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Quantum private comparison with a malicious third party

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Abstract

In this paper, we will show that quantum private comparison protocol is secure when a malicious third party is presented. The security of the protocol is considered in a cheat-sensitive model, in which the TP is kept honest by the possibility of being caught cheating. Besides, we enhance the privacy of the quantum private comparison protocol, where the participants’ inputs and the comparison result can be preserved. Furthermore, in contrast to pervious protocols requiring a large amount of quantum resources, such as entanglement and quantum memory, our protocol is based on BB84 protocol, which is more feasible for practical applications. Finally, we analyze the security of the presented protocol.

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References

  1. Yao, A.: Protocols for Secure Computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (FOCS’ 82), 160 (1982)

  2. Goldreich, O.: Foundations of Cryptography, vol. 2. Cambridge University Press, Cambridge (2004). Chapter 7

    Book  MATH  Google Scholar 

  3. Lindell, Y., Pinkas, B.: Secure multiparty computation for privacy-preserving data mining. J. Priv. Confid. 1, 59 (2009)

    Google Scholar 

  4. Chor, B., Goldreich, O., Kushilevitz E., Sudan, M.: Private Information Retrieval. In: Proceedings of the 36th Annual IEEE Conference on Foundations of Computer Science. IEEE, New York, 41 (1995)

  5. Colbeck, R.: Impossibility of secure two-party classical computation. Phys. Rev. A 76, 062308 (2007)

    ADS  Google Scholar 

  6. Crépeau, C., Gottesman, D., Smith, A.: Secure Multi-party Quantum Computation, STOC02, 643 (2002)

  7. 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 (IEEE, New York, 1984), 175 (1984)

  8. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    ADS  MATH  MathSciNet  Google Scholar 

  9. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    ADS  MathSciNet  Google Scholar 

  10. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)

    ADS  Google Scholar 

  11. Unruh, D.: Universally composable quantum multi-party computation. Adv. Cryptol. C EUROCRYPT 2010 6110, 486 (2010)

    Article  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  13. 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)

    ADS  Google Scholar 

  14. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

    ADS  Google Scholar 

  15. Sun, Z.W., Du, R.G., Long, D.Y.: Quantum secure direct communication with quantum identification. Int. J. Quantum Inf. 10, 1250008 (2012)

    MathSciNet  Google Scholar 

  16. Sun, Z.W., Du, R.G., Long, D.Y.: Quantum secure direct communication with two-photon four-qubit cluster state. Int. J. Theor. Phys. 51, 1946 (2012)

    MATH  MathSciNet  Google Scholar 

  17. Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56, 1154 (1997)

    ADS  Google Scholar 

  18. Buhrman, H., Christandl, M., Schaffner, C.: Complete insecurity of quantum protocols for classical two-party computation. Phys. Rev. Lett. 109, 160501 (2012)

    ADS  Google Scholar 

  19. 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)

    ADS  MathSciNet  Google Scholar 

  20. Jakobsson, M., Yung, M.: Advances in Cryptology - CRYPTO ’96, 1109, 186 (1996)

  21. 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 (2010)

    ADS  Google Scholar 

  22. 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 (2011)

    ADS  Google Scholar 

  23. Sun, Z., Long, D.: Cryptanalysis of an efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement, arXiv:1204.4587, (2012)

  24. Tseng, H.-Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process 11, 373 (2012)

    MATH  MathSciNet  Google Scholar 

  25. Chen, X.-B., Dou, Z., Xu, G., Wang, C., Yang, Y.: A class of protocols for quantum private comparison based on the symmetry of states. Quantum Inf. Process 13, 85 (2014)

    ADS  MATH  Google Scholar 

  26. Chen, X.-B., Su, Y., Niu, X., Yang, Y.-X.: Efficient and feasible quantum private comparison of equality against the collective amplitude damping noise. Quantum Inf. Process 13, 101 (2014)

    ADS  MATH  Google Scholar 

  27. Liu, W., Wang, Y.-B., Jiang, Z.-T., Cao, Y.-Z.: A protocol for the quantum private comparison of equality with x-type state. Int. J. Theor. Phys. 51, 69 (2011)

    MathSciNet  Google Scholar 

  28. Lin, S., Sun, Y., Liu, X.F., Yao, Z.Q.: Quantum private comparison protocol with d-dimensional Bell states. Quantum Inf. Process 12, 559–568 (2013)

    ADS  MATH  MathSciNet  Google Scholar 

  29. Liu, B., Gao, F., Jia, H., Huang, W., Zhang, W., Wen, Q.: Efficient quantum private comparison employing single photons and collective detection. Quantum Inf. Process 12, 887 (2013)

    ADS  MATH  MathSciNet  Google Scholar 

  30. Gao, F., Qin, S.J., Zhang, J., Wen, Q.Y.: Quantum private comparison protocol based on entanglement swapping of d-level Bell states. Quantum Inf. Process 12, 2793–2802 (2013)

    ADS  MATH  MathSciNet  Google Scholar 

  31. Shor Peter, W., John, P.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 441, 85 (2000)

    Google Scholar 

  32. Ben-Or, M., Horodecki, M., Leung, D.W., Mayers, D., Oppenheim, J.: The universal composable security of quantum key distribution. In: Theory of Cryptography: Proceedings of TCC 2005, (Cambridge, MA, USA, Springer, 2005) 386–406 (2005)

  33. He, G.: Quantum protocols for the millionaire problem with a third party are trivial. Int. J. Quantum Inf. 11, 1350025 (2013)

    MathSciNet  Google Scholar 

  34. Liu, X., Zhang, B., Wang, J., Tang, C., Zhao, J.: Differential phase shift quantum private comparison. Quantum Inf. Process 13, 71–84 (2014)

    ADS  Google Scholar 

  35. Li, Y., Ma, Y., Xu, S., Huang, W., Zhang, Y.: Quantum private comparison based on phase encoding of single photons. Int. J. Theor. Phys. 53, 3191–3200 (2014)

    MATH  Google Scholar 

  36. Lin, J., Yang, C., Hweng, T.: Quantum private comparison of equality protocol without a third party. Quantum Inf. Process 13, 239–247 (2014)

    MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 61272013, 61402293, 61171072 and 61202466), the Key Program for Technology and Innovation of College in Guangdong Province (No. CXZD1143), Natural Science Foundation of Guangdong Province (No. S2013040011789), Shenzhen Technology Plan (No. JCYJ20130401095947219) and Natural Science Foundation of SZU (No. 201435). We thank anonymous referees for their valuable and constructive comments.

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Correspondence to Zhiwei Sun.

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Sun, Z., Yu, J., Wang, P. et al. Quantum private comparison with a malicious third party. Quantum Inf Process 14, 2125–2133 (2015). https://doi.org/10.1007/s11128-015-0956-6

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