Skip to main content
SpringerLink
Log in

A cost-effective quantum protocol for secure multi-party multiplication

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The secure multi-party quantum multiplication is one of the primitive operations in quantum cryptography that plays an important role to design complex quantum protocols like comparison, sorting, e-voting, etc. The existing multi-party quantum multiplication protocols are efficient, but they have some security issues as these protocols have approach of (n, n) threshold. In this paper, we propose a quantum protocol for secure multi-party multiplication based on the threshold approach of (t, n), where t out of n participants can execute it efficiently. This protocol can execute efficiently if the number of secrets is more than the the number of participants because the secrets are shared among the players using the secret sharing. Moreover, the proposed protocol is more cost-effective and secure as compared to the existing protocols.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ma, L., Chang, T., Mink, A., Slattery, O., Hershman, B., Tang, X.: Experimental demonstration of a detection-time-bin-shift polarization encoding quantum key distribution system. IEEE Commun. Lett. 12(6), 459–461 (2008)

    Article  Google Scholar 

  2. Song, D., Chen, D.: Quantum key distribution based on random grouping bell state measurement. IEEE Communications Letters (2020)

  3. Shi, R.H.: Useful equations about bell states and their applications to quantum secret sharing. IEEE Commun. Lett. 24(2), 386–390 (2019)

    Article  Google Scholar 

  4. Mashhadi, S.: General secret sharing based on quantum fourier transform. Quantum Inform. Process. 18(4), 114 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  5. Sutradhar, K., Om, H.: Efficient quantum secret sharing without a trusted player. Quantum Inform. Process. 19(2), 73 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  6. Weinstein, Y.S., Pravia, M., Fortunato, E., Lloyd, S., Cory, D.G.: Implementation of the quantum fourier transform. Phys. Rev. Lett. 86(9), 1889 (2001)

    Article  ADS  Google Scholar 

  7. Emerson, J., Weinstein, Y.S., Saraceno, M., Lloyd, S., Cory, D.G.: Pseudo-random unitary operators for quantum information processing. Science 302(5653), 2098–2100 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  8. Zarmehi, F., Houshmand, M.: Controlled bidirectional quantum secure direct communication network using classical xor operation and quantum entanglement. IEEE Commun. Lett. 20(10), 2071–2074 (2016)

    Article  Google Scholar 

  9. Weinstein, Y.S.: Pseudorandom circuits from clifford-plus-t gates. Phys. Rev. A 88(6), 062303 (2013)

    Article  ADS  Google Scholar 

  10. Weinstein, Y.S.: Quantum-error-correction implementation after multiple gates. Phys. Rev. A 88(1), 012325 (2013)

    Article  ADS  Google Scholar 

  11. Brassard, C., Bennett, C.H.: Quantum cryptography: Public key distribution and coin tossing. In: International conference on computers, systems and signal processing (1984)

  12. Weinstein, Y.S., Chai, D., Xie, N.: Improving ancilla states for quantum computation. Quantum Inform. Process. 15(4), 1445–1453 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  13. Weinstein, Y.S., Hellberg, C.S.: Energetic suppression of decoherence in exchange-only quantum computation. Phys. Rev. A 72(2), 022319 (2005)

    Article  ADS  Google Scholar 

  14. Weinstein, Y.S., Hellberg, C.S.: Effects of symmetries on quantum fidelity decay. Phys. Rev. E 71(3), 035203 (2005)

    Article  ADS  Google Scholar 

  15. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  Google Scholar 

  16. Shu, H., Yu, R., Jiang, W., Yang, W.: Efficient implementation of \( k \)-nearest neighbor classifier using vote count circuit. IEEE Transactions Circ. Syst. II: Express Briefs 61(6), 448–452 (2014)

    Google Scholar 

  17. Cheng, S.T., Wang, C.Y.: Quantum switching and quantum merge sorting. IEEE Trans. Circuits Syst. I: Regular Pap. 53(2), 316–325 (2006)

    Article  MathSciNet  Google Scholar 

  18. Yang, W., Huang, L., Shi, R., He, L.: Secret sharing based on quantum fourier transform. Quantum Inform. Process. 12(7), 2465–2474 (2013)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  20. Sutradhar, K., Om, H.: A generalized quantum protocol for secure multiparty summation. Express Briefs, IEEE Transactions on Circuits and Systems II (2020)

  21. 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 

  22. Lv, S.X., Jiao, X.F., Zhou, P.: Multiparty quantum computation for summation and multiplication with mutually unbiased bases. Int. J. Theor. Phys. 58(9), 2872–2882 (2019)

    Article  MathSciNet  Google Scholar 

  23. Sutradhar, K., Om, H.: Hybrid quantum protocols for secure multiparty summation and multiplication. Sci. Rep. 10(1), 1–9 (2020)

    Article  Google Scholar 

  24. Weinstein, Y.S., Havel, T.F., Emerson, J., Boulant, N., Saraceno, M., Lloyd, S., Cory, D.G.: Quantum process tomography of the quantum fourier transform. J. Chem. Phys. 121(13), 6117–6133 (2004)

    Article  ADS  Google Scholar 

  25. Turner, L.R.: Inverse of the vandermonde matrix with applications (1966)

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Technology (ISM) Dhanbad, Dhanbad, India

    Kartick Sutradhar & Hari Om

Authors
  1. Kartick Sutradhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hari Om
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sutradhar, K., Om, H. A cost-effective quantum protocol for secure multi-party multiplication. Quantum Inf Process 20, 380 (2021). https://doi.org/10.1007/s11128-021-03334-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03334-3

Keywords

Search

Navigation