the links are liable to be tapped by sending the data in shares which makes the task of the eavesdropper harder. The security in such environments can be made greater by continuous changing of the way the shares are constructed. In the present paper we proposed a verifiable quantum -threshold secret sharing scheme using Lagrange interpolation and two qudit Bell state in -dimensional Hilbert space. As discussed in the second last section of this paper, the proposed scheme is enough secure against the fraud in secret share distribution phase as well as secret reconstruction phase.
Verifiable secret sharing schemes are important in cloud computing environments. Thus a key can be distributed over many servers by threshold secret sharing mechanism. The key is then reconstructed when needed. Secret sharing has also been suggested for sensor networks where the links are liable to be tapped by sending the data in shares which makes the task of the eavesdropper harder. The security in such environments can be made greater by continuous changing of the way the shares are constructed. In the present paper we proposed a verifiable quantum -threshold secret sharing scheme using Lagrange interpolation and two qudit Bell state in -dimensional Hilbert space. As discussed in the second last section of this paper, the proposed scheme is enough secure against the fraud in secret share distribution phase as well as secret reconstruction phase.
Abstract Secret sharing, as an important cryptographic technique, effectively reduces the risk of single points of failure and centralized leakage by distributing secret information across multiple independent entities. With the widespread application of cloud computing and cloud storage, achieving long-term secure storage and controllable recovery of sensitive data in untrusted cloud environments has become a critical issue. Traditional cloud storage solutions face potential risks of security degradation and privacy exposure under long-term operation and future quantum computing threats. This paper proposes a quantum secret sharing (QSS) scheme for cloud storage scenarios, combining the threshold secret sharing with quantum secure communication and quantum information processing to achieve distributed storage and secure reconstruction of secret information across multiple cloud servers. A quantum identity authentication mechanism is introduced to the authenticated user based on a quantum sequence. This protocol enhances the long-term security of the system during the storage phase through threshold distribution and proactive share refreshing mechanisms, and utilizes quantum states to complete the secure reconstruction of secrets during the recovery phase. Additionally, this scheme avoids direct interaction between cloud servers, improving the security in untrusted cloud environments. Security analysis shows that this protocol can effectively resist threats such as external eavesdropping and internal collusion.
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 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.
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.
A verifiable (t, n) threshold quantum secret sharing scheme with sequential communication was proposed recently. In this work, we analyze its security and then give two new participant attacks. Using the first participant attack, the first participant can obtain the dealer's secrets by himself with nonzero probability without being detected. Using the second participant attack, a dishonest participant can gain access to the dealer's secrets by himself in the secret reconstruction phase while he can make the other participants recover false secrets instead of the real ones without being detected. Furthermore, we present an effective way to prevent these attacks.
Abstract Threshold quantum secret sharing is a typical method for quantum secret sharing (QSS) schemes. In this paper, we propose a verifiable t , n threshold QSS scheme based on the d -dimensional Bell state and asymmetric binary polynomial. In this scheme, the dealer encodes the secret using the asymmetric binary polynomial and generates the corresponding secret share for each participant. Then, the dealer prepares the d -dimensional Bell state, and the participants perform corresponding unitary operations on the particles in transmission to recover the secret. With the hash function and the session key pairs, not only the cheating behavior of the dishonest participants can be detected, but also the specific cheaters can be identified. Furthermore, we consider the case when no less than t participants cooperate to recover the secret, which makes the proposed scheme more practical. Analyses show that the scheme can resist forgery attack, collusion attack and other common attacks.