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Novel Quantum Private Comparison Protocol Based on Locally Indistinguishable Product States

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Abstract

In this paper, we propose a two-party quantum private comparison (QPC) protocol using orthogonal product states. This protocol introduces a semi-honest third party who will faithfully execute the protocol and will not conspire with any of the participants. Every participant encodes the hash value of her (his) secret data into a quantum sequence of orthogonal product states. Each of these states comes from a locally indistinguishable set of product states. To ensure information security, each participant splits the quantum sequence of product states that she (he) generates into two single-particle sequences and transmits these two single-particle sequences separately. After the third party calculates and publishes the results, the two participants can know whether their secret information is equal by a simple calculation. Security and efficiency analyses show that our protocol is secure and efficient.

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References

  1. Yao, A.C.: Protocols for secure computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (FOCS’82), Washington, DC, USA, pp. 160 (1982)

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

    Article  MathSciNet  ADS  Google Scholar 

  3. 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 

  4. Lang, Y.F.: Quantum gate-based quantum private comparison. Int. J. Theor. Phys. 59, 833–840 (2020)

    Article  MathSciNet  Google Scholar 

  5. Ye, C.Q., Li, J., Cao, Z.W.: A class of protocols for multi-party quantum private comparison based on traveling mode. Quantum Inf. Process. 20 (2), 56 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  6. Lin, S., Wang, H., Guo, G.D., et al.: Authenticated multi-user quantum key distribution with single particles. Int. J. Quantum Inf. 14, 1650002 (2016)

    Article  MathSciNet  Google Scholar 

  7. Duan, M.Y.: Multi-party quantum private comparison with qudit shifting operation. Int. J. Theor. Phys. 59(10), 3079–3085 (2020)

    Article  MathSciNet  Google Scholar 

  8. Wu, W.Q., Zhou, G.L., Zhao, Y.X.: New quantum private comparison protocol without a third Party. Int. J. Theor. Phys. 59(6), 1866–1875 (2020)

    Article  MathSciNet  Google Scholar 

  9. Xu, Q.D., Chen, H.Y., Gong, L.H.: Quantum private comparison protocol based on Four-Particle GHZ States. Int. J. Theor. Phys. 59(6), 1798–1806 (2020)

    Article  MathSciNet  Google Scholar 

  10. Abulkasim, H., Farouk, A., Hamad, S.: Secure dynamic multiparty quantum private comparison. Sci. Rep. 9, 17818 (2019)

    Article  ADS  Google Scholar 

  11. Pan, H.M.: A novel pure entangled state based two-party quantum private comparison protocol. Int. J. Theor. Phys 58(11), 3822–3827 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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)

    Article  MathSciNet  ADS  Google Scholar 

  14. Jia, H.Y., Wen, Q.Y., Song, T.T., Gao, F.: Quantum protocol for millionaire problem. Opt. Commun. 284, 545–549 (2011)

    Article  ADS  Google Scholar 

  15. Yan, L.L., Zhang, S.B., Chang, Y., Sheng, Z.W., Sun, Y.H.: Semi-quantum key agreement and Private comparison protocol using Bell states. Int. J. Theor. Phys. 58, 3852–3862 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  17. Jia, H.Y., Wang, Y.B., Jiang, Z.T.: Quantum private comparison using genuine Four-particle entangled states. Int. J. Theor. Phys. 51, 1953–1960 (2012)

    Article  MathSciNet  Google Scholar 

  18. Ye, T.Y., Ji, Z.X.: Two-party quantum private comparison with five-qubit entangled states. Int. J. Theor. Phys. 56(5), 1517–1529 (2017)

    Article  MathSciNet  Google Scholar 

  19. Zhou, N.R., Xu, Q.D., Du, N.S., Gong, L.H.: Semi-quantum private comparison protocol of size relation with d-dimensional Bell states. Quantum Inf. Process. 20, 124 (2021)

    Article  MathSciNet  Google Scholar 

  20. Liu, W., Wang, Y.B., Wang, X.M.: Quantum multi-party private comparison protocol using d-dimensional Bell states. Int. J. Theor. Phys. 54, 1830–1839 (2015)

