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The Security Analysis of Quantum B92 Protocol in Collective-Rotation Noise Channel

  • Leilei Li
  • Jian LiEmail author
  • Chaoyang Li
  • Hengji Li
  • Yuguang Yang
  • Xiubo Chen
Article

Abstract

Quantum communication protocols should take the effect of noise into account in a real environment. To analyze the security of the quantum B92 protocol presented by Bennett in collective-rotation noise channel, an excellent model of noise analysis is proposed. In the security analysis, the eavesdropping can be detected with the increment of the qubits error rate (ber). When the level of noise less than 0.50, it will cause a larger bit error rate if the eavesdropper Eve wants to obtain the same amount of information. In our analysis, Eve can maximally get about 50% of the key from the communication when the noise level approximates to 0.5. We also presented a new idea in analyzing the protocol security in collective-rotation noise channel with the idea of the Markov process.

Keywords

The quantum B92 protocol Collective rotation noise Security analysis Qubit error rate Information entropy 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No.U1636106, No.61472048 and No.61572053).

References

  1. 1.
    Allati, A.E., Baz, M.E., Hassouni, Y.: Quantum key distribution via tripartite coherent states. Quantum Inf. Process. 10(5), 589–602 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bennett, C.H., Brassard, G.: An update on quantum cryptography. Lect. Notes Comput. Sci. 196, 475–480 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bennett, C.H., Brassard, G., Crepeau, C., Maurer, U.M.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chang, Y., Zhang, S.B., Zhu, J.M.: Comment on ”flexible protocol for quantum private query based on b92 protocol”. Quantum Inf. Process. 16(3), 86 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    Chong, S.K., Hwang, T.: Quantum key agreement protocol based on bb84. Opt. Commun. 283(6), 1192–1195 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    Dong, H., Li, D., Xiu, X., Gao, Y.: A deterministic secure quantum communication protocol through a collective rotation noise channel. Int. J. Quantum Inf. 8(08), 1389–1395 (2010)CrossRefzbMATHGoogle Scholar
  8. 8.
    Etengu, R., Abbou, F.M., Wong, H.Y., Abid, A., Nortiza, N., Setharaman, A.: Performance comparison of bb84 and b92 satellite-based free space quantum optical communication systems in the presence of channel effects. J. Opt. Commun. 32(1), 37–47 (2011)CrossRefGoogle Scholar
  9. 9.
    Fu-Guo, D., Xi-Han, L., Chun-Yan, L., Ping, Z., Hong-Yu, Z.: Eavesdropping on the ‘ping-pong’ quantum communication protocol freely in a noise channel. Chin. Phys. 16(2), 277 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    Hsu, J.L., Chong, S.K., Hwang, T., Tsai, C.W.: Dynamic quantum secret sharing. Quantum Inf. Process. 12(1), 331–344 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hwang, T., Luo, Y.P., Yang, C.W., Lin, T.H.: Quantum authencryption: one-step authenticated quantum secure direct communications for off-line communicants. Quantum Inf. Process. 13(4), 925–933 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    Jian, L., Na, L., Li, L.L., Tao, W.: One step quantum key distribution based on epr entanglement. Sci. Rep. 6, 28767 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    Jian, L., Yang, Y.G., Chen, X.B., Zhou, Y.H., Shi, W.M.: Practical quantum private database queries based on passive round-robin differential phase-shift quantum key distribution. Sci. Rep. 6, 31738 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Jiang, Y., Zhang, S., Yang, F., Chang, Y., Zhang, H.: Quantum secret sharing protocol and its modeling checking. Laser and Optoelectronics Progress 54(12), 122704 (2017)CrossRefGoogle Scholar
  15. 15.
