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Improvements on “Secure multi-party quantum summation based on quantum Fourier transform”

  • Cai ZhangEmail author
  • Mohsen Razavi
  • Zhiwei Sun
  • Haozhen Situ
Article
  • 28 Downloads

Abstract

Recently, a quantum multi-party summation protocol based on the quantum Fourier transform has been proposed (Yang et al. in Quantum Inf Process 17:129, 2018). The protocol claims to be secure against both outside and participant attacks. However, a closer look reveals that the player in charge of generating the required multi-partite entangled states can launch two kinds of attacks to learn about other parties’ private integer strings without being caught. In this paper, we present these attacks and propose countermeasures to make the protocol secure again. The improved protocol not only can resist these attacks but also remove the need for the quantum Fourier transform and encoding quantum operations by participants.

Keywords

Quantum summation Quantum Fourier transform Participant attacks 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61902132, 11647140, 61602316, 61502179, 61472452, 61202398), the Natural Science Foundation of Guangdong Province of China (Grant Nos. 2018A030310147, 2014A030310265), and the Science and Technology Innovation Projects of Shenzhen (No. JCYJ20170818140234295). Mohsen Razavi acknowledges the support of UK EPSRC Grant EP/M013472/1. Cai Zhang is sponsored by the State Scholarship Fund of the China Scholarship Council. All data generated in this paper can be reproduced by the provided methodology.

References

  1. 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, pp. 175–179. IEEE Press, Bangalore (1984)Google Scholar
  2. 2.
    Xu, G., Xiao, K., Li, Z.P., et al.: Controlled secure direct communication protocol via the three-qubit partially entangled set of states. Comput. Mater. Contin.: CMC 58(3), 809–827 (2019)CrossRefGoogle Scholar
  3. 3.
    Chen, X.B., Tang, X., Xu, G., et al.: Cryptanalysis of secret sharing with a single d-level quantum system. Quantum Inf. Process. 17, 225 (2018)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56, 1154 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pp. 643–652 (2002)Google Scholar
  6. 6.
    Chau, H.F.: Quantum-classical complexity-security tradeoff in secure multiparty computations. Phys. Rev. A 61(3), 032308 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A. Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: 47th Annual IEEE Symposium on Foundations of Computer Science, 2006. FOCS’06, pp. 249–260 (2006)Google Scholar
  8. 8.
    Smith, A.: Multi-party Quantum Computation (2010). arXiv:quant-ph/0111030
  9. 9.
    Xu, G., Chen, X.B., Dou, Z., et al.: Novel criteria for deterministic remote state preparation via the entangled six-qubit state. Entropy 18, 267 (2016)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, X.B., Sun, Y.R., Xu, G., et al.: Controlled bidirectional remote preparation of three-qubit state. Quantum Inf. Process. 16, 244 (2017)ADSCrossRefGoogle Scholar
  11. 11.
    Li, J., Chen, X.B., Sun, X.M., et al.: Quantum network coding for multi-unicast problem based on 2d and 3d cluster states. Sci. China Inf. Sci. 59, 042301 (2016)CrossRefGoogle Scholar
  12. 12.
    Chen, X.B., Wang, Y.L., Xu, G., et al.: Quantum network communication with a novel discrete-time quantum walk. IEEE Access 7, 13634–13642 (2019)CrossRefGoogle Scholar
  13. 13.
    Heinrich, S.: Quantum summation with an application to integration. J. Complex. 18(1), 1–50 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Heinrich, S., Novak, E.: On a problem in quantum summation. J. Complex. 19(1), 1–18 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Heinrich, S., Kwas, M., Woźniakowski, H.: Quantum Boolean summation with repetitions in the worst-average setting. In: Niederreiter, H. (ed.) Monte Carlo and Quasi-Monte Carlo Methods, pp. 243–258. Springer, Heidelberg (2004)Google Scholar
  16. 16.
    Du, J.Z., Chen, X.B., Wen, Q.Y., et al.: Secure multiparty quantum summation. Acta Phys. Sin. 56(11), 6214 (2007)MathSciNetGoogle Scholar
  17. 17.
    Huang, W., Wen, Q.Y., Liu, B., et al.: Quantum anonymous ranking. Phys. Rev. A 89(3), 032325 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    Sun, Z., Yu, J., Wang, P., et al.: Quantum private comparison with a malicious third party. Quantum Inf. Process. 14, 2125–2133 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    Wang, Q., Yu, C., Gao, F., et al.: Self-tallying quantum anonymous voting. Phys. Rev. A 94, 022333 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    Ji, Z.X., Zhang, H.G., Wang, H.Z., et al.: Quantum protocols for secure multi-party summation. Quantum Inf. Process. 18(6), 168 (2019)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhang, C., Sun, Z.W., 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)CrossRefGoogle Scholar
  22. 22.
    Liu, W., Wang, Y.B., Fan, W.Q.: An novel protocol for the quantum secure multi-party summation based on two-particle Bell states. Int. J. Theor. Phys. 56(9), 2783–2791 (2017)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhang, C., Razavi, M., Sun, Z., et al.: Quantum summation based on quantum teleportation. Entropy 21(7), 719 (2019)ADSCrossRefGoogle Scholar
  24. 24.
    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(11), 2793 (2010)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zhang, C., Sun, Z.W., Huang, X., et al.: Three-party quantum summation without a trusted third party. Int. J. Quantum Inf. 13(02), 1550011 (2015)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Shi, R.H., Mu, Y., Zhong, H., et al.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Shi, R.H., Zhang, S.: Quantum solution to a class of two-party private summation problems. Quantum Inf. Process. 16(9), 225 (2017)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Yang, H.Y., Ye, T.Y.: Secure multi-party quantum summation based on quantum Fourier transform. Quantum Inf. Process. 17(6), 129 (2018)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Li, C.Y., Zhou, H.Y., Wang, Y., et al.: Secure quantum key distribution network with bell states and local unitary operations. Chin. Phys. Lett. 22(5), 1049–1052 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Li, C.Y., Li, X.H., Deng, F.G., Zhou, P., Liang, Y.J., et al.: Efficient quantum cryptography network without entanglement and quantum memory. Chin. Phys. Lett. 23(11), 2896 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    Gu, J., Hwang, T.: Improvement on “Secure multi-party quantum summation based on quantum Fourier transform” (2019). arXiv:1907.02656

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and InformaticsSouth China Agricultural UniversityGuangzhouChina
  2. 2.School of Electronic and Electrical EngineeringUniversity of LeedsLeedsUK
  3. 3.School of Artificial IntelligenceShenzhen PolytechnicShenzhenChina
  4. 4.Center for Quantum ComputingPeng Cheng LaboratoryShenzhenChina

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