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Quantum direct secret sharing with efficient eavesdropping-check and authentication based on distributed fountain codes

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Abstract

We propose to use a simple and effective way to achieve secure quantum direct secret sharing. The proposed scheme uses the properties of fountain codes to allow a realization of the physical conditions necessary for the implementation of no-cloning principle for eavesdropping-check and authentication. In our scheme, to achieve a variety of security purposes, nonorthogonal state particles are inserted in the transmitted sequence carrying the secret shares to disorder it. However, the positions of the inserted nonorthogonal state particles are not announced directly, but are obtained by sending degrees and positions of a sequence that are pre-shared between Alice and each Bob. Moreover, they can confirm that whether there exists an eavesdropper without exchanging classical messages. Most importantly, without knowing the positions of the inserted nonorthogonal state particles and the sequence constituted by the first particles from every EPR pair, the proposed scheme is shown to be secure.

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References

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

    Article  MathSciNet  ADS  Google Scholar 

  2. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of National Computer Conference, vol. 48, pp. 313–317. AFI-PS Press, Montvale, NJ (1979)

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Deng, F.G., Zhou, H.Y., Long, G.L.: Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys. Lett. A. 337, 329–334 (2005)

    Article  ADS  MATH  Google Scholar 

  7. Deng, F.G., Long, G.L., Zhou, H.Y.: An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs. Phys. Lett. A. 340, 43–50 (2005)

    Article  ADS  MATH  Google Scholar 

  8. Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A Math Gen. 39, 14089–14099 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hao, L., Li, J.L., Long, G.L.: Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci China. Phys. Mech. Astron. 53(3), 491–495 (2010)

    Article  ADS  Google Scholar 

  10. Rupert, U., Richard, H.: Quantum information: Sharing quantum secrets. Nature. 501, 37 (2013)

    Article  Google Scholar 

  11. Lin, Q., Chan, W.H., Long, D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A. 82, 022303–022308 (2010)

    Article  ADS  Google Scholar 

  12. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A. 61, 042311–042318 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  13. Song, S.Y., Wang, C.: Recent development in quantum communication. Chin. Sci. Bull. 57(36), 4694–4700 (2012)

    Article  Google Scholar 

  14. Tsai, C.W., Hwang, T.: Multiparty quantum secret sharing based on two special entangled states. Sci China Phys. Mech. Astron. 3, 460–464 (2012)

    Article  ADS  Google Scholar 

  15. Massoud, H.D., Elham, F.: A novel and efficient multiparty quantum secret sharing scheme using entangled states. Sci China Phys. Mech. Astron. 55(10), 1828–1831 (2012)

    Article  ADS  Google Scholar 

  16. Jiang, M., Huang, X., Zhou, L.L., Zhou, Y.M., Zeng, J.: An efficient scheme for multi-party quantum state sharing via non-maximally entangled states. Chin. Sci. Bull. 57(10), 1089–1094 (2012)

    Article  Google Scholar 

  17. Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A. 71, 044301–044306 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A. 72, 022303–022306 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  19. Zhang, Z.J.: Multiparty secret sharing of quantum information via cavity QED. Opt. Commun. 261, 199–202 (2006)

    Article  ADS  Google Scholar 

  20. Zhang, Z.J.: Multiparty quantum secret sharing based on the improved Boström-Felbinger protocol. Opt. Commun. 269, 418–422 (2007)

    Article  ADS  Google Scholar 

  21. Zhang, Z.J.: Multiparty quantum secret sharing scheme of classical messages by swapping qudit-state entanglement. Int. J. Mod. Phys. C. 18, 1885–1901 (2007)

    Article  ADS  MATH  Google Scholar 

  22. Hao, L., Wang, C., Long, G.L.: Quantum secret sharing protocol with four state Grover algorithm and its proof-of-principle experimental demonstration. Opt. Commun. 284, 3639–3642 (2011)

    Article  ADS  Google Scholar 

  23. Wei, K.J., Ma, H.Q., Yang, J.H.: Experimental circular quantum secret sharing over telecom fiber network. Opt. Express 21, 16664–16669 (2013)

    ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Anderson, C.A.N., Joern, M.Q., Hideki, I.: Improving quantum secret sharing schemes. Phys. Rev. A. 64, 042311–042315 (2001)

    Article  Google Scholar 

  26. Gheorghiu, V.: Generalized semiquantum secret sharing schemes. Phys. Rev. A. 85, 052309–052319 (2012)

    Article  ADS  Google Scholar 

  27. Fortescue, B., Gour, G.: Reducing the quantum communication cost of quantum secret sharing. IEEE Trans. Inf. Theory 58(10), 6659–6666 (2012)

