The improvement and extension of quantum secret sharing (QSS) using orthogonal product states (OPS) are studied in this paper. Based on such three typical schemes, a quantitative analysis on security is provided. The paper also discusses the simplification measures and their effect on security, and then the possibility to extend is proved. Finally, several conclusions about the methods to improve the security, simplify the schemes and extend to one-to-many situation are given.
The improvement and extension of quantum secret sharing (QSS) using orthogonal product states (OPS) are studied in this paper. Based on such three typical schemes, a quantitative analysis on security is provided. The paper also discusses the simplification measures and their effect on security, and then the possibility to extend is proved. Finally, several conclusions about the methods to improve the security, simplify the schemes and extend to one-to-many situation are given.
Based on an orthogonal set of product states of two three-state particles, a new quantum secret sharing scheme is proposed, which uses a novel distribution strategy so that continuous and independent measurements, rather than particle-wise coordinated ones, are performed. As a result, it is convenient and efficient to implement. The scheme is also secure against several common attacks and gets rid of partial-information leakage due to the revised coding method. Moreover, the quantitative analysis shows that the security can be further improved by using more product states from appropriate multiple sets.
We propose an efficient quantum secret sharing scheme with orthogonal product states in the 3×3 Hilbert space. Different from Hsu and Li's scheme [Phys. Rev. A 71, 022321 (2005)], this scheme utilizes a novel distribution strategy which sends the qutrits of basis states and superpositions to two separated observers respectively. The theoretical analysis shows that the intrinsic efficiency for qutrits in this scheme approaches 100% and the total efficiency of this scheme is higher than that of the aforementioned scheme. Furthermore, the security and some possible eavesdropping strategies are also examined in this paper.
Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.
Quantum secret sharing (QSS) protocols without entanglement have showed high security by virtue of the characteristics of quantum mechanics. However, it is still a challenge to compare the security of such protocols depending on quantitative security analysis. Based on our previous security analysis work on protocols using single qubits and two-level unitary operations, QSS protocols with single qutrits and three-level unitary operations are considered in this paper. Under the Bell-state attack we propose, the quantitative security analyses according to different three-level unitary operations are provided respectively in the one-step and two-step situations. Finally, important conclusions are drawn for designing and implementing such QSS protocols. The method and results may also contribute to analyze the security of other high-level quantum cryptography schemes based on unitary operations.
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.
As an important branch of quantum secure multi-party computation, quantum secret sharing (QSS) can distribute secret information among dishonest network nodes without revealing the secrets. In this study, a new four-party QSS protocol based on locally indistinguishable orthogonal product (LIOP) states is first proposed for quantum network communication. Then, the general multiparty QSS model based on LIOP states will be expanded. Combined with the property of LIOP states and obfuscating operation, the source node can send the secrets to different destination nodes in the quantum network. Accordingly, it is proven that the destination nodes have to work together to recover the shared secrets against some existing attacks. Furthermore, no entangled resources and complicated operations are required in the presented protocol. We hope the results could make positive effects to the development of quantum secure communication in the future.