Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

A Note on the Instantiability of the Quantum Random Oracle

  • Conference paper
  • First Online:
Post-Quantum Cryptography (PQCrypto 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12100))

Included in the following conference series:

Abstract

In a highly influential paper from fifteen years ago [10], Canetti, Goldreich, and Halevi showed a fundamental separation between the Random Oracle Model (ROM) and the standard model. They constructed a signature scheme which can be proven secure in the ROM, but is insecure when instantiated with any hash function (and thus insecure in the standard model). In 2011, Boneh et al. defined the notion of the Quantum Random Oracle Model (QROM), where queries to the random oracle may be made in quantum superposition. Because the QROM generalizes the ROM, a proof of security in the QROM is stronger than one in the ROM. This leaves open the possibility that security in the QROM could imply security in the standard model. In this work, we show that this is not the case, and that security in the QROM cannot imply standard-model security. We do this by showing that the original schemes that show a separation between the standard model and the ROM are also secure in the QROM. We consider two schemes that establish such a separation, one with length-restricted messages, and one without, and show both to be secure in the QROM. Our results give further understanding to the landscape of proofs in the ROM versus the QROM or standard model, and point towards the QROM and ROM being much closer to each other than either is to standard model security.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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.

    We assume a canonical encoding of functions into binary strings, under which s is the description of a function. Complexity is measured under security parameter \(\lambda \).

  2. 2.

    According to Google Scholar, [4] has a citation count at 5089 (November 2019), which would be ranked top 20 at a (dated) list of most cited computer science papers [12].

References

  1. Ambainis, A., Hamburg, M., Unruh, D.: Quantum security proofs using semi-classical oracles. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 269–295. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_10

    Chapter  Google Scholar 

  2. Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems: the hardness of quantum rewinding. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pp. 474–483. IEEE (2014)

    Google Scholar 

  3. Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid-encryption problem. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_11

    Chapter  Google Scholar 

  4. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM (1993)

    Google Scholar 

  5. Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0053428

    Chapter  Google Scholar 

  6. Bernstein, D.J., Hülsing, A., Kölbl, S., Niederhagen, R., Rijneveld, J., Schwabe, P.: The SPHINCS\(^{+}\) signature framework. In: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS 2019, pp. 2129–2146 (2019)

    Google Scholar 

  7. 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 

  8. Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching (1996). arXiv:quant-ph/9605034

  9. Canetti, R., Goldreich, O., Halevi, S.: On the random-oracle methodology as applied to length-restricted signature schemes. In: Theory of Cryptography Conference, TCC 2004, pp. 40–57 (2004)

    Google Scholar 

  10. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004). A preliminary version appeared in STOC 1998

    Article  MathSciNet  Google Scholar 

  11. Chiesa, A., Manohar, P., Spooner, N.: Succinct arguments in the quantum random oracle model. Cryptology ePrint Archive, Report 2019/834 (2019). https://eprint.iacr.org/2019/834

  12. CiteseerX: Most cited computer science citations (2015). https://citeseerx.ist.psu.edu/stats/citations

  13. Don, J., Fehr, S., Majenz, C., Schaffner, C.: Security of the Fiat-Shamir transformation in the quantum random-oracle model. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 356–383. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_13

    Chapter  MATH  Google Scholar 

  14. Eaton, E.: Leighton-Micali hash-based signatures in the quantum random-oracle model. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 263–280. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_13

    Chapter  Google Scholar 

  15. Eaton, E., Song, F.: Making existential-unforgeable signatures strongly unforgeable in the quantum random-oracle model. In: 10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015. LIPIcs, vol. 44, pp. 147–162. Schloss Dagstuhl (2015)

    Google Scholar 

  16. 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 

  17. Goldwasser, S., Kalai, Y.T.: On the (in) security of the Fiat-Shamir paradigm. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 102–113. IEEE (2003)

    Google Scholar 

  18. Hallgren, S., Smith, A., Song, F.: Classical cryptographic protocols in a quantum world. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 411–428. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_23

    Chapter  Google Scholar 

  19. Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_12

    Chapter  MATH  Google Scholar 

  20. Hülsing, A., Rijneveld, J., Song, F.: Mitigating multi-target attacks in hash-based signatures. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 387–416. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_15

    Chapter  Google Scholar 

  21. 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 

  22. Kiltz, E., O’Neill, A., Smith, A.: Instantiability of RSA-OAEP under chosen-plaintext attack. J. Cryptol. 30(3), 889–919 (2017). https://doi.org/10.1007/s00145-016-9238-4

    Article  MathSciNet  MATH  Google Scholar 

  23. Koblitz, N., Menezes, A.J.: The random oracle model: a twenty-year retrospective. Des. Codes Cryptogr. 77(2), 587–610 (2015). https://doi.org/10.1007/s10623-015-0094-2

    Article  MathSciNet  MATH  Google Scholar 

  24. Maurer, U., Renner, R., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_2

    Chapter  Google Scholar 

  25. Micali, S.: Computationally sound proofs. SIAM J. Comput. 30(4), 1253–1298 (2000)

    Article  MathSciNet  Google Scholar 

  26. Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_8

    Chapter  Google Scholar 

  27. NIST: Post-quantum cryptography (2019). https://csrc.nist.gov/Projects/post-quantum-cryptography

  28. Ben Sasson, E., et al.: Zerocash: decentralized anonymous payments from bitcoin. In: 2014 IEEE Symposium on Security and Privacy, pp. 459–474. IEEE (2014)

    Google Scholar 

  29. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  30. 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 

  31. Zhandry, M.: How to construct quantum random functions. In: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pp. 679–687. IEEE (2012)

    Google Scholar 

  32. Zhandry, M.: A note on the quantum collision and set equality problems. Quantum Inf. Comput. 15(7–8), 557–567 (2015)

    MathSciNet  Google Scholar 

  33. Zhandry, M.: How to record quantum queries, and applications to quantum indifferentiability. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 239–268. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_9

    Chapter  Google Scholar 

Download references

Acknowledgments

E.E. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) for grant 401230696. F.S. acknowledges the support by the National Science Foundation.

Author information

Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Edward Eaton

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, USA

    Fang Song

Authors
  1. Edward Eaton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edward Eaton .

Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Jintai Ding

  2. Inria, Paris, France

    Jean-Pierre Tillich

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Eaton, E., Song, F. (2020). A Note on the Instantiability of the Quantum Random Oracle. In: Ding, J., Tillich, JP. (eds) Post-Quantum Cryptography. PQCrypto 2020. Lecture Notes in Computer Science(), vol 12100. Springer, Cham. https://doi.org/10.1007/978-3-030-44223-1_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-44223-1_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-44222-4

  • Online ISBN: 978-3-030-44223-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation