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Quantum private comparison of equality protocol without a third party

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Abstract

This paper presents a novel quantum private comparison protocol that uses Einstein–Podolsky–Rosen pairs. The proposed protocol allows two parties to secretly compare their information without exposing their actual contents. The technique of entanglement swapping enables the comparison to be achieved without the help of a third party. Moreover, because the proposed protocol employs one-step transmission and decoy photons, it is secure against the various quantum attacks in existence thus far.

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References

  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, India (1984)

  2. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390(6660), 575–579 (1997)

    Article  ADS  Google Scholar 

  4. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  5. Zhang, Z.J.: Multiparty quantum secret sharing of secure direct communication. Phys. Lett. A 342(1–2), 60–66 (2005)

    Article  ADS  MATH  Google Scholar 

  6. Zhang, Z.J.: Multiparty secret sharing of quantum information via cavity QED. Opt. Commun. 261(1), 199–202 (2006)

    Article  ADS  Google Scholar 

  7. Zhang, Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Phys. A 361(1), 233–238 (2006)

    Article  ADS  Google Scholar 

  8. Hwang, T., Hwang, C.-C., Yang, C.-W., Li, C.-M.: Revisiting Deng et al.’s multiparty quantum secret sharing protocol. Int. J. Theor. Phys. 50(9), 2790–2798 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng, F.-G., Long, G., Liu, X.-S.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68(4), 042317 (2003)

    Article  ADS  Google Scholar 

  10. Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187902 (2002)

    Article  ADS  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. Yang, C.-W., Hwang, T.: Improved QSDC protocol over a collective-dephasing noise channel. Int. J. Theor. Phys. 51(12), 3941–3950 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science (1982)

  14. Yao, A.C.-C.: How to generate and exchange secrets. In: Proceedings of the 27th Annual Symposium on Foundations of Computer Science (1986)

  15. Boudot, F., Schoenmakers, B., Traoré, J.: A fair and efficient solution to the socialist millionaires’ problem. Discret Appl. Math. 111(1–2), 23–36 (2001)

    Article  MATH  Google Scholar 

  16. Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56(2), 1154–1162 (1997)

    Article  ADS  Google Scholar 

  17. 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(5), 055305 (2009)

    Google Scholar 

  18. Yang, Y.G., Cao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scripta 80(6), 065002 (2009)

    Google Scholar 

  19. Lin, J., Tseng, H.-Y., Hwang, T.: Intercept-resend attacks on Chen et al.’s quantum private comparison protocol and the improvements. Opt. Commun. 284(9), 2412–2414 (2011)

    Article  ADS  Google Scholar 

  20. Chang, Y.-J., Tsai, C.-W., Hwang, T.: Multi-user private comparison protocol using GHZ class states. Quantum Inf. Process. 12(2), 1077–1088 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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(7), 1561–1565 (2010)

    Article  ADS  Google Scholar 

  22. Liu, W., Wang, Y.B., Cui, W.: Quantum private comparison protocol based on bell entangled states. Commun. Theor. Phys 57(4), 583–588 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Tseng, H.-Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11(2), 373–384 (2012)

    Google Scholar 

  24. 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(1), 69–77 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. Xu, G.A., Chen, X.B., Wei, Z.H., Li, M.J., Yang, Y.X.: An efficient protocol for the quantum private comparison of equality with a four-qubit cluster state. Int. J. Quantum Inf. 10(4) (2012)

  26. Liu, W., Wang, Y.B., Jiang, Z.T.: An efficient protocol for the quantum private comparison of equality with W state. Opt. Commun. 284(12), 3160–3163 (2011)

    Article  ADS  Google Scholar 

  27. 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. 12(2), 887–897 (2013)

    Google Scholar 

  28. Zhang, W.-W., Zhang, K.-J.: Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party. Quantum Inf. Process. 12(5), 1981–1990 (2013)

    Google Scholar 

  29. Chen, X.-B., Su, Y., Niu, X.-X., Yang, Y.-X.: Efficient and feasible quantum private comparison of equality against the collective amplitude damping noise. Quantum Inf. Process. doi:10.1007/s11128-012-0505-5 (2012)

  30. Li, Y.-B., Qin, S.-J., Yuan, Z., Huang, W., Sun, Y.: Quantum private comparison against decoherence noise. Quantum Inf. Process. 12(6), 2191–2205 (2013)

    Google Scholar 

  31. Pan, J.W., Bouwmeester, D., Weinfurter, H., Zeilinger, A.: Experimental entanglement swapping: entangling photons that never interacted. Phys. Rev. Lett. 80(18), 3891–3894 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Zukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71(26), 4287–4290 (1993)

    Article  ADS  Google Scholar 

  33. Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1–2), 23–25 (2006)

    Article  ADS  MATH  Google Scholar 

  34. Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.J.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72(4), 044302 (2005)

    Article  ADS  Google Scholar 

  35. Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.J.: Improving the security of multiparty quantum secret sharing against Trojan horse attack (vol 72, art no 044302, 2005). Phys. Rev. A 73(4), 049901 (2006)

    Google Scholar 

  36. 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. Quantum Phys. arXiv:quant-ph/0508168v1 (2005)

  37. 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(5), 054302 (2006)

    Article  ADS  Google Scholar 

  38. Yang, C.-W., Hwang, T., Luo, Y.-P.: Enhancement on “quantum blind signature based on two-state vector formalism”. Quantum Inf. Process. 12(1), 109–117 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. Lin, J., Hwang, T.: An enhancement on Shi et al.’s multiparty quantum secret sharing protocol. Opt. Commun. 284(5), 1468–1471 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  40. Damgard, I.B.: A design principle for hash functions. Adv Cryptol. 89(435), 416–427 (1990)

    Google Scholar 

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Acknowledgments

We would like to thank the anonymous reviewers for their very valuable comments, which greatly enhanced the clarity of this paper. We would also like to thank the National Science Council of Republic of China, for the financial support of this research under Contract No. NSC 100-2221-E-006-152-MY3.

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Correspondence to Tzonelih Hwang.

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Lin, J., Yang, CW. & Hwang, T. Quantum private comparison of equality protocol without a third party. Quantum Inf Process 13, 239–247 (2014). https://doi.org/10.1007/s11128-013-0645-2

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  • DOI: https://doi.org/10.1007/s11128-013-0645-2

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