基于量子图态的量子秘密共享

Quantum secret sharing with quantum graph states

本文基于量子图态的几何结构特征,利用生成矩阵分割法,提出了一种量子秘密共享方案.利用量子图态基本物理性质中的稳定子实现信息转移的模式、秘密信息的可扩展性以及新型的组恢复协议,为安全的秘密共享协议提供了多重保障.更重要的是,方案针对生成矩阵的循环周期问题和因某些元素不存在本原元而不能构造生成矩阵的问题提出了有效的解决方案.在该方案中,利用经典信息与量子信息的对应关系提取经典信息,分发者根据矩阵分割理论获得子秘密集,然后将子秘密通过酉操作编码到量子图态中,并分发给参与者,最后依据该文提出的组恢复协议及图态相关理论得到秘密信息.理论分析表明,该方案具有较好的安全性及信息的可扩展性,适用于量子网络通信中的秘密共享,保护秘密数据并防止泄露.

Quantum secret sharing is an important way to achieve secure communications, which has critical applications in the field of information security for its physical properties. According to the perspective of the practical applications, improving the confidentiality and integrity of secret sharing schemes is a good method to increase the security and reliability of communications. In this paper, we propose a quantum secret sharing scheme based on generator matrix segmentation and the structural features of quantum graph states. The security of the secure secret sharing scheme is guaranteed by the pattern of transferring information by stabilizers, scalability of the information and new recovery strategy provided by the entanglement of the related graph states. It puts forward an effective solution to the problem of matrix cycle period, where some numbers without the primitive element cannot construct the generation matrix. First of all, the physical properties of quantum bits （qubits）, such as uncertainty principle, no-cloning theorem and indistinguishability, not only optimize the classical schemes but also ensure the absolute safety of communication. Secondly, the application of matrix segmentation makes secret information has better scalability. It improves the coding diversity and the di？culty in deciphering. Thirdly, the favorable entanglement properties and mature experiment preparation techniques of graph states provide an approach to the practical applications. The superiority of the yielded graph states is described in graphical fashion with an elegant stabilizer. Fourthly, the shu？ing operation can ensure the independence of the message among participants. Therefore, Eve can not obtain any useful information by measuring randomly. Two group-recovery protocols are proposed to show the secret recovering processing through rebuilding sub-secrets among legal cooperative participants. In the scheme design, the dealer extracts the classical secret information according to the corresponding principle between the classical and quantum information, and divides the classical secret through generated matrix which is produced with the primitive elements in finite domain satisfying the linear independence for any k column vectors. Then the dealer encodes information into graph states and distributes particles to the legal participants with unitary operations. Subsequently, the credible center obtains sub-secrets by the theory of graph states and the group recovery protocol. He can achieve the initial classical secret via the inverse algorithm of matrix segmentation. After getting the classical secret, he recovers quantum secret according to the relationship between classical information and quantum information. Theoretical analysis shows that this scheme can provide better security and scalability of the information. It is appropriate to realize the secret sharing in the quantum network communication to protect secrets from eavesdropping. Also, it can provide an approach to designing diverse and scalable quantum secure communication schemes based on quantum graph states, the algorithm of matrix segmentation, and group-recovery protocol.