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 \(G_{ab}\) 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 \(Z_{d}\) or \(X_{d}\) 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.
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 (G_{ab}) 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 (Z_{d}) or (X_{d}) 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.
Based on the teleportation by quantum walk, a quantum secret sharing scheme with credible authentication is proposed.Using the Hash function and quantum local operation, combined with the two-step quantum walks circuit on the line, the identity authentication and the teleportation of the secret information in distribution phase are realized.Participants collaborate honestly to recover secret information based on particle measurement results, preventing untrusted agents and external attacks from obtaining useful information.Due to the application of quantum walk, the sender does not need to prepare the necessary entangled state in advance, simply encodes the information to be sent in the coin state, and applies the conditional shift operator between the coin space and the position space to produce the entangled state necessary for quantum teleportation.Security analysis shows that the protocol can effectively resist intercept/resend attacks, entanglement attacks, participant attacks, and impersonation attacks.In addition, the quantum walk circuit used has been implemented in many different physical systems and experiments, so this quantum secret sharing scheme may be achievable in the future.
Abstract A dynamic quantum secret sharing protocol with authentication is proposed based on quantum walks. The protocol can share specific secrets and also update the secret information periodically based on the existing quantum walks structure. Participants can be added or removed while keeping the original secret unchanged. This is more flexible in practical applications. Before the secrets are shared, each participant is authenticated to ensure the legitimacy of all participants’ identities. In addition, the protocol uses single photons as quantum resources, avoiding the complex preparation of entangled states, which makes the protocol more advantageous and potential in practical applications. Security analyses show that the protocol is resistant to collusion attack and other common attacks.
Abstract Quantum walks, as the quantum mechanical counterpart of classical random walks, is an advanced tool for constructing quantum algorithms. Quantum secret sharing protocols based on quantum walks reduce the demand for entangled state preparation and simplify the complexity of quantum operations. However, existing quantum secret sharing protocols based on quantum walks have relatively limited functionality. This paper proposes a hierarchical quantum secret sharing protocol based on two-direction quantum walks on a circle and linear homogeneous recurrence relations. In this protocol, the secret distributor first verifies the participants’ identities simultaneously using a symmetric bivariate polynomial, then uses two-particle product states to carry secrets and encrypts them using evolution operators and global shifting operators. Finally, participants who satisfy the hierarchical access structure can simultaneously reconstruct their private classical sequence and quantum state sequence. Correctness analyses demonstrate that qualified participants can accurately obtain and reconstruct the secret information. In terms of security, the protocol can resist both external and internal attacks simultaneously. Lastly, efficiency analysis and comparisons demonstrate that the protocol outperforms other quantum secret sharing protocols based on quantum walks and holds an efficiency advantage.
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.
The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational (Z) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.
Abstract Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography, enabling secure distribution of sensitive information among multiple parties. However, existing protocols often suffer from vulnerabilities such as collusion attacks, uneven share distribution, and protocol failure due to random basis selection. This paper proposes a novel QSS protocol that integrates hash-based measurement basis derivation with decoy photon-enhanced eavesdropping detection. The scheme ensures fair and deterministic secret reconstruction while eliminating the need for entangled states or complex quantum operations, thereby significantly reducing the quantum operational complexity and hardware requirements. The protocol’s correctness, security against both internal and external adversaries, and efficiency in terms of qubit usage, transmission delay, and computational overhead are rigorously analyzed. Notably, the protocol supports dynamic participant management, allowing agents to join or leave securely without re-executing the entire protocol. Comparative analysis demonstrates that the proposed approach outperforms existing QSS protocols across multiple performance metrics. By minimizing quantum resource requirements-such as the elimination of entanglement generation and complex quantum operations-our protocol enhances compatibility with near-term quantum networks, thus facilitating the transition from theoretical QSS models to experimentally feasible implementations.