Abstract In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the ℂ d ⊗ ℂ d framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a (t,n)-threshold architecture, a strategic choice that augments the protocol’s practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.
Abstract In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the ℂ d ⊗ ℂ d framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a (t,n)-threshold architecture, a strategic choice that augments the protocol’s practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.
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.
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.
A verifiable quantum secret sharing protocol using quantum walks on a lattice is proposed in this paper. The protocol utilizes generalized Bell states as the initial quantum resource, integrating the quantum walk evolution operator U with the global shift operator Gab to facilitate joint encrypted transmission among multiple participants. A bidirectional identity authentication mechanism based on hash functions is introduced to ensure the legitimacy of all communication parties, which effectively resists impersonation attacks. Random decoy particles are randomly prepared in either the Zd or Xd basis and inserted into the transmission sequence, enabling real-time eavesdropping detection on the quantum channel. In the secret reconstruction phase, a public verification mechanism is designed to allow participants to verify the correctness of the recovered secret and identify internal dishonest behaviors. Security analysis demonstrates that the protocol achieves information-theoretic security, resisting typical external attacks such as intercept-resend, measure-resend, and entangle-measure attacks, as well as collusion attacks from dishonest internal participants. Compared with existing quantum-walk-based secret sharing schemes, the proposed protocol maintains high qubit efficiency while supporting both identity authentication and public verifiability, thus possessing stronger practicality and security.
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 fundamental primitive in quantum cryptography. The existing QSS protocols are either [Formula: see text]-threshold or [Formula: see text]-threshold access structure, where [Formula: see text] denotes the number of players and [Formula: see text] denotes the threshold number of players. Here, we introduce a novel verifiable QSS scheme that executes a restricted hyperstar access structure by using entangled states. Our method involves encoding selected quantum states and their corresponding measurements to yield outcomes of either [Formula: see text] or [Formula: see text]. Furthermore, we give the validation of the scheme through the system of equations derived from the measurements, which then guarantees the honesty of the participants. At last, we also analyze the security of our scheme in two primary quantum attacks, such as external attacks and internal attacks.