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.
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 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 Quantum secret sharing aims to securely distribute private information among multiple participants, such that only authorized subsets can collaboratively reconstruct the secret. However, current research remains largely exploratory, and most existing protocols are limited to sharing low‐dimensional quantum states and lack hierarchical capabilities. To overcome these limitations, we propose a novel hierarchical quantum secret sharing protocol with identity authentication. Specifically, we construct ‐dimensional disentangler and isometric transformation operations. These are applied to compress arbitrary ‐dimensional entangled states, with each compression corresponding to one hierarchical level. For a given hierarchical participant structure, the entangled particles of the compressed states are allocated as secret shares among the participants. Authorized participants within the same level collaboratively reconstruct the original quantum state using the conjugate transposes of disentangler operations and isometric transformations. Security analysis confirms the protocols resilience against common attacks, including intercept‐resend, entangle‐measure, and dishonest participant attacks. Compared with existing similar protocols, our scheme demonstrates superior performance in terms of quantum efficiency and other metrics.
Abstract Quantum secret sharing plays an essential role in quantum cryptography. This paper proposes a dynamic hierarchical quantum multi-secret sharing scheme based on linear homogeneous recurrence (LHR) relations. In the scheme, the distributor aggregates multiple secrets into a single master secret using the Chinese Remainder theorem (CRT), and then implements a special hierarchical structure based on LHR relations, generating corresponding shares for the participants. Participants use the generalized Pauli operators to encode their shares into the quantum state to reconstruct multiple secrets. During the transmission of the quantum state, participants can authenticate each other, thereby enhancing the security of the communication process. Additionally, the proposed scheme is dynamic, allowing for the dynamic update of the participants’ set. Security analysis demonstrates that the scheme can resist measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, forgery attacks, collusion attacks, as well as revoked or downgraded participant attacks.
This paper presents a novel quantum secure multi-party summation protocol based on one-direction quantum walks on a circle (ODQWC), which allows the summation computation of different integer sequences from “n” secret holders. Crucially, it ensures that this process does not infringe on the privacy of these secret holders by delivering quantum walk states in a circular pattern. Our proposed protocol employs two-particle product states rather than quantum entangled states as the initial quantum resource and eliminates the need for different secret holders to perform quantum entanglement swapping operations. Instead, it emphasizes imposing one-direction evolution operators on quantum walk states. Additionally, our protocol requires single-particle measurements. Security analysis validates that our proposed protocol can effectively counter external attacks and those initiated by participants. Under specific conditions, our proposed protocol can be adapted into a quantum secure multi-party bit summation protocol based on ODQWC.
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.