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 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.
With the rise of quantum computing, traditional cryptography is facing serious threats. Secret sharing, as an important primitive of cryptography, is also affected. Because secret sharing is widely used in many fields, researchers have started to explore quantum secret sharing (QSS). QSS uses basic principles of quantum mechanics to provide strong security and can protect against both eavesdropping and malicious attacks. However, most existing QSS studies focus on specific situations and lack the flexibility needed for complex multiparty environments. In this work, we propose a general QSS framework that can be applied to different scenarios. We first design a basic [Formula: see text] QSS protocol, and then extend it to support multiparty communication and dynamic changes in participants. Our security analysis shows that the proposed method keeps strong security, uses fewer resources, and works independently without the need for a trusted third party (TP). This protocol offers a unified solution that can meet different application needs and provides a new approach to handling diverse QSS tasks more efficiently.
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 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 Quantum secret sharing (QSS) plays a crucial role in quantum cryptography as a privacy preserving scheme. Designing an efficient QSS protocol requires addressing three key challenges: 1) dynamic agent membership (handling agents joining or leaving during execution), 2) adversarial resilience (ensuring robustness against dishonest agents), and 3) practical optimization (improving computational and communication efficiency while minimizing implementation cost). In this paper, a verifiable dynamic threshold QSS (VDQSS) protocol with authentication capability is proposed. The protocol employs single particles for both authentication and share distribution, combining homogeneous linear recursion (HLR) with mutually unbiased bases (MUBs) to reconstruct multiple secrets. This approach significantly enhances security while reducing protocol complexity. The correctness and practicality of the protocol are validated through experimental simulations. Analytical results demonstrate its robustness against common attacks, providing reliable security guarantees for quantum communications. Compared to existing QSS protocols, the protocol offers enhanced simplicity and practical applicability.
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 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.