    Google Scholar 

  28. Sarvepalli, P., Raussendorf, R.: Matroids and quantum-secret-sharing scheme. Phys. Rev. A. 81, 052333–052341 (2010)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  30. Yang, Y.G., Jia, X., Wang, H.Y., Zhang, H.: Verifiable quantum (k, n) threshold secret sharing. Quantum Inf. Process. 11, 1619–1625 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  31. Gao, G.: Secure multiparty quantum secret sharing with the collective eavesdropping-check character. Quantum Inf. Process. 12, 55–68 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Li, L.Z., Qiu, D.W., Mateus, P.: Quantum secret sharing with classical Bobs. J. Phys. A Math. Theor. 46, 045304–045314 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Nie, Y.Y., Li, Y.H., Wang, Z.S.: Semi-quantum information splitting using GHZ-type states. Quantum Inf. Process. 12, 437–448 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A. 65, 032302–032304 (2002)

    Article  ADS  Google Scholar 

  35. Beige, A., Englert, B.G., Kurtsiefer, C., Weinfurter, H.: Secure communication with a publicly known key. Acta Physica A. 101, 357–370 (2002)

    Article  ADS  MATH  Google Scholar 

  36. Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902–187906 (2002)

    Article  ADS  Google Scholar 

  37. Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A. 68, 042317 (2003)

    Google Scholar 

  38. Zhang, Z.J.: Multiparty quantum secret sharing of secure direct communication. Phys. Lett. A. 342, 60–66 (2005)

    Article  ADS  MATH  Google Scholar 

  39. Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Gui, L.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A. 71, 044305–044308 (2005)

    Article  ADS  Google Scholar 

  40. Li, B.K., Yang, Y.G., Wen, Q.Y.: Threshold quantum secret sharing of secure direct communication. Chin. Phys. Lett. 26(1), 010302–010306 (2009)

    Article  ADS  Google Scholar 

  41. Han, L.F., Liu, Y.M., Liu, J., Zhang, Z.J.: Multiparty quantum secret sharing of secure direct communication using single photons. Opt. Commun. 281, 2690–2694 (2008)

    Article  ADS  Google Scholar 

  42. Du, R.G., Sun, Z.W., Wang, B.H., Long, D.Y.: Quantum secret sharing of secure direct communication using one-time pad. Int. J. Theor. Phys. 51, 2727–2736 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  43. Byers, J.W., Luby, M., Mitzenmacher, M., Rege, A.: A digital fountain approach to reliable distribution of bulk data. In: Martha Steenstrup (Ed.) Proceedings of the ACM SIGCOMM ’98 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM ’98). ACM, New York, NY, USA, (1998)

  44. Lin, Y., Liang, B., Li, B.: Data Persistence in Large-Scale Sensor Networks with Decentralized Fountain Codes. In: INFOCOM 2007. 26th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, 6–12 May 2007, pp. 1658–1666. IEEE, Anchorage, Alaska, USA (2007)

  45. 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, Bangalore, India, pp. 175–179 (1984)

  46. Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Dense-coding attack on three-party quantum key distribution protocols. IEEE J. Quantum Electron. 47(5), 630–635 (2011)

    Article  ADS  Google Scholar 

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Acknowledgments

The authors are grateful to the two anonymous referees for their valuable comments and suggestions which helped improve the presentation of this paper. Hong Lai has been supported in part by an International Macquarie University Research Excellence Scholarship (iMQRES). This work is also supported by the National Basic Research Program of China (973 Program) (Grant No. 2010CB923200), the National Natural Science Foundation of China (No. 61377067). The work is also supported by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), P. R. China.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing , 100876, China

    Hong Lai & Jinghua Xiao

  2. Department of Computing, Macquarie University, Sydney, NSW , 2109, Australia

    Hong Lai, Mehmet A. Orgun & Josef Pieprzyk

  3. Corporate Analytics, The Australian Taxation Office, Sydney, NSW , 2000, Australia

    Liyin Xue

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  1. Hong Lai
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Correspondence to Hong Lai.

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Lai, H., Xiao, J., Orgun, M.A. et al. Quantum direct secret sharing with efficient eavesdropping-check and authentication based on distributed fountain codes. Quantum Inf Process 13, 895–907 (2014). https://doi.org/10.1007/s11128-013-0699-1

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