Security analysis with improved design of post-confirmation mechanism for quantum sealed-bid auction with single photons

  • Ke-Jia Zhang
  • Leong-Chuan Kwek
  • Chun-Guang Ma
  • Long Zhang
  • Hong-Wei Sun
Article
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Abstract

Quantum sealed-bid auction (QSA) has been widely studied in quantum cryptography. For a successful auction, post-confirmation is regarded as an important mechanism to make every bidder verify the identity of the winner after the auctioneer has announced the result. However, since the auctioneer may be dishonest and collude with malicious bidders in practice, some potential loopholes could exist. In this paper, we point out two types of collusion attacks for a particular post-confirmation technique with EPR pairs. And it is not difficult to see that there exists no unconditionally secure post-confirmation mechanism in the existing QSA model, if the dishonest participants have the ability to control multiparticle entanglement. In the view of this, we note that some secure implementation could exist if the participants are supposed to be semi-quantum, i.e., they can only control single photons. Finally, two potential methods to design post-confirmation mechanism are presented in this restricted scenario.

Keywords

Quantum sealed-bid auction Post-confirmation Single photons 

Notes

Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant Nos. 11647128, 61472097; the Natural Science Foundation of Heilongjiang Province under Grant Nos. A2016007; the China Scholarship Council (Grant No. 201607320084); Youth Foundation of Heilongjiang University under Grant No. QL201501 and Hei Long Jiang Postdoctoral Foundation from December, 2017.

