Skip to main content
Log in

A Trusted Third-Party E-Payment Protocol Based on Locally Indistinguishable Orthogonal Product States

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We propose an electronic payment (E-payment) protocol with a trusted third-party. Quantum key distribution protocol, single-particle unitary operation, one-time pad and orthogonal product states (OPSs) which are locally indistinguishable, are used to ensure the protocol’s security. In our protocol, the information that needs to be transmitted is encoded as a quantum sequence of OPSs that cannot be precisely discriminated by local operations and classical communication (LOCC). All the particles of each OPS are transmitted in a separate way, which can guarantee the protocol’s security. In addition, once there is a dispute among the participants, a trusted third party Trent will resolve the dispute.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Chaum, D., Heyst, E.: Group signatures, advances in cryptology-Eurocrypt91. In: LNCS 547, pp 257–265. Springer, Berlin (1991)

  2. Maitland, G., Boyd, C.: Fair electronic cash based on a group signature scheme, ICICS 2001. In: LNCS 2229, pp 461–465. Springer, Berlin (2001)

  3. Canard, S., Traor, J.: On fair E-cash systems based on group signature schemes, ACISP 2003. In: LNCS 2727, pp 237–248. Springer, Berlin (2003)

  4. Traor, J.: Group signatures and their relevance to privacy-protecting offline electronic cash systems, ACISP 1999. In: LNCS 1587, pp 228–243. Springer, Berlin (1999)

  5. Qiu, W., Chen, K., Gu, D.: A new off-line privacy protecting E-cash system with revocable anonymity, ISC 2002. In: LNCS 2433, pp 177–190. Springer, Berlin (2002)

  6. Chaum, D.: Blind signature for untraceable payments. In: Advances in Cryptology Proceeding of Crypto82, pp 199–203. Springer, New York (1983)

  7. Wen, X.J., Nie, Z.: An E-payment system based on quantum blind and group signature. Phys. Scr. 82(6), 5468–5478 (2010)

    Google Scholar 

  8. Wen, X.J., Chen, Y.Z., Fang, J.B.: An inter-bank E-payment protocol based on quantum proxy blind signature. Quantum Inf. Process. 12(1), 549–558 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  9. Cai, X.Q., Wei, C.Y.: Cryptanalysis of an inter-bank E-payment protocol based on quantum proxy blind signature. Quantum Inf. Process. 12(4), 1651–1657 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  10. Zhou, R.G., Li, W., Huan, T.T., et al.: An online banking system based on quantum cryptography communication. Int. J. Theor. Phys. 53(7), 1–14 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  11. Zhang, J.Z., Yang, Y.Y., Xie, S.C.: A third-party E-payment protocol based on quantum group blind signature. Int. J. Theor. Phys. 56(9), 2981–2989 (2017)

    Article  MathSciNet  Google Scholar 

  12. Shao, A.X., Zhang, J.Z., Xie, S.C.: An E-payment protocol based on quantum multi-proxy blind signature. Int. J. Theor. Phys. 56(4), 1241–1248 (2017)

    Article  Google Scholar 

  13. Niu, X.F., Zhang, J.Z., Xie, S.C., Chen, B.Q.: A third-party E-payment protocol based on quantum multi-proxy blind signature. Int. J. Theor. Phys. 57(8), 2563–2573 (2018)

    Article  MathSciNet  Google Scholar 

  14. Guo, X., Zhang, J.Z., Xie, S.C.: A trusted third-party E-payment protocol based on quantum blind signature without entanglement. Int. J. Theor. Phys. 57(9), 2657–2664 (2018)

    Article  Google Scholar 

  15. Zhang, J.L., Hu, M.S., Jia, Z.J., et al.: A novel E-payment protocol implented by blockchain and quantum signature. Int. J. Theor. Phys. 58(4), 1315–1325 (2019)

    Article  MathSciNet  Google Scholar 

  16. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441–444 (2000)

    Article  ADS  Google Scholar 

  17. Mayers, D.: Unconditional security in quantum cryptography. J. ACM. 48(3), 351–406 (2001)

    Article  MathSciNet  Google Scholar 

  18. Inamon, H., Lutkenhaus, N., Mayers, D.: Unconditional security of practical quantum key distribution. Eur. Phys. J. D. 41(3), 599–627 (2007)

