Secret sharing is a cryptographic primitive which plays a central role in various tasks including secure multi-party computation and key management. Quantum schemes for secret sharing commonly rely on multi-particle entangled quantum states, which remains challenging with current experimental technologies. Firstly, in this paper we present a (t,n) quantum secret sharing scheme based on quantum walks on a circle, which only involves two-particle product states as the initial quantum resource. When recovering the secrets, it requires at least t participants sequentially completing their operations on the communicated state, while less than t participants can not acquire any information about the secrets. Secondly, a verification mechanism is designed, which can detect cheats with an asymptotic probability 100%. Finally, we show that the scheme is perfectly correct and is secure against common attacks including collusion attack. In conclusion, the proposed scheme will be useful for quantum communication networks due to its inherent scalability, flexibility and information-theoretical security.
Secret sharing is a cryptographic primitive which plays a central role in various tasks including secure multi-party computation and key management. Quantum schemes for secret sharing commonly rely on multi-particle entangled quantum states, which remains challenging with current experimental technologies. Firstly, in this paper we present a (t,n) quantum secret sharing scheme based on quantum walks on a circle, which only involves two-particle product states as the initial quantum resource. When recovering the secrets, it requires at least t participants sequentially completing their operations on the communicated state, while less than t participants can not acquire any information about the secrets. Secondly, a verification mechanism is designed, which can detect cheats with an asymptotic probability 100%. Finally, we show that the scheme is perfectly correct and is secure against common attacks including collusion attack. In conclusion, the proposed scheme will be useful for quantum communication networks due to its inherent scalability, flexibility and information-theoretical 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 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.
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 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.
A verifiable (t, n) threshold quantum secret sharing scheme with sequential communication was proposed recently. In this work, we analyze its security and then give two new participant attacks. Using the first participant attack, the first participant can obtain the dealer's secrets by himself with nonzero probability without being detected. Using the second participant attack, a dishonest participant can gain access to the dealer's secrets by himself in the secret reconstruction phase while he can make the other participants recover false secrets instead of the real ones without being detected. Furthermore, we present an effective way to prevent these 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.