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Quantum Information Processing

, Volume 12, Issue 6, pp 2241–2249 | Cite as

A quantum protocol for millionaire problem with Bell states

Article

Abstract

We propose a quantum protocol for the millionaire problem with Bell states, where two distrustful parties can compare the values of their fortune with the help of a semi-dishonest third party. The efficiency of our protocol is higher than that of previous protocols for millionaire problem. In our protocol, any information about the values of their fortune will not be leaked out. The security of our protocol is also discussed.

Keywords

Quantum cryptography Secure multiparty computation   Millionaire problem 

Notes

Acknowledgments

This work is supported by NSFC (Grant Nos. 61272057, 61170270, 61100203, 61003286, 61121061), NCET (Grant No. NCET-10-0260), SRFDP (Grant No. 20090005110010), Beijing Natural Science Foundation (Grant Nos. 4112040, 4122054), the Fundamental Research Funds for the Central Universities (Grant No. 2011YB01).

References

  1. 1.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India. IEEE, New York, pp. 175–179 (1984)Google Scholar
  2. 2.
    Ekert, A.K.: Quantum cryptography based on Bell theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121–3124 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    Liu, B., Gao, F., Wen, Q.Y.: Single-photon multiparty quantum cryptographic protocols with collective detection. IEEE J. Quantum Electron. 47, 1389–1390 (2011)ADSGoogle Scholar
  5. 5.
    Huang, W., Guo, F.Z., Huang, Z., Wen, Q.Y., Zhu, F.C.: Three-particle QKD protocol against a collective noise. Opt. Commun. 284, 536–540 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Hillery, M., Buzěk, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    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)ADSCrossRefGoogle Scholar
  9. 9.
    Lin, S., Wen, Q.Y., Gao, F., Zhu, F.C.: Quantum secure direct communication with chi-type entangled states. Phys. Rev. A 78, 064304 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Zhang, W.-W, Gao, F, Liu, B., et al.: A watermark strategy for quantum images based on quantum fourier transform. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0423-6
  11. 11.
    Zhang, W.-W., Gao, F., Liu, B., et al. : A quantum watermark protocol. Int. J. Theor. Phys. (2012). doi: 10.1007/s10773-012-1354-9
  12. 12.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (FOCS’ 82), Washington, DC, USA, p. 160 (1982)Google Scholar
  13. 13.
    Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56(2), 1154–1162 (1997)ADSCrossRefGoogle Scholar
  14. 14.
    Yang, Y.G., Wen, Q.Y.: An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J. Phys. A Math. Theor. 42, 055305 (2009)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Yang, Y.G., Cao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scr. 80(6), 065002 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    Liu, W., Wang, Y.-B., Cui, W.: Quantum private comparison protocol based on Bell entangled states. Commun. Theor. Phys. 57, 583–588 (2012)ADSMATHCrossRefGoogle Scholar
  17. 17.
    Chen, X.-B., Xu, G., Niu, X.-X., Wen, Q.-Y., Yang, Y.-X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement. Opt. Commun. 283, 1561–1565 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Liu, W., Wang, Y.-B., Jiang, Z.-T.: An efficient protocol for the quantum private comparison of equality with W state. Opt. Commun. 284, 3160–3163 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Liu, W., Wang, Y.-B., Jiang, Z.-T., Cao, Y.-Z.: A protocol for the quantum private comparison of equality with \(\chi \)-type state. Int. J. Theor. Phys. 51, 69–77 (2012)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Liu, W., Wang, Y.-B., Jiang, Z.-T., Cao, Y.-Z., Cui, W.: New quantum private comparison protocol using \(\chi \)-type state. Int. J. Theor. Phys. 51, 1953–1960 (2012)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Liu, W., Wang, Y.B.: Quantum private comparison based on GHZ entangled states. Int. J. Theor. Phys. doi: 10.1007/s10773-012-1246-z
  22. 22.
    Jia, H.-Y., Wen, Q.-Y., Li, Y.-B., Gao, F.: Quantum private comparison using genuine four-particle entangled states. Int. J. Theor. Phys. 51, 1187–1194 (2012)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Liu, B., Gao, F., Jia, H.-Y., Huang, W., Zhang, W.-W., Wen, Q.-Y.: Efficient quantum private comparison employing single photons and collective detection. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0439-y
  24. 24.
    Tseng, H.-Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11, 373–384 (2012)MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Yang, Y.-G., Xia, J., Jia, X., Zhang, H.: Comment on “Quantum private comparison protocols with a semi-honest third party”. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0433-4
  26. 26.
    Zhang, W.-W., Zhang, K.-J.: Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0507-3
  27. 27.
    Jia, H.Y., Wen, Q.Y., Song, T.T., Gao, F.: Quantum protocol for millionaire problem. Opt. Commun. 284, 545–549 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    Lin, S., Sun, Y., Liu, X.-F., Yao, Z.-Q.: Quantum private comparison protocol with d-dimensional Bell states. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0395-6
  29. 29.
    Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)ADSCrossRefGoogle Scholar
  30. 30.
    Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: A simple participant attack on the Bradler C-Dusek protocol. Quantum Inf. Comput. 7, 329 (2007)MathSciNetMATHGoogle Scholar
  31. 31.
    Qin, S.J., Gao, F., Wen, Q.Y., et al.: Cryptanalysis of the Hillery–Buzek–Berthiaume quantum secret-sharing protocol. Phys. Rev. A 76, 062324 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Gao, F., Wen, Q.Y., Zhu, F.C.: Comment on: “Quantum exam” [Phys. Lett. A, 350:174 (2006)]. Phys. Lett. A 360, 748 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    Gao, F., Qin, S.J., Wen, Q.Y., et al.: Cryptanalysis of multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger state. Opt. Commun. 283, 192 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Gao, F., Guo, F.Z., Wen, Q.Y., et al.: Comment on “Experimental demonstration of a quantum protocol for Byzantine agreement and liar detection”. Phys. Rev. Lett. 101, 208901 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    Song, T.T., Zhang, J., Gao, F., et al.: Participant attack on quantum secret sharing based on entanglement swapping. Chin. Phys. B 18, 1333 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    Guo, F.Z., Qin, S.J., Gao, F., et al.: Participant attack on a kind of MQSS schemes based on entanglement swapping. Eur. Phys. J. D 56, 445 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    Lin, S., Gao, F., Guo, F.Z., et al.: Comment on “Multiparty quantum secret sharing of classical messages based on entanglement swapping”. Phys. Rev. A 76, 036301 (2007)MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Lin, S., Wen, Q.Y., Gao, F., et al.: Improving the security of multiparty quantum secret sharing based on the improved Bostrom–Felbinger protocol. Opt. Commun. 281, 4553 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Wei-Wei Zhang
    • 1
    • 2
  • Dan Li
    • 1
  • Ke-Jia Zhang
    • 1
  • Hui-Juan Zuo
    • 1
  1. 1.State key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.State Key Laboratory of Information Security, Institute of SoftwareChinese Academy of SciencesBeijingChina

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