Skip to main content
Log in

Cryptanalysis and improvement of a quantum communication-based online shopping mechanism

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Recently, Chou et al. (Electron Commer Res 14:349–367, 2014) presented a novel controlled quantum secure direct communication protocol which can be used for online shopping. The authors claimed that their protocol was immune to the attacks from both external eavesdropper and internal betrayer. However, we find that this protocol is vulnerable to the attack from internal betrayer. In this paper, we analyze the security of this protocol to show that the controller in this protocol is able to eavesdrop the secret information of the sender (i.e., the customer’s shopping information), which indicates that it cannot be used for secure online shopping as the authors expected. Accordingly, an improvement of this protocol, which could resist the controller’s attack, is proposed. In addition, we present another protocol which is more appropriate for online shopping. Finally, a discussion about the difference in detail of the quantum secure direct communication process between regular quantum communications and online shopping is given.

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.

Similar content being viewed by others

References

  1. Knill, E., Laflamme, R., Zurek, W.H.: Resilient quantum computation. Science 279, 342–345 (1998)

    Article  ADS  Google Scholar 

  2. Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

    Article  ADS  Google Scholar 

  3. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. Santa Fe (1994)

  4. Bennett, C.H., Brassard, G.. In: Proceedings IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pp. 175–179. IEEE Press, New York (1984)

  5. Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  6. Deng, F.G., Long, G.L.: Bidirectional quantum key distribution protocol with practical faint laser pulses. Phys. Rev. A 70, 012311 (2004)

    Article  ADS  Google Scholar 

  7. Song, S.Y., Wang, C.: Recent development in quantum communication. Chin. Sci. Bull. 57, 4694–4700 (2012)

    Article  Google Scholar 

  8. Liu, B., Gao, F., Wen, Q.Y.: Single-photon multiparty quantum cryptographic protocols with collective detection. IEEE J. Quantum Electron. 47, 1383–1390 (2011)

    Article  ADS  Google Scholar 

  9. Lin, S., Guo, G.D., et al.: Quantum key distribution: defeating collective noise without reducing efficiency. Quantum Inf. Comput. 14, 845–856 (2014)

    MathSciNet  Google Scholar 

  10. Hillery, M., Buzěk, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A. 59, 1829–1834 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  11. Wang, T.Y., Wen, Q.Y., Chen, X.B., Guo, F.Z., Zhu, F.C.: An efficient and secure multiparty quantum secret sharing scheme based on single photons. Opt. Commun. 281, 6130–6134 (2008)

    Article  ADS  Google Scholar 

  12. Yang, Y.G., Teng, Y.W., Chai, H.P., Wen, Q.Y.: Fault-tolerant quantum secret sharing against collective noise. Phys. Scr. 83, 025003 (2011)

    Article  ADS  Google Scholar 

  13. Sun, Y., Deng, J.Z., Qin, S.J.: Quantum secret sharing with bidirectional authentication. Acta Phys. Sin. 57, 4689–4694 (2008)

    MATH  Google Scholar 

  14. Yan, F.L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005)

    Article  ADS  Google Scholar 

  15. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  16. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

    Article  ADS  Google Scholar 

  17. Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68, 042317 (2003)

    Article  ADS  Google Scholar 

  18. Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

    Article  ADS  Google Scholar 

  19. Wang, C., Deng, F.G., Long, G.L.: Multi-step quantum secure direct communication using multi-particle Green–Horne–Zeilinger state. Opt. Commun. 253, 15–20 (2005)

    Article  ADS  Google Scholar 

  20. Huang, W., Wen, Q.Y., Jia, H.Y., Qin, S.J., Gao, F.: Fault tolerant quantum secure direct communication with quantum encryption against collective noise. Chin. Phys. B 21, 100308 (2012)

    Article  ADS  Google Scholar 

  21. Long, G.L., Deng, F.G., Wang, C., Li, X.H., et al.: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys. China 2, 251 (2007)

    Article  ADS  Google Scholar 

  22. Deng, F.G., Li, X.H., Li, C.Y., et al.: Quantum secure direct communication network with Einstein–Podolsky–Rosen pairs. Phys. Lett. A 359, 359–365 (2006)

  23. Zhang, W.W., Gao, F., Liu, B., Wen, Q.Y., Chen, H.: A watermark strategy for quantum images based on quantum fourier transform. Quantum Inf. Process. 12, 793–803 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Zhang, W.W., Gao, F., Liu, B., Jia, H.Y.: A quantum watermark protocol. Int. J. Theor. Phys. 52, 504–513 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. Yang, Y.G., Peng, X., Tian, J., Zhang, H.: Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 13, 1931–1936 (2014)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84, 022344 (2011)

    Article  ADS  Google Scholar 

  27. Zhang, K.J., Song, T.T., Zuo, H.J., Zhang, W.W.: A secure quantum group signature scheme based on Bell states. Phys. Scr. 87, 045012 (2013)

