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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 difficulty 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 shuffling 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.
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Keywords:
- quantum secret sharing /
- graph states /
- generated matrix /
- group-recovery protocol
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[1] Shamir A 1979 Commun. ACM 22 612
[2] Feng L J, Zhang Y J, Zhang L, Xia Y J 2015 Chin. Phys. B 24 103
[3] Zhou N R, Cheng H L, Tao X Y, Gong L H 2014 Quantum Inf. Process. 13 513
[4] Tang S Q, Yuan J B, Wang X W, Kuang L M 2015 Chin. Phys. Lett. 32 040303
[5] Gong L H, Song H C, He C S, Liu Y, Zhou N R 2014 Phys. Scr. 89 240
[6] Sun W, Yin H L, Sun X X, Chen T Y 2016 Acta Phys. Sin. 65 080301 (in Chinese) [孙伟, 尹华磊, 孙祥祥, 陈腾云 2016 物理学报 65 080301]
[7] Gong L H, Liu Y, Zhou N R 2013 Int. J. Theor. Phys. 52 3260
[8] Guo Y, Zhao Y 2013 Quantum Inf. Process. 12 1125
[9] Gao G 2014 Int. J. Theor. Phys. 53 2231
[10] Li Y X, Wang X M 1993 J. Commun. 14 22 (in Chinese)[李元兴, 王新梅1993 通信学报14 22]
[11] Mei T, Dai Q, Zhang M 2008 Commun. Tech. 11 288(in Chinese) [梅挺, 代群, 张明2008 通信技术11 288]
[12] Song Y, Li Z H, Li Y M 2013 Acta Electr. Sin. 02 220(in Chinese) [宋云, 李志慧, 李永明2013 电子学报02 220]
[13] Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910
[14] Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188
[15] Looi S Y, Li Y, Gheorghiu V, Griffiths R B 2008 Phys. Rev. A 78 042303
[16] Nielsen M A 2004 Phys. Rev. Lett. 93 040503
[17] Kiesel N, Schmid C, Weber U, Tóth G, Ghne O, Ursin R, Weinfurter H 2005 Phys. Rev. Lett. 95 210502
[18] Leibfried D, Knill E, Seidelin S, Britton J, Blakestad R B, Chiaverini J, Hume D B, Itano W M, Jost J D, Langer C, Ozeri R, Reichle R, Wineland D J 2005 Nature 438 639
[19] Keet A, Fortescue B, Markham D, Sander B C 2010 Phys. Rev. A 82 062315
[20] Bartlett S D, de Guise H, Sanders B C 2002 Phys. Rev. A 65 052316
[21] Markham D, Sanders B C 2008 Phys. Rev. A 78 042309
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