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.
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.
Abstract Most of Quantum Secret Sharing(QSS) are (n, n) threshold 2-level schemes, in which the 2-level secret cannot be reconstructed until all n shares are collected. In this paper, we propose a (t, n) threshold d-level QSS scheme, in which the d-level secret can be reconstructed only if at least t shares are collected. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability. Moreover, in this scheme, any one of the participants does not know the other participants’ shares, even the trusted reconstructor Bob1 is no exception. The transformation of the particles includes some simple operations such as d-level CNOT, Quantum Fourier Transform(QFT), Inverse Quantum Fourier Transform(IQFT), and generalized Pauli operator. The transformed particles need not to be transmitted from one participant to another in the quantum channel. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack. Performance comparison shows that it has lower computation and communication costs than other similar schemes when 2 < t < n − 1.
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 (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 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.
Quantum secret sharing (QSS) is a cryptographic protocol that utilizes fundamental principles of quantum mechanics to securely distribute and reconstruct secret information among multiple participants. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications. The preparation of entangled state is constrained by a short quantum coherence time, low state fidelity, etc., which makes it difficult to implement entangled resource-dependent QSS protocols. In this work, a novel practical and verifiable multi-party QSS protocol is proposed based on orthogonal product states, which are easier to prepare than entangled states. During the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into the corresponding orthogonal product states according to the encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD), which is used to hide the initial quantum sequence information through subsequent particle transformation operations. After preparing the orthogonal product states, the distributor reorganizes the particles by position, extracting particles at the same position from each state to form new sequences, shuffling their order, then applying Hadamard operations using a pre-shared key, inserting decoy particles, and sending the sequences to the participants. After receiving it, participants conduct eavesdropping detection, use the same key for the inverse transformations, retain one particle from each sequence, and sequentially pass the remaining particles until the last participant receives a complete set, triggering state verification with the arbiter distributor. If the verification is successful, the particles will be returned to the first participant and the return stage will follow the same procedure. Only after both the transmission and return stage verifications have passed, will the distributor reveal the initial particle positions, allowing participants to collaboratively reconstruct the secret. In the protocol, the secret distributor acts as an arbitrator to verify the particle state information together with participants at designated points (the end of the transmission stage and the end of the return stage) in order to determine whether the particle-state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering that the number of participants may change during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, It can be proven that our protocol can effectively resist the existing common attack. Using Qiskit simulation experiments, the core quantum procedures of the protocol can be successfully modeled. The experimental results provide strong computational validation of the theoretical feasibility of the protocol.
In quantum cryptography, quantum secret sharing (QSS) is a fundamental primitive. QSS can be used to create complex and secure multiparty quantum protocols. Existing QSS protocols are either at the (n,n) threshold 2 level or at the (t,n) threshold d level with a trusted player, where n denotes the number of players and t denotes the threshold number of players. Here, we propose a secure d-level QSS protocol for sharing a secret with efficient simulation. This protocol is more secure, flexible, and practical as compared to the existing QSS protocols: (n,n) threshold 2-level and (t,n) threshold d-level with a trusted player. Further, it does not disclose any information about the secret to players. Its security analysis shows that the intercept-resend, intercept, entangle-measure, forgery, collision and collusion attacks are not possible in this protocol.