    Article  ADS  Google Scholar 

  19. Gao, F., Qin, S.J., Guo, F.Z., et al.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84(2), 022344 (2011)

    Article  ADS  Google Scholar 

  20. Xu, G.B., Wen, Q.Y., Qin, S.J., et al.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93(3), 032341 (2016)

    Article  ADS  Google Scholar 

  21. Cao, T.Q., Yang, Y.H., et al.: Minimal number of runs and the sequential scheme for local discrimination between special unitary operations. Sci. Rep. 6, 26696 (2016)

    Article  ADS  Google Scholar 

  22. Xu, G.B., Wen, Q.Y., Gao, F., Qin, S.J., Zuo, H.J.: Local indistinguishability of multipartite orthogonal product bases. Quantum Inf. Process. 16, 276 (2017)

    Article  ADS  Google Scholar 

  23. Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Quantum key agreement with EPR pairs and single-particle measurements. Quantum Inf. Process. 13(3), 649–663 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. Zhang, J.L., Zhang, J.Z., Xie, S.C.: Improvement of a quantum proxy blind signature scheme. Int. J. Theor. Phys. 57(6), 1612–1621 (2018)

    Article  MathSciNet  Google Scholar 

  25. Tian, J.H., Zhang, J.Z., Li, Y.P.: A quantum multi-proxy blind signature scheme based on genuine four-qubit entangled state. Int. J. Theor. Phys. 55(2), 809–816 (2016)

    Article  MathSciNet  Google Scholar 

  26. Jiang, D.H., Xu, Y.L., Xu, G.B.: Arbitrary quantum signature based on local indistinguishability of orthogonal product states. Int. J. Theor. Phys. 58(3), 1036–1045 (2019)

    Article  MathSciNet  Google Scholar 

  27. Jiang, D.H., Wang, X.J., Xu, G.B., Lin, J.Q.: A denoising-decomposition model combining TV minimisation and fractional derivatives. East Asia J. Appl. Math. 8, 447–462 (2018)

    Article  Google Scholar 

  28. Liu, H.N., Liang, X.Q., Jiang, D.H., Zhang, Y.H., Xu, G.B.: Multi-party quantum key agreement protocol with bell states and single particles. Int. J. Theor. Phys. 58(5), 1659–1666 (2019)

    Article  Google Scholar 

  29. Jiang, D.H., Xu, G.B.: Multiparty quantum key agreement protocol based on locally indistinguishable orthogonal product states. Quantum Inf. Process. 17, 180 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. Liang, X.Q., Wu, Y.L., Zhang, Y.H., Wang, S.S., Xu, G.B.: Quantum multi-proxy blind signature scheme based on four-qubit cluster states. Int. J. Theor. Phys. 58(1), 31–39 (2019)

    Article  Google Scholar 

  31. Jiang, D.H., Wang, J., Liang, X.Q., et al.: Quantum voting scheme based on locally indistinguishable orthogonal product states. Int. J. Theor. Phys. 59, 436–444 (2020)

    Article  MathSciNet  Google Scholar 

  32. He, Y.F., Ma, W.P.: Three-party quantum secure direct communication against collective noise. Quantum Inf. Process. 16, 252 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  33. Jiang, D.H., Hu, Q.Z., Liang, X.Q., Xu, G.B.: A novel quantum multi-signature protocol based on locally indistinguishable orthogonal product states. Quantum Inf. Process. 18, 268 (2019)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by Shandong Provincial Natural Science Foundation (Grants No. ZR2019MF023), National Natural Science Foundation of China (Grants No. 61701343), Open Foundation of State Key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2019-2-01) and SDUST Research Fund.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guang-Bao Xu.

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

Jiang, DH., Hu, QZ., Liang, XQ. et al. A Trusted Third-Party E-Payment Protocol Based on Locally Indistinguishable Orthogonal Product States. Int J Theor Phys 59, 1442–1450 (2020). https://doi.org/10.1007/s10773-020-04413-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04413-4

Keywords

Navigation