    Article  MathSciNet  Google Scholar 

  21. Ji, Z.X., Ye, T.Y.: Multi-party quantum private comparison based on the entanglement swapping of d-level cat states and d-level Bell states. Quantum Inf. Process. 16, 177 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  22. Wu, W.Q., Ma, X.X.: Quantum private comparison protocol without a third party. Int. J. Theor. Phys. 59, 1854–1865 (2020)

    Article  MathSciNet  Google Scholar 

  23. Jiang, L.Z.: Semi-quantum private comparison based on Bell states. Quantum Inf. Process. 19, 180 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  24. Zhang, Z.C., Gao, F., Tian, G.J., Cao, T.Q., Wen, Q.Y.: Nonlocality of orthogonal product basis quantum states. Phys. Rev. A 90, 022313 (2014)

    Article  ADS  Google Scholar 

  25. Wang, Y.L., Li, M.S., Zheng, Z.J., Fei, S.M.: Nonlocality of orthogonal product-basis quantum states. Phys. Rev. A 92, 032313 (2015)

    Article  ADS  Google Scholar 

  26. Xu, G.B., Wen, Q.Y., Qin, S.J., Yang, Y.H., Gao, F.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93, 032341 (2016)

    Article  ADS  Google Scholar 

  27. Zhang, Z.C., Gao, F., Cao, Y., Qin, S.J., Wen, Q.Y.: Local indistinguishability of orthogonal product states. Phys. Rev. A 93, 012314 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  28. Xu, G.B., Yang, Y.H., Wen, Q.Y., Qin, S.J., Gao, F.: Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system. Sci. Rep. 6, 31048 (2016)

    Article  ADS  Google Scholar 

  29. Zhang, X.Q., Weng, J., Tan, X.Q., Luo, W.Q.: Indistinguishability of pure orthogonal product states by LOCC. Quantum Inf. Process. 16, 168 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  30. Xu, G.B., Jiang, D.H.: Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system. Quantum Inf. Process. 20, 128 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  31. Zhang, Z.C., Gao, F., Qin, S.J., Yang, Y.H., Wen, Q.Y.: Nonlocality of orthogonal product states. Phys. Rev. A 92, 012332 (2015)

    Article  ADS  Google Scholar 

  32. Wang, T.Y., Wen, Q.Y., Chen, X.B.: Cryptanalysis and improvement of a multi-user quantum key distribution protocol. Opt. Commun. 283(24), 5261–5263 (2010)

    Article  ADS  Google Scholar 

  33. Chen, X.B., et al.: Cryptanalysis of secret sharing with a single d-level quantum system. Quantum Inf. Process. 17, 225 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  34. Lin, J., Hwang, T.: New circular quantum secret sharing for remote agents. Quantum Inf. Process. 12, 685–697 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  35. Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635–5638 (2000)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  37. Liu, W., Wang, Y.B.: Quantum private comparison based on GHZ entangled states. Int. J. Theor. Phys. 51, 3596–3604 (2012)

    Article  MathSciNet  Google Scholar 

  38. Zhang, W.W., Li, D., Li, Y.B.: Quantum private comparison protocol with W states. Int. J. Theor. Phys. 53, 1723–1729 (2014)

    Article  Google Scholar 

  39. Li, J., Zhou, H.F., Jia, L., Zhang, T.T.: An efficient protocol for the private comparison of equal information based on four-particle entangled W state and Bell entangled states swapping. Int. J. Theor. Phys. 53, 2167–2176 (2014)

    Article  MathSciNet  Google Scholar 

  40. Zha, X.W., Yu, X.Y., Cao, Y., Wang, S.K.: Quantum private comparison protocol with five-particle Cluster states. Int. J. Theor. Phys. 57, 3874–3881 (2018)

    Article  Google Scholar 

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grants No. 62171264), Shandong Provincial Natural Science Foundation (Grants No. ZR2019MF023) and SDUST Research Fund.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Dong-Huan Jiang & Ke-Ke Tang

  2. College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Guang-Bao Xu

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  1. Dong-Huan Jiang
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  2. Ke-Ke Tang
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  3. Guang-Bao Xu
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Correspondence to Guang-Bao Xu.

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Jiang, DH., Tang, KK. & Xu, GB. Novel Quantum Private Comparison Protocol Based on Locally Indistinguishable Product States. Int J Theor Phys 60, 4122–4128 (2021). https://doi.org/10.1007/s10773-021-04962-2

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