References

  1. 1.
    Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Grover, L.K.: A fast quantum mechanical algorithm for database search, quant-ph/9605043v3 (1996)Google Scholar
  3. 3.
    Gisin, N., Ribordy, G., Tittel, W., et al.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)ADSMATHCrossRefGoogle Scholar
  4. 4.
    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, New York (1984)Google Scholar
  5. 5.
    Ekert, A.K.: Quantum cryptography based on bell theorem. Phys. Rev. Lett. 67, 661–663 (1991)ADSMathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)ADSMathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Bennett, C.H., Brassard, G., et al.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)ADSMathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gao, F., Guo, F.Z., Wen, Q.Y., et al.: Quantum key distribution without alternative measurements and rotations. Phys. Lett. A 349, 53–58 (2006)ADSMATHCrossRefGoogle Scholar
  9. 9.
    Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648–651 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    Hillery, M., Buz\(\breve{e}\)k, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)Google Scholar
  11. 11.
    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    Chen, X.B., Niu, X.X., Zhou, X.J., Yang, Y.X.: Multi-party quantum secret sharing with the single-particle quantum state to encode the information. Quantum Inf. Proc. 12(1), 365–380 (2013)ADSMathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    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)ADSCrossRefGoogle Scholar
  15. 15.
    Lin, S., Wen, Q.Y., Zhu, F.C.: Quantum secure direct communication with X-type entangled states. Phys. Rev. A 78, 064304 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Gottesman, D., Chuang, I.: Quantum digital signatures, quant-ph/0105032v2 (2001)Google Scholar
  17. 17.
    Zeng, G.H., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79, 054307 (2009)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Zou, X.F., Qiu, D.W.: Security analysis and improvements of arbitrated quantum signature schemes. Phys. Rev. A 82, 042325 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    Yang, Y.G., Wang, Y., Teng, Y.W., Chai, H.P., Wen, Q.Y.: Scalable arbitrated quantum signature of classical messages with multi-signers. Commun. Theor. Phys. 54, 84 (2010)ADSMATHCrossRefGoogle Scholar
  21. 21.
    Wang, T.Y., Wei, Z.L.: One-time proxy signature based on quantum cryptography. Quantum Inf. Proc. 11(2), 455–463 (2012)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Chen, X.B., Xu, G., Niu, X.X., Wen, Q.Y., Yang, Y.X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement. Opt. Commun. 283(7), 1561–1565 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Proc. 11(2), 373–384 (2012)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    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(5), 055305 (2009)ADSMathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Yang, Y.G., Cao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scr. 80(6), 065002 (2009)ADSMATHCrossRefGoogle Scholar
  26. 26.
    Liu, W., Wang, Y.B., Jiang, Z.T.: An efficient protocol for the quantum private comparison of equality with \(W\) state. Opt. Commun. 284(12), 3160–3163 (2011)ADSGoogle Scholar
  27. 27.
    Liu, B., Gao, F., Jia, H.Y., Huang, W., Zhang, W.W., Wen, Q.Y.: Efficient quantum private comparison employing single photons and collective detection. Quantum Inf. Proc. 12(2), 887–897 (2013)ADSMathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Wang, Q.L., Yu, C.H., Gao, F., Qi, H.Y., Wen, Q.Y.: Self-tallying quantum anonymous voting. Phys. Rev. A 94, 022333 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    Bao, N., Halpern, N.Y.: Quantum voting and violation of Arrow’s impossibility theorem. Phys. Rev. A 95, 062306 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    Naseri, M.: Secure quantum sealed-bid auction. Opt. Commun. 282, 1939 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    Zhao, Z.W., Naseri, M., Zheng, Y.Q.: Secure quantum sealed-bid auction with post-confirmation. Opt. Commun. 283(16), 3194–3197 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Wang, Z.Y.: Quantum secure direct communication and quantum sealed-bid auction with EPR pairs. Commun. Theor. Phys. 54(6), 997–1002 (2010)ADSMATHCrossRefGoogle Scholar
  33. 33.
    Liu, W.J., Wang, H.B., Yuan, G.L., Xu, Y., Chen, Z.Y., An, X.X., Ji, F.G., Gnitou, G.T.: Multiparty quantum sealed-bid auction using single photons as message carrier. Quantum Inf. Proc. 15, 869–879 (2016)ADSMathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Yang, Y.G., Naseri, M., Wen, Q.Y.: Improved secure quantum sealed-bid auction. Opt. Commun. 282(20), 4167–4170 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    Qin, S.J., Gao, F., Wen, Q.Y., Meng, L.M., Zhu, F.C.: Cryptanalysis and improvement of a secure quantum sealed-bid auction. Opt. Commun. 282(19), 4014–4016 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    Liu, Y.M., Wang, D., Liu, X.S., Zhang, Z.J.: Revisiting Naseri’s secure quantum sealed-bid auction. Int. J. Quantum Inf. 7(6), 1295–1301 (2009)MATHCrossRefGoogle Scholar
  37. 37.
    Zheng, Y.Q., Zhao, Z.W.: Comment on: secure quantum sealed-bid auction. Opt. Commun. 282(20), 4182 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    He, L.B., Huang, L.S., Yang, W., Xu, R., Han, D.Q.: Cryptanalysis and melioration of secure quantum sealed-bid auction with post-confirmation. Quantum Inf. Proc. 11(6), 1359–1369 (2012)ADSMathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    Luo, Y., Zhao, Z.W., Zhao, Z.J., Long, H.M., Su, W., Yang, Y.X.: The loophole of the improved secure quantum sealed-bid auction with post-confirmation and solution. Quantum Inf. Proc. 12(1), 295–302 (2013)ADSMATHCrossRefGoogle Scholar
  40. 40.
    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(9), 3147–3153 (2014)MATHCrossRefGoogle Scholar
  41. 41.
    Liu, W.J., Wang, F., Ji, S., Qu, Z.-G., Wang, X.-J.: Attacks and improvement of quantum sealed-bid auction with EPR pairs. Commun. Theor. Phys. 61(6), 686–690 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    Lo, H.K., Chau, H.F.: Is quantum bit commitment really possible? Phys. Rev. Lett. 78, 3410 (1997)ADSCrossRefGoogle Scholar
  43. 43.
    Sharma, R.D., Thapliyal, K., Pathak, A.: Quantum sealed-bid auction using a modified scheme for multiparty circular quantum key agreement. Quantum Inf. Proc. 16, 169 (2017)ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Ke-Jia Zhang
    • 1
    • 2
    • 3
  • Leong-Chuan Kwek
    • 3
    • 4
    • 5
  • Chun-Guang Ma
    • 1
  • Long Zhang
    • 2
  • Hong-Wei Sun
    • 2
  1. 1.School of Computer Science and TechnologyHarbin Engineering UniversityHarbinChina
  2. 2.School of Mathematical ScienceHeilongjiang UniversityHarbinChina
  3. 3.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  4. 4.MajuLabCNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654SingaporeSingapore
  5. 5.National Institute of EducationNanyang Technological UniversitySingaporeSingapore

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