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A Novel Quantum Protocol for Private Set Intersection

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Abstract

Private set intersection(PSI) allows two parties to get all common elements of their private sets without leaking any information about their sets. In this paper, we present a novel PSI protocol which is based on quantum Fourier transform. Correctness analysis shows that our protocol can get the result correctly. And the security of our protocol is also analyzed, it can resist most of outside attacks, such as Trojan horse attack, intercept-resend attack, entanglement-and-measure attack, man-in-the-middle attack and so on. And it also can overcome participant attacks.

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References

  1. Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Proc. of EUROCRYPT, LNCS 3027, Interlaken, Switzerland, pp. 1–19 (2004)

  2. Li, Y., Tygar, J., Hellerstein, J.: Private matching. In: Proceedings of Computer Security in the 21st Century, pp. 25–50 (2005)

  3. Zhan, J., Cabrera, L., Osman, G., Shah, R.: Using private matching for securely querying genomic sequences. In: Proceedings of IEEE Third International Conference on Privacy, Security, Risk and Trust (passat) and Third International Conference On Social Computing (socialcom), pp 1163–1168 (2011)

  4. Chun, J.Y., Hong, D., Jeong, I.R., Lee, D.H.: Privacy-preserving disjunctive normal form operations on distributed sets. Inform. Sci. 231(10), 113–122 (2013)

    Article  MathSciNet  Google Scholar 

  5. Pervez, Z., Awan, A.A., Khattak, A.M., Lee, S., Huh, E.N.: Privacy-aware searching with oblivious term matching for cloud storage. J. Supercomput. 63(2), 538–560 (2013)

    Article  Google Scholar 

  6. Narayanan, A., Thiagarajan, N., Lakhani, M., Hamburg, M., Boneh, D.: Location privacy via private proximity testing. In: Proceedings of the Network and Distributed System Security Symposium, (San Diego, CA USA) (2011)

  7. Wu, M.E., Chang, S.Y., Lu, C.J., Sun, H.M.: A communication-efficient private matching scheme in Client-Server model. Inform. Sci. 275(10), 348–359 (2014)

    Article  MathSciNet  Google Scholar 

  8. Hazay, C., Lindell, Y.: Efficient protocols for set intersection and patten matching with security against malicious and covert adversaries. In: Proceedings of Theory of Cryptography Conference (TCC), New York, USA, LNCS 4948: pp. 155–175 (2008)

  9. Liu, L., Cao, Z.: Private matching protocols without error probability

  10. Kerschbaum, F.: Outsourced private set intersection using homomorphic encryption. In: Proc. ACM ASIACCS, pp. 85–86 (2012)

  11. Shao, Z.Y., Yan, B.: Private set intersection via public key encryption with keywords search. Secur. Commun. Netw. 8(3), 396–402 (2015)

    Article  Google Scholar 

  12. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer SIAM. J. Comput. 26, 1484 (1997)

    MathSciNet  MATH  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, 055305 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  14. Chen, X.B., Xu, G., Niu, X.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)

    Article  ADS  Google Scholar 

  15. Liu, W., Wang, Y.B., Jiang, Z.T.: An efficient protocol for the quantum private comparison of equality with w state. Opt. Commun. 284, 1561–1565 (2011)

    Article  ADS  Google Scholar 

  16. 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 (2011)

    Article  Google Scholar 

  17. Chen, X.B., Xu, G., Yang, Y.X., Wen, Q.Y.: An efficient protocol for the secure multi-party quantum summation. Int. J. Theor. Phys. 49, 2793–2804 (2010)

    Article  MathSciNet  Google Scholar 

  18. Shi, R.H., Mu, Y., Zhong, H., Cui, J., Zhang, S.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)

    Article  ADS  Google Scholar 

  19. Wei, C.Y., et al.: Error Tolerance Bound in QKD-based Quantum Private Query. IEEE J. Sel. Areas Commun. 38, 517–527 (2020)

