Cryptanalysis and Improvement of the Semi-Quantum Key Distribution Robust against Combined Collective Noise

  • Chia-Wei Tsai
  • Chun-Wei YangEmail author


This study reveals a design flaw in the semi-quantum key distribution (SQKD) robust against combined collective noise [International Journal of Theoretical Physics, Vol. 57, Issue 11 (2018) 3410–3418]. With this flaw, Tsai and Hwang’s SQKD protocol violates the definition of a semi-quantum environment. To solve this flaw, an improved SQKD protocol based on Tsai and Hwang’s scheme is proposed.


Semi-quantum key distribution Collective noise Quantum communication Quantum cryptography 



We would like to thank the anonymous reviewers and the editor for their very valuable comments, which greatly enhanced the clarity of this paper. This research was partially supported by the Ministry of Science and Technology, Taiwan, R.O.C. (Grant Nos. MOST 106-2218-E-039-002-MY3 and MOST 107-2218-E-218-004-MY2), and China Medical University (Grant No. CMU107-N-11).


  1. 1.
    Zanardi, P., Rasetti, M.: Noiseless Quantum Codes. Phys. Rev. Lett. 79(17), 3306–3309 (1997)ADSCrossRefGoogle Scholar
  2. 2.
    Knill, E., Laflamme, R., Viola, L.: Theory of quantum error correction for general noise. Phys. Rev. Lett. 84(11), 2525–2528 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lidar, D.A., Bacon, D., Kempe, J., Birgitta Whaley, K.: Protecting quantum information encoded in decoherence-free states against exchange errors. Phys. Rev. A. 61(5), 052307 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science. 290(5491), 498–501 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    Kempe, J., Bacon, D., Lidar, D., Whaley, K.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A. 63(4), 042307 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    Basharov, A.M., Gorbachev, V.N., Trubilko, A.I., Yakovleva, E.S.: One-way gates based on EPR, GHZ and decoherence-free states of W class. Phys. Lett. A. 373(38), 3410–3412 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yang, C.-W., Tsai, C.-W., Hwang, T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China Phys. 54(3), 496–501 (2011)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Yang, C.-W., Tsai, C.-W., Hwang, T.: Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises. Quantum Inf. Process. 11(1), 113–122 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yang, C.-W., Hwang, T.: Quantum dialogue protocols immune to collective noise. Quantum Inf. Process. 12(6), 2131–2142 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Yang, C.-W., Hwang, T.: Fault tolerant quantum key distributions using entanglement swapping of GHZ states over collective-noise channels. Quantum Inf. Process. 12(10), 3207–3222 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Yang, C.-W., Hwang, T.: Fault tolerant authenticated quantum direct communication immune to collective noises. Quantum Inf. Process. 12(11), 3495–3509 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Yang, C.-W., Tsai, C.-W., Hwang, T.: Fault tolerant deterministic quantum communications using GHZ states over collective-noise channels. Quantum Inf. Process. 12(9), 3043–3055 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Yang, C.-W., Hwang, T.: Trojan horse attack free fault-tolerant quantum key distribution protocols. Quantum Inf. Process. 13(3), 781–794 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Yang, C.-W., Tsai, C.-W., Hwang, T.: Fault-tolerant controlled quantum secure direct communication over a collective quantum noise channel. Laser Phys. 24(10), 105203 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    Tsai, C.-L., Hwang, T.: Semi-quantum key distribution robust against combined collective noise. Int. J. Theor. Phys. 57(11), 3410–3418 (2018)CrossRefGoogle Scholar
  17. 17.
    Bennett, C.H., Brassard, G., Robert, J.M.: Privacy amplification by public discussion. SIAM J. Comput. 17(2), 210–229 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Bennett, C.H., Brassard, G., Crepeau, C., Maurer, U.M.: Generalized privacy amplification. IEEE Trans. Inf. Theory. 41(6), 1915–1923 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical Bob. Phys. Rev. Lett. 99(14), 140501 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Boyer, M., Gelles, R., Kenigsberg, D., Mor, T.: Semiquantum key distribution. Phys. Rev. A. 79(3), 032341 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Zou, X., Qiu, D., Li, L., Wu, L., Li, L.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A. 79(5), 052312 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Krawec, W.O.: Mediated semiquantum key distribution. Phys. Rev. A. 91(3), (2015)Google Scholar
  23. 23.
    Zou, X., Qiu, D., Zhang, S., Mateus, P.: Semiquantum key distribution without invoking the classical party’s measurement capability. Quantum Inf. Process. 14(8), 2981–2996 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Li, Q., Chan, W.H., Zhang, S.: Semiquantum key distribution with secure delegated quantum computation. Sci. Rep. 6, (2016)Google Scholar
  25. 25.
    Yu, K.-F., Gu, J., Hwang, T., Gope, P.: Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing. Quantum Inf. Process. 16(8), 194 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Yu, K.-F., Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated semi-quantum key distribution protocol using Bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Liu, Z.-R., Hwang, T.: Mediated semi-quantum key distribution without invoking quantum measurement. Ann. Phys. 530(4), 1700206 (2018)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Zou, X., Qiu, D.: Three-step semiquantum secure direct communication protocol. Sci China Phys Mech. 57(9), 1696–1702 (2014)CrossRefGoogle Scholar
  29. 29.
    Zhang, M.-H., Li, H.-F., Xia, Z.-Q., Feng, X.-Y., Peng, J.-Y.: Semiquantum secure direct communication using EPR pairs. Quantum Inf. Process. 16(5), (2017)Google Scholar
  30. 30.
    Luo, Y.-P., Hwang, T.: Authenticated semi-quantum direct communication protocols using Bell states. Quantum Inf. Process. 15(2), 947–958 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Li, Q., Chan, W.H., Long, D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A. 82(2), 022303 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Lin, J., Yang, C.-W., Tsai, C.-W., Hwang, T.: Intercept-resend attacks on semiquantum secret sharing and the improvements. Int. J. Theor. Phys. 52(1), 156–162 (2013)CrossRefzbMATHGoogle Scholar
  33. 33.
    Yang, C.-W., Hwang, T.: Efficient key construction on semi-quantum secret sharing protocols. Int. J. Quant. Infor. 11(05), 1350052 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Nie, Y.Y., Li, Y.H., Wang, Z.S.: Semi-quantum information splitting using GHZ-type states. Quantum Inf. Process. 12(1), 437–448 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringSouthern Taiwan University of Science and TechnologyTainan CityTaiwan
  2. 2.Center for General EducationChina Medical UniversityTaichung CityTaiwan
  3. 3.College of Humanities and SciencesChina Medical UniversityTaichung CityTaiwan

Personalised recommendations