Advertisement

International Journal of Theoretical Physics

, Volume 58, Issue 11, pp 3797–3814 | Cite as

Multiparty Semi-Quantum Secret Sharing with d-Level Single-Particle States

  • Ye Chong-Qiang
  • Ye Tian-Yu
  • He De
  • Gan Zhi-GangEmail author
Article

Abstract

All previous semi-quantum secret sharing (SQSS) protocols have four common features: (1) they adopt product states or entangled states as quantum carriers; (2) the particles prepared by the quantum party are transmitted in a tree-type way; (3) they require the classical parties to possess the measurement capability; and (4) they are only suitable for two-level quantum system. In this paper, we generalize the SQSS concept into the d-level quantum system and propose two multiparty semi-quantum secret sharing (MSQSS) protocols with d-level single-particle states which do not require the classical parties to have the measurement capability. In the first protocol, the particles prepared by the quantum party are transmitted in a tree-type way, while in the second protocol, the particles prepared by the quantum party are transmitted in a circular way. The proposed MSQSS protocols are secure against some famous attacks, such as the intercept-resend attack, the measure-resend attack, the entangle-measure attack and the participant attack.

Keywords

Semi-quantum cryptography Multiparty semi-quantum secret sharing (MSQSS) d-level single- particle states Measurement capability 

PACS

03.67.Dd 03.67.Hk 03.67.Pp 

Notes

Acknowledgments

Funding by the Natural Science Foundation of Zhejiang Province (Grant No.LY18F020007), the Public Welfare Project Foundation of Zhejiang Provincial Science and Technology Department (Grant No. LGG18F020006) and the Foundation of Zhejiang Provincial Education Department (Grant No. Y201737672) is gratefully acknowledged.

