Skip to main content
SpringerLink
Log in

Quantum money with mintage supervision

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The quantum unclonable theorem solves the problem of uncounterfeitability in quantum money schemes, however, few of them consider imposing limits on the minting capacity of banks, and thus, they may generate more quantum money than users require or distribute the same currency multiple times for their own benefit. In this paper, a quantum money scheme with supervision is proposed. First, a third-party regulator is introduced to jointly mint and verify the quantum virtual money together with the minter (i.e., bank) and the minter can no longer carry out mintage and verification independently. Second, the regulator is set to be a purely classical party and the minter undertakes most of quantum computing work, which makes it possible for regulator to mint and verify the quantum money through classical channel. Last, the security analysis shows that the proposed quantum money scheme is secure against any polynomial time attackers.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Availability of data and material

All data generated or analyzed during this study are included in this published article

References

  1. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)

    Article  MATH  ADS  Google Scholar 

  2. Dieks, D.G.B.J.: Communication by epr devices. Phys. Lett. A 92(6), 271–272 (1982)

    Article  ADS  Google Scholar 

  3. Park, J.L.: The concept of transition in quantum mechanics. Found. Phys. 1(1), 23–33 (1970)

    Article  ADS  Google Scholar 

  4. Wiesner, S.: Conjugate coding. ACM Sigact News 15(1), 278–288 (1983)

    Article  MATH  Google Scholar 

  5. Nagaj, D., Sattath, O., Brodutch, A., Unruh, D.: An adaptive attack on Wiesner’s quantum money. Quantum Inf. Comput. 16(11), 1048–1070 (2016)

    MathSciNet  Google Scholar 

  6. Lutomirski, A.: An online attack against Wiesner’s quantum money. arXiv preprint arXiv:1010.0256 (2010)

  7. Bennett, C.H., Brassard, G., Breidbart, S., Wiesner, S.: Quantum cryptography, or unforgeable subway tokens. In: Advances in Cryptology, pp. 267-275.Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0602-4_26 (1983)

  8. Mosca, M., Stebila, D.: Uncloneable quantum money. In: Canadian Quantum Information Students Conference (CQISC) (2006)

  9. Ben-David, S., Sattath, O.: Quantum tokens for digital signatures. arXiv preprint arXiv:1609.09047 (2016)

  10. Georgiou, M., Kerenidis, I.: New constructions for quantum money. In: In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015) https://doi.org/10.4230/LIPIcs.TQC.2015.92 (2015)

  11. Pastawski, F., Yao, N.Y., Jiang, L., Lukin, M.D., Cirac, J.I.: Unforgeable noise-tolerant quantum tokens. PNAS 109(40), 16079–16082 (2012). https://doi.org/10.1073/pnas.1203552109

    Article  ADS  Google Scholar 

  12. Gavinsky, D.: Quantum money with classical verification. In: 2012 IEEE 27th Conference on Computational Complexity, pp. 42-52. https://doi.org/10.1109/CCC.2012.10 (2012)

  13. Radian, R., Sattath, O.: Semi-quantum money. J. Cryptol. 35(2), 1–70 (2022). https://doi.org/10.1007/s00145-021-09418-8

    Article  MathSciNet  MATH  Google Scholar 

  14. Brakerski, Z., Christiano, P., Mahadev, U., Vazirani, U., Vidick, T.: A cryptographic test of quantumness and certifiable randomness from a single quantum device. J. ACM 68(5), 1–47 (2021). https://doi.org/10.1145/3441309

    Article  MathSciNet  MATH  Google Scholar 

  15. Aaronson, S.: Quantum copy-protection and quantum money. In: In 2009 24th Annual IEEE Conference on Computational Complexity, pp. 229-242. https://doi.org/10.1109/CCC.2009.42 (2009)

  16. Lutomirski, A., Aaronson, S., Farhi, E., Gosset, D., Hassidim, A., Kelner, J., Shor, P.: Breaking and making quantum money: toward a new quantum cryptographic protocol. arXiv preprint arXiv:0912.3825 (2009)

  17. Farhi, E., Gosset, D., Hassidim, A., Lutomirski, A., Shor, P.: Quantum money from knots. In: In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 276-289. https://doi.org/10.1145/2090236.2090260 (2012)

  18. Mosca, M., Stebila, D.: Quantum coins. Error-correcting codes, finite geometries and cryptography 523, 35–47 (2010)

  19. Zhandry, M.: Quantum lightning never strikes the same state twice. or: quantum money from cryptographic assumptions. J. Cryptol. 34(1), 1–56 (2021). https://doi.org/10.1007/s00145-020-09372-x

    Article  MathSciNet  MATH  Google Scholar 

  20. Coladangelo, A., Sattath, O.: A quantum money solution to the blockchain scalability problem. Quantum 4, 297 (2020)

    Article  Google Scholar 

  21. Raz, R.: A parallel repetition theorem. SIAM J. Comput. 27(3), 763–803 (1998). https://doi.org/10.1145/225058.225181

    Article  MathSciNet  MATH  Google Scholar 

  22. Boneh, D., Zhandry, M.: Quantum-secure message authentication code. In: In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 592-608. https://doi.org/10.1007/978-3-642-38348-9_35 (2013)

  23. Gagliardoni, T., Hlsing, A., Schaffner, C.: Semantic security and indistinguishability in the quantum world. In: In Annual international cryptology conference, pp. 60-89. https://doi.org/10.1007/978-3-662-53015-3_3 (2016)

Download references

Author information

Authors and Affiliations

  1. School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Min Xiao & Lisheng Pi

Authors
  1. Min Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lisheng Pi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lisheng Pi.

Ethics declarations

Consent to participate

All the authors listed have approved the manuscript that is enclosed.

Consent for publication

Informed consent for publication was obtained from all participants.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, M., Pi, L. Quantum money with mintage supervision. Quantum Inf Process 22, 118 (2023). https://doi.org/10.1007/s11128-023-03864-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03864-y

Keywords

Search

Navigation