    Article  Google Scholar 

  20. Gao, F., Qin, S.J., Huang, W., Wen, Q.Y.: Quantum private query: a new kind of practical quantum cryptographic protocols. Sci. China-Phys. Mech. Astron. 62, 070301 (2019)

    Article  Google Scholar 

  21. Wei, C.Y., Cai, X.Q., Liu, B., et al.: A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure. IEEE Trans. Comput. 67, 2–8 (2018)

    Article  MathSciNet  Google Scholar 

  22. Shi, R.H., Mu, Y., Zhong, H., et al.: An efficient quantum scheme for Private Set Intersection. Quantum Inf. Process. 15, 363–371 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  23. Shi, R.H., Zhang, M.W.: A feasible quantum protocol for private set intersection cardinality. IEEE ACCESS 7, 72105–72112 (2019)

    Article  Google Scholar 

  24. Shi, R.H.: Quantum private computation of cardinality of set intersection and union. European Phys. J. D, 72(221) (2018)

  25. Qin, H.W., Tso, R.L., Dai, Y.W.: Quantum secret sharing by using Fourier transform on orbital angular momentum. IET Information Security (2018)

  26. Chaabouni, R, Lipmaa, H, Zhang, B.: A non-interactive range proof with constant communication. In: Proceedings of International Conference on Financial Cryptography and Data Security, Kralendijk, 179–199 (2012)

  27. Gao, F., Qin, S.J., Wen, Q.Y., et al.: A simple participant attack on the Bradler-Dusek protocol. Quantum Inf. Comput. 7, 329 (2007)

    MathSciNet  MATH  Google Scholar 

  28. Qin, S.J., Gao, F., Wen, Q.Y., et al.: Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secretsharing protocol. Phys. Rev. A 76(06), 2007 (2324)

    Google Scholar 

  29. 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)

    Article  ADS  MathSciNet  Google Scholar 

  30. 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)

    Article  ADS  Google Scholar 

  31. 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)

    Article  ADS  Google Scholar 

  32. 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)

    Article  ADS  Google Scholar 

  33. Chen, X.B., Tang, X., Xu, G., Dou, Z., Chen, Y.L., Yang, Y.X.: Cryptanalysis of secret sharing with a single d-level quantum system. Quantum Inf. Process. 17, 225 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  34. Li, L., Shi, R.H.: A Novel and Efficient Quantum Private Comparison Scheme. J. Korean Phys. Soc. 75(1), 15–21 (2019)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported in part by the 2019 National Social Science Foundation Art Major Project, Network Culture Security Research, under Grant 19zd12, in part by the High-Quality and Cutting-Edge Disciplines Construction Project for Universities in Beijing (Internet Information, Communication University of China), in part by the National Natural Science Foundation of China under Grant 61502437 and Grant 61773352, and in part by the Fundamental Research Funds for the Central Universities.

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Wen Liu and Hanwen Yin. The first draft of the manuscript was written by Wen Liu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Wen Liu.

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  • The research didn’t involve animals and human participants.

  • This work was supported in part by the 2019 National Social Science Foundation Art Major Project, Network Culture Security Research, under Grant 19zd12, in part by the High-Quality and Cutting-Edge Disciplines Construction Project for Universities in Beijing (Internet Information, Communication University of China), in part by the National Natural Science Foundation of China under Grant 61502437 and Grant 61773352, and in part by the Fundamental Research Funds for the Central Universities.

  • The authors have no relevant financial or non-financial interests to disclose.

  • The authors have no conflicts of interest to declare that are relevant to the content of this article.

  • All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

  • The authors have no financial or proprietary interests in any material discussed in this article.

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Liu, W., Yin, HW. A Novel Quantum Protocol for Private Set Intersection. Int J Theor Phys 60, 2074–2083 (2021). https://doi.org/10.1007/s10773-021-04824-x

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