References

  1. 1.
    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. pp. 175–179 (1984)Google Scholar
  2. 2.
    Ekert, A.K.: Quantum cryptography based on bells theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)ADSMathSciNetzbMATHGoogle Scholar
  3. 3.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121–3124 (1992)ADSMathSciNetzbMATHGoogle Scholar
  4. 4.
    Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85(26), 5635 (2000)ADSGoogle Scholar
  5. 5.
    Hwang, W.Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91(5), 057901 (2003)ADSGoogle Scholar
  6. 6.
    Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A. 78(2), 022321 (2008)ADSGoogle Scholar
  7. 7.
    Zhang, C.M., Song, X.T., Treeviriyanupab, P., et al.: Delayed error verification in quantum key distribution. Chin. Sci. Bull. 59(23), 2825–2828 (2014)Google Scholar
  8. 8.
    Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A. 65(3), 032302 (2002)ADSGoogle Scholar
  9. 9.
    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(4), 042317 (2003)ADSGoogle Scholar
  10. 10.
    Gu, B., Huang, Y.G., Fang, X., Zhang, C.Y.: A two-step quantum secure direct communication protocol with hyperentanglement. Chin. Phys. B. 20(10), 100309 (2011)ADSGoogle Scholar
  11. 11.
    Wang, J., Zhang, Q., Tang, C.J.: Quantum secure direct communication based on order rearrangement of single photons. Phys. Lett. A. 358(4), 256–258 (2006)ADSzbMATHGoogle Scholar
  12. 12.
    Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A. 59(3), 1829–1834 (1999)ADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A. 59(1), 162–168 (1999)ADSGoogle Scholar
  14. 14.
    Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648–651 (1999)ADSGoogle Scholar
  15. 15.
    Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A. 61(4), 042311 (2000)ADSMathSciNetGoogle Scholar
  16. 16.
    Li, Y., Zhang, K., Peng, K.: Multiparty secret sharing of quantum information based on entanglement swapping. Phys. Lett. A. 324(5), 420–424 (2004)ADSMathSciNetzbMATHGoogle Scholar
  17. 17.
    Xiao, L., Long, G.L., Deng, F.G., et al.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A. 69(5), 052307 (2004)ADSGoogle Scholar
  18. 18.
    Deng, F.G., Long, G.L., Zhou, H.Y.: An efficient quantum secret sharing scheme with Einstein-Podolsky- Rosen pairs. Phys. Lett. A. 340(1–4), 43–50 (2005)ADSzbMATHGoogle Scholar
  19. 19.
    Wang, T.Y., Wen, Q.Y., Chen, X.B., et al.: An efficient and secure multiparty quantum secret sharing scheme based on single photons. Opt. Commun. 281(24), 6130–6134 (2008)ADSGoogle Scholar
  20. 20.
    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(14), 3639–3642 (2011)ADSGoogle Scholar
  21. 21.
    Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Lett. A. 310(4), 247–251 (2003)ADSMathSciNetzbMATHGoogle Scholar
  22. 22.
    Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A. 78(4), 042309 (2008)ADSMathSciNetzbMATHGoogle Scholar
  23. 23.
    Keet, A., Fortescue, B., Markham, D., et al.: Quantum secret sharing with qudit graph states. Phys. Rev. A. 82(6), 062315 (2010)ADSGoogle Scholar
  24. 24.
    Qin, H., Dai, Y.: Dynamic quantum secret sharing by using d-dimensional GHZ state. Quantum Inf. Process. 16(3), 64 (2017)ADSMathSciNetzbMATHGoogle Scholar
  25. 25.
    Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical bob. Phys. Rev. Lett. 99(14), 140501 (2007)ADSMathSciNetzbMATHGoogle Scholar
  26. 26.
    Boyer, M., Gelles, R., Kenigsberg, D., et al.: Semiquantum key distribution. Phys. Rev. A. 79(3), 032341 (2009)ADSMathSciNetzbMATHGoogle Scholar
  27. 27.
    Lu, H., Cai, Q.Y.: Quantum key distribution with classical Alice. Int. J. Quantum Inf. 6(6), 1195–1202 (2008)zbMATHGoogle Scholar
  28. 28.
    Zhang, X.Z., Gong, W.G., Tan, Y.G., et al.: Quantum key distribution series network protocol with M-classical Bobs. Chin. Phys. B. 18(6), 2143–2148 (2009)ADSGoogle Scholar
  29. 29.
    Tan, Y.G., Lu, H., Cai, Q.Y.: Comment on “Quantum key distribution with classical Bob”. Phys. Rev. Lett. 102(9), 098901 (2009)ADSMathSciNetGoogle Scholar
  30. 30.
    Zou, X.F., Qiu, D.W., Li, L.Z., et al.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A. 79(5), 052312 (2009)ADSGoogle Scholar
  31. 31.
    Boyer, M., Mor, T.: Comment on “Semiquantum-key distribution using less than four quantum states”. Phys. Rev. A. 83(4), 046301 (2011)ADSGoogle Scholar
  32. 32.
    Wang, J., Zhang, S., Zhang, Q., et al.: Semiquantum key distribution using entangled states. Chin. Phys. Lett. 28(10), 100301 (2011)ADSGoogle Scholar
  33. 33.
    Miyadera, T.: Relation between information and disturbance in quantum key distribution protocol with classical Alice. Int. J. Quantum Inf. 9(6), 1427–1435 (2011)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Krawec, W.O.: Restricted attacks on semi-quantum key distribution protocols. Quantum Inf. Process. 13(11), 2417–2436 (2014)ADSMathSciNetzbMATHGoogle Scholar