    Article  ADS  Google Scholar 

  28. Liu, B., Gao, F., Jia, H.Y., et al.: Efficient quantum private comparison employing single photons and collective detection. Quantum Inf. Process. 12, 887–897 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  29. Wen, X.J., Liu, Y., Zhou, N.R.: Realizable quantum broadcasting multi-signature scheme. Int. J. Mod. Phys. B 22, 4251–4259 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. 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 

  31. Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11, 373–384 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  32. Li, Y.B., Wen, Q.Y., Gao, F., et al.: Information leak in Liu et al.’s quantum private comparison and a new protocol. Eur. Phys. J. D 66, 110 (2012)

    Article  ADS  Google Scholar 

  33. Zhang, W.W., Li, D., Zhang, K.J., Zuo, H.J.: A quantum protocol for millionaire problem with Bell states. Quantum Inf. Process. 12, 2241–2249 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels. Sci. China Phys. Mech. Astron. 56, 1670–1678 (2013)

    Article  ADS  Google Scholar 

  35. Huang, W., Wen, Q.Y., Liu, B., et al.: Quantum anonymous ranking. Phys. Rev. A 89, 032325 (2014)

    Article  ADS  Google Scholar 

  36. Wen, X.J.: An E-payment system based on quantum group signature. Phys. Scr. 82, 065403–065407 (2010)

    Article  Google Scholar 

  37. Wen, X.J., Nie, Z.: An E-payment system based on quantum blind and group signature. In: Proceedings of International Symposium on Data, Privacy, and E-Commerce, America (2010)

  38. 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, 549–558 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Dense-coding attack on three-party quantum key distribution protocols. IEEE J. Quantum Electron. 47, 630–635 (2011)

    Article  ADS  Google Scholar 

  41. Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Cryptanalysis of a multi-party quantum key agreement protocol with single particles. Quantum Inf. Process. 13, 1651–1657 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  42. Lo, H.K., Ko, T.M.: Some attacks on quantum-based cryptographic protocols. Quantum Inf. Comput. 5, 40–47 (2005)

    MATH  MathSciNet  Google Scholar 

  43. Liu, B., Gao, F., Wen, Q.Y.: Eavesdropping and improvement to multiparty quantum secret sharing with collective eavesdropping-check. Int. J. Theor. Phys. 51, 1211–1223 (2012)

    Article  MATH  Google Scholar 

  44. Gao, F., Guo, F.Z., Wen, Q.Y., Zhu, F.C.: Comment on “experimental demonstration of a quantum protocol for Byzantine agreement and liar detection”. Phys. Rev. Lett. 101, 208901 (2008)

    Article  ADS  Google Scholar 

  45. Gao, F., Wen, Q.Y., Zhu, F.C.: Comment on: “Quantum exam”. Phys. Lett. A 360, 748 (2007)

    Article  ADS  Google Scholar 

  46. Qin, S.J., Gao, F., Guo, F.Z., Wen, Q.Y.: Comment on “Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair”. Phys. Rev. A 82, 036301 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  47. Gisin, N., Fasel, S., Kraus, B., Zbinden, H., Ribordy, G.: Trojan-horse attacks on quantum-key-distribution systems. Phys. Rev. A 73, 022320 (2006)

    Article  ADS  Google Scholar 

  48. Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: A simple participant attack on the brádler-dušek protocol. Quantum Inf. Comput. 7, 329–334 (2007)

    MATH  MathSciNet  Google Scholar 

  49. Wang, Q.L., Zhang, W.W., Su, Q.: Revisiting “The loophole of the improved secure quantum sealed-bid auction with post-confirmation and solution”. Int. J. Theor. Phys. 53, 3147–3153 (2014)

    Article  MATH  Google Scholar 

  50. Wang, Q.L., Zhang, K.J.: Security analysis and improvement of the dining cryptographer problem-based anonymous quantum communication via non-maximally entanglement state analysis. Int. J. Theor. Phys. 54, 106–115 (2015)

    Article  Google Scholar 

  51. Chou, Y.H., Lin, F.J., Zeng, G.J.: An efficient novel online shopping mechanism based on quantum communication. Electron. Commer. Res. 14, 349–367 (2014)

    Article  Google Scholar 

  52. Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351, 23 (2006)

    Article  ADS  MATH  Google Scholar 

  53. Li, X.H., Deng, F.G., Zhou, H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74, 054302 (2006)

    Article  ADS  Google Scholar 

  54. D’Ariano, G.M., Lo Presti, P., Paris, M.G.A.: Using entanglement improves the precision of quantum measurements. Phys. Rev. Lett. 87, 270404 (2001)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by NSFC (Grant Nos. 61272057, 61170270, 61309029), Beijing Higher Education Young Elite Teacher Project (Grant Nos. YETP0475, YETP0477), BUPT Excellent Ph.D. Students Foundation (Grant No. CX201441).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ying-Hui Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, W., Yang, YH. & Jia, HY. Cryptanalysis and improvement of a quantum communication-based online shopping mechanism. Quantum Inf Process 14, 2211–2225 (2015). https://doi.org/10.1007/s11128-015-0958-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-0958-4

Keywords

Navigation