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Quantum Information Processing

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01-01-2014

A multiparty error-correcting method for quantum secret sharing

Authors: Rui-Ke Chen, Ying-Ying Zhang, Jian-Hong Shi, Feng-Guang Li

Published in: Quantum Information Processing | Issue 1/2014

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Abstract

Quantum secret sharing (QSS) refers to the process in which the secret is divided into several sub-secrets and sent to different users utilizing quantum technology. Only the user belonging to a specific subset (authorized set) can reconstruct the initial secret correctly. In principle, the authorized set can regain the initial secret exactly via sub-secrets. However, when realizing QSS in practice, because of the interference of various noises, the secret obtained by the authorized set may not be consistent with the initial one. For a particular kind of QSS protocols, in which the bitwise XOR of sub-secrets is equal to the initial secret theoretically, we propose a feasible multiparty error-correcting method based on binary search technique and two-party Cascade error-correcting method. With this method, we can solve the problem that the authorized set cannot regain the initial secret correctly. Finally, we analyze the optimal block length, the amount of leaked information, and realize tripartite error-correcting method by experimental simulation.

previous article Asymmetric “4+2” protocol for quantum key distribution with finite resources

next article One-insider attack of quantum secret sharing protocol with collective eavesdropping-check

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Hillery, M., Buzk, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)MathSciNetCrossRefADS

Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648–651 (1999)CrossRefADS

Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)MathSciNetCrossRefADS

Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162–168 (1999)CrossRefADS

Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum secret splitting and quantum state sharing. Phys. Lett. A 354(3), 190–195 (2006)MathSciNetCrossRefADSMATH

Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)CrossRefADS

Shi, R.H., Huang, L.S., Yang, W., Zhong, H.: Multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 283(11), 2476–2480 (2010)CrossRefADS

Chen, X.B., Niu, X.X., Zhou, X.J., Yang, Y.X.: Multi-party quantum secret sharing with the single-particle quantum state to encode the information. Quantum Inf. Process. 12, 365–380 (2013)MathSciNetCrossRefADSMATH

Dehkordi, M.H., Fattahi, E.: Threshold quantum secret sharing between multiparty and multiparty using Greenberger–Horne–Zeilinger state. Quantum Inf. Process. 12, 1299–1306 (2013)CrossRefADSMATH

10.

Guo, Y., Zhao, Y.Q.: High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis. Quantum Inf. Process. 12, 1125–1139 (2013)MathSciNetCrossRefADSMATH

11.

Hsu, J.L., Chong, S.K., Hwang, T.: Dynamic quantum secret sharing. Quantum Inf. Process. 12, 331–344 (2013)MathSciNetCrossRefADSMATH

12.

Lin, J., Hwang, T.: New circular quantum secret sharing for remote agents. Quantum Inf. Process. 12, 685–697 (2013)MathSciNetCrossRefADSMATH

13.

Shi, R.H., Zhong, H.: Multiparty quantum secret sharing with the pure entangled two-photon states. Quantum Inf. Process. (2012). doi:10.1007/s11128-011-0239-9

14.

Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247–251 (2003)MathSciNetCrossRefADSMATH

15.

Zhang, Z.J., Li, Y., Man, X.Z.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)MathSciNetCrossRefADSMATH

16.

Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78(4), 042309 (2008)MathSciNetCrossRefADSMATH

17.

Keet, A., Forescue, B., Markham, D., Sanders, B.C.: Quantum secret sharing with qudit graph states. Phys. Rev. A 82(6), 062315 (2010)CrossRefADS

18.

Sarvepalli, P.: Nonthreshold quantum secret-sharing schemes in the graph-state formalism. Phys. Rev. A 86(4), 042303 (2012)CrossRefADS

19.

Tittel, W., Zbinden, H., Gisin, N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63, 042301 (2001)CrossRefADS

20.

Chen, Y., Zhang, A.N., Zhao, Z., Zhou, X.Q., Lu, C.Y., Peng, C.Z., Yang, T., Pan, J.W.: Experimental quantum secret sharing and third-man quantum cryptography. Phys. Rev. Lett. 95(20), 200502 (2005)CrossRefADS

21.

Bogdanski, J., Ahrens, J., Bourennane, M.: Sagnac secret sharing over telecom fiber networks. Opt. Express 17(2), 1055–1063 (2009)CrossRefADS

22.

Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. In: Advanced in Cryptology C Proceedings of EUROCRYPT93, Lecture Notes in Computer Science, vol. 765, pp. 410–423 (1994)

23.

Sugimoto, T., Yamazaki, K.: A study on secret key reconciliation protocol “Cascade”. Trans. IEICE E83-A(10), 1987–1991 (2000)

24.

Timothy, C.: An emprical analysis of the Cascade secret key reconciliation protocol for quantum key distribution. Master thesis, Air Force Institute of Technology, Air University, pp. 12–09 (2011)

25.

Buttler, W.T., Lamoreaux, S.K., Torgerson, J.R., Nickel, G.H., Donahue, C.H., Peterson, C.G.: Fast, efficient error reconciliation for quantum cryptography. Phys. Rev. A 67(5), 052303 (2003)CrossRefADS

26.

Zhao, F., Fu, M.X., Wang, F.Q., Lu, Y.Q., Liao, C.J., Liu, S.H. (2007) Error reconciliation for practical quantum cryptography. Optik 118, 502–506

27.

Han, J., Qian, X.: Auto-adaptive interval selection for quantum key distribution. Quantum Inf. Comput. 9(7–8), 693–700 (2009)MathSciNetMATH

28.

Yan, H., Peng, X., Lin, X.X., Jiang, W., Lin, T., Guo, H.: Efficiency of Winnow protocol in secret key reconciliation. In: World Congress on Computer Science and Information Engineering, pp. 238–242 (2009)

29.

Pearson, D.: High-speed QKD reconciliation using forward error correction. In: AIP Conference Proceedings, vol. 734, p. 299 (2004)

30.

Kasai, K., Matsumoto, R., Sakaniwa, K.: Information reconciliation for QKD with rate-compatible non-binary LDPC codes. In: International Symposium on Information Theory and Its Applications, pp. 922–927 (2010)

31.

Elkouss, D., Martinez-Mateo, J., Martin, V.: Information Reconciliation for Quantum Key Distribution. Quantum Inf. Comput. 11, 226–238 (2011)MathSciNetMATH

32.

Martinez-Mateo, J., Elkouss, D., Martin, V.: Blind reconciliation. Quantum Inf. Comput. 12, 791–812 (2012)MATH

33.

Martinez-Mateo, J., Elkouss, D., Martin, V.: Key reconciliation for high performance quantum key distribution. Scientific reports 3, p. 1576 (2013). doi:10.1038/srep01576

Title: A multiparty error-correcting method for quantum secret sharing
Authors: Rui-Ke Chen
Ying-Ying Zhang
Jian-Hong Shi
Feng-Guang Li
Publication date: 01-01-2014
Publisher: Springer US
Published in: Quantum Information Processing / Issue 1/2014
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-013-0716-4

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