Abstract Numerous high-quality quantum secret sharing (QSS) protocols have been proposed as integral components of quantum cryptography. However, only a limited number effectively integrate both dynamic and verifiable characteristics. This paper proposes a verifiable dynamic (t, n) QSS protocol based on the asymmetric binary polynomial and the d-dimensional Bell states. In the protocol, the dealer can find out the internal fraudsters by verifying whether an agent has used a correct share. The agents can also verify the correctness of the shares provided by the dealer. Besides, the dealer has the capability to independently adding or revoking of agents without requiring assistance from other agents. Furthermore, the protocol requires at least t agents to recover the secret, which makes the proposed protocol more flexible and practical than existing protocols. Our protocol shows good robustness against the intercept-and-resend, the entangle-and-measure, the internal, and the dishonest revoked agent attacks.
Abstract Numerous high-quality quantum secret sharing (QSS) protocols have been proposed as integral components of quantum cryptography. However, only a limited number effectively integrate both dynamic and verifiable characteristics. This paper proposes a verifiable dynamic (t, n) QSS protocol based on the asymmetric binary polynomial and the d-dimensional Bell states. In the protocol, the dealer can find out the internal fraudsters by verifying whether an agent has used a correct share. The agents can also verify the correctness of the shares provided by the dealer. Besides, the dealer has the capability to independently adding or revoking of agents without requiring assistance from other agents. Furthermore, the protocol requires at least t agents to recover the secret, which makes the proposed protocol more flexible and practical than existing protocols. Our protocol shows good robustness against the intercept-and-resend, the entangle-and-measure, the internal, and the dishonest revoked agent 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.
Quantum secret sharing occupies an important position in quantum cryptography. In this document, a dynamic (t, n) threshold quantum secret sharing scheme is proposed based on homogeneous LFSR sequences and d-dimensional Bell states. The secret shared among agents in this scheme is determined by the distributor and the scheme enables the update of agents without the help of other agents. More, this paper considers the case when no less than t agents cooperate in secret reconstruction, which makes the proposed scheme more flexible and practical than the existing ones. Finally, our scheme is not only resistant to eavesdropping, collusion, dishonest revoked agent, and in-attacker’s cheating attacks, but also agents can verify for themselves that the shared secrets are correct.
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 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.
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 ( t , n ) -threshold quantum secret sharing (QSS) offers greater flexibility than ( n , n ) schemes. However, conventional ( t , n ) protocols require a complete restart of the quantum communication procedure for each new round, causing quantum resource consumption and transmission costs to grow linearly with the number of rounds. By exploiting the reusability of coin particles in discrete-time quantum walks (QWs), this paper proposes a multi-round ( t, n )—threshold QSS protocol. The protocol requires quantum transmission only in the first round to establish the QW structure; all subsequent rounds of secret message delivery proceed without occupying the quantum channel. The coin particles remain unmeasured and are cyclically reused across rounds, while only the position particles need to be refreshed. Regarding correctness, a rigorous proof of multi-round decoding based on state-vector evolution and mathematical induction is provided. Performance analysis shows that the number of quantum transmissions in the proposed protocol is independent of the number of sharing rounds, freeing multi-round sharing from the constraint of quantum-channel maintenance costs. In addition, the protocol employs only single photons, avoiding the preparation of complex entangled states, and integrates dual verification for both identity authentication and secret correctness, effectively resisting typical attacks such as intercept-resend, forgery, and internal collusion. The protocol provides a new approach toward low-cost and practical multi-round QSS.