  35. 35.
    Yang, Y.G., Sun, S.J., Zhao, Q.Q.: Trojan-horse attacks on quantum key distribution with classical Bob. Quantum Inf. Process. 14(2), 681–686 (2015)ADSMathSciNetzbMATHGoogle Scholar
  36. 36.
    Yu, K.F., Yang, C.W., Liao, C.H., et al.: Authenticated semi-quantum key distribution protocol using Bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)ADSMathSciNetzbMATHGoogle Scholar
  37. 37.
    Krawec, W.O.: Mediated semiquantum key distribution. Phys. Rev. A. 91(3), 032323 (2015)ADSGoogle Scholar
  38. 38.
    Zou, X.F., Qiu, D.W., Zhang, S.Y.: Semiquantum key distribution without invoking the classical party’s measurement capability. Quantum Inf. Process. 14(8), 2981–2996 (2015)ADSMathSciNetzbMATHGoogle Scholar
  39. 39.
    Li, Q., Chan, W.H., Zhang, S.Y.: Semiquantum key distribution with secure delegated quantum computation. Sci. Rep. 6, 19898 (2016)ADSGoogle Scholar
  40. 40.
    Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. China Phys. Mech. Astron. 57(9), 1696–1702 (2014)ADSGoogle Scholar
  41. 41.
    Luo, Y.P., Hwang, T.: Authenticated semi-quantum direct communication protocols using Bell states. Quantum Inf. Process. 15(2), 947–958 (2016)ADSMathSciNetzbMATHGoogle Scholar
  42. 42.
    Zhang, M.H., Li, H.F., Xia, Z.Q., et al.: Semiquantum secure direct communication using EPR pairs. Quantum Inf. Process. 16(5), 117 (2017)ADSzbMATHGoogle Scholar
  43. 43.
    Li, Q., Chan, W.H., Long, D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A. 82(2), 022303 (2010)ADSGoogle Scholar
  44. 44.
    Wang, J., Zhang, S., Zhang, Q., et al.: Semiquantum secret sharing using two-particle entangled state. Int. J. Quantum Inf. 10(5), 1250050 (2012)MathSciNetzbMATHGoogle Scholar
  45. 45.
    Li, L.Z., Qiu, D.W., Mateus, P.: Quantum secret sharing with classical Bobs. J. Phys. A Math. Theor. 46(4), 045304 (2013)ADSMathSciNetzbMATHGoogle Scholar
  46. 46.
    Lin, J., Yang, C.W., Tsai, C.W., et al.: Intercept-resend attacks on semi-quantum secret sharing and the improvements. Int. J. Theor. Phys. 52(1), 156–162 (2013)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Yang, C.W., Hwang, T.: Efficient key construction on semi-quantum secret sharing protocols. Int. J. Quantum Inf. 11(5), 1350052 (2013)MathSciNetzbMATHGoogle Scholar
  48. 48.
    Xie, C., Li, L.Z., Qiu, D.W.: A novel semi-quantum secret sharing scheme of specific bits. Int. J. Theor. Phys. 54(10), 3819–3824 (2015)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Yin, A., Fu, F.: Eavesdropping on semi-quantum secret sharing scheme of specific bits. Int. J. Theor. Phys. 55(9), 4027–4035 (2016)MathSciNetzbMATHGoogle Scholar
  50. 50.
    Gao, G., Wang, Y., Wang, D.: Multiparty semiquantum secret sharing based on rearranging orders of qubits. Mod. Phys. Lett. B. 30(10), 1650130 (2016)ADSMathSciNetGoogle Scholar
  51. 51.
    Tavakoli, A., Herbauts, I., Zukowski, M., et al.: Secret sharing with a single d-level quantum system. Phys. Rev. A. 92(3), 03030 (2015)Google Scholar
  52. 52.
    Ye, C.Q., Ye, T.Y.: Circular multi-party quantum private comparison with n-level single-particle states. Int. J. Theor. Phys. 58(4), 1282–1294 (2019)MathSciNetzbMATHGoogle Scholar
  53. 53.
    Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A. 351(1–2), 23–25 (2006)ADSzbMATHGoogle Scholar
  54. 54.
    Deng, F.G., Zhou, P., Li, X.H., Li, C.Y., Zhou, H.Y.: Robustness of two-way quantum communication protocols against Trojan horse attack. arXiv: quant-ph/0508168 (2005)Google Scholar
  55. 55.
    Li, X.H., Deng, F.G., Zhou, H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A. 74, 054302 (2006)ADSGoogle Scholar
  56. 56.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)ADSzbMATHGoogle Scholar
  57. 57.
    Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: A simple participant attack on the Bradler-Dusek protocol. Quantum Inf. Comput. 7, 329 (2007)MathSciNetzbMATHGoogle Scholar
  58. 58.
    Gao, F.Z., Wen, Q.Y., Zhu, F.C.: Comment on: “quantum exam”[Phys Lett A 350(2006)174]. Phys. Lett. A. 360(6), 748–750 (2007)ADSGoogle Scholar
  59. 59.
    Guo, F.Z., Qin, S.J., Gao, F., Lin, S., Wen, Q.Y., Zhu, F.C.: Participant attack on a kind of MQSS schemes based on entanglement swapping. Eur. Phys. J. D. 56(3), 445–448 (2010)ADSGoogle Scholar
  60. 60.
    Qin, S.J., Gao, F., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret sharing protocol. Phys. Rev. A. 76(6), 062324 (2007)ADSGoogle Scholar
  61. 61.
    Nie, Y.Y., Li, Y.H., Wang, Z.S.: Semi-quantum information splitting using GHZ-type states. Quantum Inf. Process. 12, 437–448 (2013)ADSMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information & Electronic EngineeringZhejiang Gongshang UniversityHangzhouPeople’s Republic of China

Personalised recommendations