    Li, J., Chen, Y.H., Pan, Z.S., Sun, F.Q., Li, N., Li, L.L.: Security analysis of bb84 protocol in the collective-rotation noise channel. Acta Physica Sinica Chinese Edition 65(3), 030302 (2016)Google Scholar
  16. 16.
    Li, L., Li, H., Li, C., Chen, X., Chang, Y., Yang, Y., Li, J.: The security analysis of e91 protocol in collective-rotation noise channel. Int. J. Distrib. Sens. Netw. 14(5), 1550147718778192 (2018)CrossRefGoogle Scholar
  17. 17.
    Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Lo, H.K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283(5410), 2050 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    Matsumoto, R.: Improved asymptotic key rate of the b92 protocol. In: IEEE international symposium on information theory proceedings, pp. 351–353 (2014)Google Scholar
  20. 20.
    Niu, H.C., Ren, B.C., Wang, T.J., Hua, M., Deng, F.G.: Faithful entanglement sharing for quantum communication against collective noise. Int. J. Theor. Phys. 51(8), 2346–2352 (2012)CrossRefzbMATHGoogle Scholar
  21. 21.
    Pan, J.W., Bouwmeester, D.: Experimental quantum teleportation. Nature 390(390), 575 (1997)ADSzbMATHGoogle Scholar
  22. 22.
    Quan, Z.: Modification of b92 protocol and the proof of its unconditional security. Acta Phys. Sin. 51(7), 1446–1447 (2002)Google Scholar
  23. 23.
    Quan, Z., ChaoJing, T., ShenQiang, Z.: Modification of b92 protocol and the proof of its unconditional security. Acta Phys. Sin. 51(7), 1446–1447 (2002)Google Scholar
  24. 24.
    Stojanovic, A.D., Ramos, R.V., Matavulj, P.S.: Authenticated b92 qkd protocol employing synchronized optical chaotic systems. Opt. Quant. Electron. 48(5), 1–7 (2016)CrossRefGoogle Scholar
  25. 25.
    Su, B.B., Zhou, Y.Y., Zhou, X.J.: B92 protocol analysis related to the same basis eavesdropping. In: IEEE international conference on cloud computing and big data analysis, pp. 189–192 (2016)Google Scholar
  26. 26.
    Valivarthi, R., Puigibert, M.L.G., Zhou, Q., Aguilar, G.H., Verma, V.B., Marsili, F., Shaw, M.D., Nam, S.W., Oblak, D., Tittel, W.: Quantum teleportation across a metropolitan fibre network. Natare Photonics 10, 676–680 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Wan, L., Huang, Y., Huang, C.: Quantum noise theory for phonon transport through nanostructures. Physica B Condensed Matter 510, 22–28 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    Wang, X.B.: Fault tolerant quantum key distribution protocol with collective random unitary noise. Phys. Rev. A 72(5), 762–776 (2004)MathSciNetGoogle Scholar
  29. 29.
    Yang, C.W., Hwang, T.: Improved qsdc protocol over a collective-dephasing noise channel. Int. J. Theor. Phys. 51(12), 3941–3950 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Yang, Y.G., Teng, Y.W., Chai, H.P., Wen, Q.Y.: Revisiting the security of secure direct communication based on ping-pong protocol[quantum inf. process. 8, 347 (2009)]. Quantum Inf. Process. 10(3), 317–323 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Zhiyong, Z., Yanbo, W., Min, H., Jian, W.: Intercept-resent eavesdropping in polarization-drift quantum cryptography. Chinese Journal of Quantum Electronics 33(1), 44–50 (2016)Google Scholar
  32. 32.
    Zhou, X.Y., Zhang, C.H., Zhang, C.M., Wang, Q.: Obtaining better performance in the measurement-device-independent quantum key distribution with heralded single-photon sources. Phys. Rev. A 96(5), 052337 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    Zou, M., Zhang, G.: Information investigation for b92 protocol in quantum cryptography. Proc Spie 5631, 181–191 (2005)CrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.School of Computer ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.College of Computer Science and TechnologyBeijing University of TechnologyBeijingChina
  3. 3.School of Cyberspace SecurityBeijing University of Posts and TelecommunicationsBeijingChina

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