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Multi-party quantum summation without a third party based on d-dimensional Bell states

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Abstract

This paper presents a novel n-party quantum summation protocol without the help of a third party via using d-dimensional Bell states. The proposed protocol has inserted decoy photons to prevent various types of the outsider attacks. All participants, respectively, perform the shifting operation to encode their private secrets on quantum particle sequences composed of the first particles of all d-dimensional Bell states. Then, the proposed n-party quantum summation protocol can resist individual attack and \((n-2)\)-party collusion attack. As an example, this paper compares the presented multi-party quantum summation protocol with other schemes in terms of different indicators.

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References

  1. He, G.P.: Quantum private comparison protocol without a third party. Int. J. Quantum Inf. 15(2), 1750014 (2016)

    Article  MathSciNet  Google Scholar 

  2. Wu, W.Q., Cai, Q.Y., Wu, S.M., et al.: Cryptanalysis and improvement of Ye et al’s quantum private comparison protocol. Int. J. Theor. Phys. 58(6), 1892–1900 (2019)

  3. Wu, W.Q., Zhang, H.G.: Cryptanalysis of Zhang et al’s Quantum Private Comparison and the Improvement. Int. J. Theor. Phys. 58(6), 1854–1860 (2019)

  4. Wu, W.Q., Ma, X.X.: Quantum private comparison protocol without a third party. Int. J. Theor. Phys. 59(6), 1854–1865 (2020)

    Article  MathSciNet  Google Scholar 

  5. Xu, T.T., Li, Z.H., Bai, C.M., et al.: A New Improving Quantum Secret Sharing Scheme. Int. J. Theor. Phys. 56, 1–10 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  6. Bai, C.M., Li, Z.H., Xu, T.T., et al.: Quantum secret sharing using the d-dimensional GHZ state. Quantum Inf. Process. 16(3), 59 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Quantum public key cryptosystem based on bell states. Int. J. Theor. Phys. 56(11), 3431–3440 (2017)

    Article  MathSciNet  Google Scholar 

  8. Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Bit-oriented quantum public-key cryptosystem based on bell states. Int. J. Theor. Phys. 57(12), 1–11 (2018)

    MathSciNet  MATH  Google Scholar 

  9. Hillery, M., Ziman, M., Buz̆ek, V., et al.: Towards quantum-based privacy and voting. Phys. Lett. A 349(1–4), 75–81 (2006)

    Article  ADS  Google Scholar 

  10. Chen, X.B., Xu, G., Yang, Y.X., et al.: An efficient protocol for the secure multi-party quantum summation. Int. J. Theor. Phys. 49(11), 2793–2804 (2010)

    Article  MathSciNet  Google Scholar 

  11. Zhang, C., Sun, Z., Huang, Y., et al.: High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 53(3), 933–941 (2014)

    Article  Google Scholar 

  12. Shi, R.H., Mu, Y., Zhong, H., et al.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)

    Article  ADS  Google Scholar 

  13. Zhang, C., Razavi, M., Sun, Z.W., et al.: Improvements on “Secure multi-party quantum summation based on quantum Fourier transform.” Quantum Inf. Process. 18, 336 (2019)

  14. Zhang, C., Situ, H., Huang, Q., et al.: Multi-party quantum summation with a single d-level quantum system. Int. J. Quantum Inf. 17(03), 1154–652 (2019)

    Article  MathSciNet  Google Scholar 

  15. Zhang, C., Sun, Z.W., Huang, X., et al.: Three-party quantum summation without a trusted third party. Int. J. Quantum Inf. 13(2), 1550011 (2015)

    Article  MathSciNet  Google Scholar 

  16. Zhang, C., Situ, H., Huang, Q., et al.: Multi-party quantum summation without a trusted third party based on single particles. Int. J. Quantum Inf. 15(2), 1750010 (2017)

    Article  MathSciNet  Google Scholar 

  17. Yang, H.Y., Ye, T.Y.: Secure multi-party quantum summation based on quantum Fourier transform. Quantum Inf. Process. 17(6), 129 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  18. Wu, W.Q., Zhang, H.G.: A quantum query algorithm for computing the degree of a perfect nonlinear Boolean function. Quantum Inf. Process. 18(3), 62 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  19. 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, pp. 175–179 (1984)

  20. Gao, F., Qin, S.J., Wen, Q.Y., et al.: A simple participant attack on the Bradler-Dusek protocol. Quantum Inf. Comput. 7(4), 329–334 (2007)

    MathSciNet  MATH  Google Scholar 

  21. Liu, B., Xiao, D., Jia, H.Y., et al.: Collusive attacks to circle-type multi-party quantum key agreement protocols. Quantum Inf. Process. 15, 2113–2124 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  22. Zhang, C., Razavi, M., Sun, Z.W., et al.: Multi-party quantum summation based on quantum teleportation. Entropy 21(7), 719 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  23. Zhang, C., Sun, Z., Huang, Y., et al.: High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 53(3), 933–941 (2014)

    Article  Google Scholar 

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Acknowledgements

The authors are supported by the Natural Science Foundation of HeBei Province Nos. F2021201199, Science and technology research project of Hebei higher education Nos. ZD2021011.

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Correspondence to WanQing Wu or XiaoXue Ma.

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Wu, W., Ma, X. Multi-party quantum summation without a third party based on d-dimensional Bell states. Quantum Inf Process 20, 200 (2021). https://doi.org/10.1007/s11128-021-03142-9

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