Advertisement

Quantum Information Processing

, Volume 12, Issue 8, pp 2877–2888 | Cite as

Expansible quantum secret sharing network

  • Ying Sun
  • Sheng-Wei Xu
  • Xiu-Bo Chen
  • Xin-Xin Niu
  • Yi-Xian Yang
Article

Abstract

In the practical applications, member expansion is a usual demand during the development of a secret sharing network. However, there are few consideration and discussion on network expansibility in the existing quantum secret sharing schemes. We propose an expansible quantum secret sharing scheme with relatively simple and economical quantum resources and show how to split and reconstruct the quantum secret among an expansible user group in our scheme. Its trait, no requirement of any agent’s assistant during the process of member expansion, can help to prevent potential menaces of insider cheating. We also give a discussion on the security of this scheme from three aspects.

Keywords

Member expansion Single-particle Quantum secret sharing  Quantum cryptography 

Notes

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant Nos. 61103210, 61272514, 61202451, 61003287, 61170272), the Specialized Research Fund for the Doctoral Program of Higher Education (20100005120002), the Fok Ying Tong Education Foundation (No. 131067) and the Fundamental Research Funds for the Central Universities (Grant Nos. YZDJ1103, YZDJ1102, BUPT2012RC0221).

References

  1. 1.
    Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of National Computer Conference, pp. 313–317. AFIPS, New York (1979)Google Scholar
  2. 2.
    Shamir, A.: How to share a secret. Commun. ACM 22, 612 (1979)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Bandyopadhyay, S.: Teleportation and secret sharing with pure entangled states. Phys. Rev. A 62, 012308 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Tittel, W., Zbinden, H., Gisin, N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63, 042301 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Guo, G.-P., Guo, G.-C.: Quantum secret sharing without entanglement. Phys. Lett. A 310, 247–251 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Zhang, Z.J., Yang, J., Man, Z.X., Li, Y.: Multiparty secret sharing of quantum information using and identifying Bell states. Eur. Phys. J. D 33, 133–136 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Deng, F.-G., Li, X.-H., Li, C.-Y., Zhou, P., Zhou, H.-Y.: Multiparty quantum state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs. Phys. Rev. A 72, 044301 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Deng, F.-G., Li, X.-H., Li, C.-Y., Zhou, P., Zhou, H.-Y.: Quantum state sharing of an arbitrary two-qubit state with two-photon entanglements and Bell-state measurements. Eur. Phys. J. D 39, 459–464 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    Gordon, G., Rigolin, G.: Generalized quantum-state sharing. Phys. Rev. A 73, 062316 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    Zheng, S.B.: Splitting quantum information via W states. Phys. Rev. A 74, 054303 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    Bogdanski, J., Rafiei, N., Bourennane, M.: Experimental quantum secret sharing using telecommunication fiber. Phys. Rev. A 78, 062307 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Yu, I.-C., Lin, F.-L., Huang, C.-Y.: Quantum secret sharing with multilevel mutually (un)biased bases. Phys. Rev. A 78, 012344 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    Sun, Y., Wen, Q-y, Gao, F., Chen, X-b, Zhu, F-c: Multiparty quantum secret sharing based on Bell measurement. Opt. Commun. 282, 3647–3651 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    Choudhury, S., Muralidharan, S., Panigrahi, P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42, 115303 (2009)MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Sarvepalli, P., Raussendorf, R.: Matroids and quantum-secret-sharing schemes. Phys. Rev. A 81, 052333 (2010)MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Li, Q., Chan, W.H., Long, D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82, 022303 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Wang, T.-Y., Wen, Q.-Y.: Security of a kind of quantum secret sharing with single photons. Quantum Inf. Comput. 11, 434–443 (2011)MathSciNetMATHGoogle Scholar
  24. 24.
    Yang, Y.G., Wang, Y., Chai, H.P., et al.: Member expansion in quantum (\(t, n\)) threshold secret sharing schemes. Opt. Commun. 284, 3479–3482 (2011)Google Scholar
  25. 25.
    Jia, H.Y., Wen, Q.Y., Gao, F., et al.: Dynamic quantum secret sharing. Phys. Lett. A 376, 1035–1041 (2012)MathSciNetADSMATHCrossRefGoogle Scholar
  26. 26.
    Hsu, J.-L., Chong, S.-K., Hwang, T., Tsai, C.-W.: Dynamic quantum secret sharing. Quantum Inf. Process. Publish online: (04 March 2012)Google Scholar
  27. 27.
    Pan, G.X., Liu, Y.M., Zhang, Z.J.: Classical communication and entanglement cost in preparing a class of multi-qubit states. Commun. Theor. Phys. 49, 631–634 (2008)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Liu, Y.M., Wang, Z.Y., Liu, X.S., Zhang, Z.J.: Symmetric and probabilistic multiparty remote state preparation via the positive-operator-valued measure. Int. J. Quantum Inf. 7, 991 (2009)MATHCrossRefGoogle Scholar
  29. 29.
    Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.J.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 044302 (2005)Google Scholar
  30. 30.
    Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: A simple participant attack on the brádler-dušek protocol. Quantum Inf. Comput. 7, 329–334 (2007)Google Scholar
  31. 31.
    Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179. Bangalore, India (1984)Google Scholar
  32. 32.
    Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)ADSCrossRefGoogle Scholar
  33. 33.
    Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    Stinespring, W.F., Am, P.: Positive functions on C\(^{*}\)-algebras. Math. Soc. 6, 211–216 (1955)Google Scholar
  35. 35.
    Ioffe, L., Mézard, M.: Asymmetric quantum error correcting codes. Phys. Rev. A 75, 86–90 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ying Sun
    • 1
  • Sheng-Wei Xu
    • 1
  • Xiu-Bo Chen
    • 2
  • Xin-Xin Niu
    • 2
  • Yi-Xian Yang
    • 2
  1. 1.Beijing Electronic Science and Technology InstituteBeijingChina
  2. 2.Information Security CenterBeijing University of Posts and TelecommunicationsBeijingChina

Personalised recommendations