Skip to main content

Revisiting Post-quantum Fiat-Shamir

  • Conference paper
  • First Online:
Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11693))

Included in the following conference series:

Abstract

The Fiat-Shamir transformation is a useful approach to building non-interactive arguments (of knowledge) in the random oracle model. Unfortunately, existing proof techniques are incapable of proving the security of Fiat-Shamir in the quantum setting. The problem stems from (1) the difficulty of quantum rewinding, and (2) the inability of current techniques to adaptively program random oracles in the quantum setting. In this work, we show how to overcome the limitations above in many settings. In particular, we give mild conditions under which Fiat-Shamir is secure in the quantum setting. As an application, we show that existing lattice signatures based on Fiat-Shamir are secure without any modifications.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    2-extractability is often called “special soundness” in the literature.

References

  1. Alwen, J., Krenn, S., Pietrzak, K., Wichs, D.: Learning with rounding, revisited. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 57–74. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_4

    Chapter  Google Scholar 

  2. Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems: the hardness of quantum rewinding. In: 55th FOCS, pp. 474–483. IEEE Computer Society Press, October 2014

    Google Scholar 

  3. Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3

    Chapter  MATH  Google Scholar 

  4. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Denning, D.E., Pyle, R., Ganesan, R., Sandhu, R.S., Ashby, V. (eds.) ACM CCS 93, pp. 62–73. ACM Press, November 1993

    Google Scholar 

  5. Boneh, D., Zhandry, M.: Secure signatures and chosen ciphertext security in a quantum computing world. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 361–379. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_21

    Chapter  MATH  Google Scholar 

  6. Dagdelen, Ö., Fischlin, M., Gagliardoni, T.: The Fiat-Shamir transformation in a quantum world. Cryptology ePrint Archive, Report 2013/245 (2013). http://eprint.iacr.org/2013/245

  7. Ducas, L., et al.: Crystals-dilithium: a lattice-based digital signature scheme. IACR Trans. Cryptographic Hardware Embed. Syst. 2018(1), 238–268 (2018)

    MathSciNet  Google Scholar 

  8. Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12

    Chapter  Google Scholar 

  9. Kiltz, E., Lyubashevsky, V., Schaffner, C.: A concrete treatment of Fiat-Shamir signatures in the quantum random-oracle model. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 552–586. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_18

    Chapter  MATH  Google Scholar 

  10. Lyubashevsky, V.: Lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_43

    Chapter  Google Scholar 

  11. Liu, Q., Zhandry, M.: Revisiting post-quantum Fiat-Shamir. Cryptology ePrint Archive, Report 2019/262 (2019). https://eprint.iacr.org/2019/262

  12. Pointcheval, D., Stern, J.: Provably secure blind signature schemes. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 252–265. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034852

    Chapter  Google Scholar 

  13. Targhi, E.E., Unruh, D.: Quantum security of the Fujisaki-Okamoto and OAEP transforms. Cryptology ePrint Archive, Report 2015/1210 (2015). http://eprint.iacr.org/2015/1210

  14. Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135–152. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_10

    Chapter  Google Scholar 

  15. Unruh, D.: Non-interactive zero-knowledge proofs in the quantum random oracle model. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 755–784. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_25

    Chapter  MATH  Google Scholar 

  16. Unruh, D.: Collapse-binding quantum commitments without random oracles. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 166–195. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_6

    Chapter  Google Scholar 

  17. Unruh, D.: Computationally binding quantum commitments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 497–527. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_18

    Chapter  Google Scholar 

  18. Unruh, D.: Post-quantum security of Fiat-Shamir. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 65–95. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_3

    Chapter  Google Scholar 

  19. Watrous, J.: Zero-knowledge against quantum attacks. In: Kleinberg, J.M. (eds.) 38th ACM STOC, pp. 296–305. ACM Press, May 2006

    Google Scholar 

  20. Zhandry, M.: Secure identity-based encryption in the quantum random oracle model. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 758–775. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_44

    Chapter  MATH  Google Scholar 

  21. Zhandry, M.: How to record quantum queries, and applications to quantum indifferentiability. Cryptology ePrint Archive, Report 2018/276 (2018). https://eprint.iacr.org/2018/276

Download references

Acknowledgements

This work is supported in part by NSF and DARPA. Opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF or DARPA.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qipeng Liu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liu, Q., Zhandry, M. (2019). Revisiting Post-quantum Fiat-Shamir. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11693. Springer, Cham. https://doi.org/10.1007/978-3-030-26951-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26951-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26950-0

  • Online ISBN: 978-3-030-26951-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics