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(Tightly) QCCA-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model

  • Keita XagawaEmail author
  • Takashi Yamakawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11505)

Abstract

This paper studies indistinguishability against quantum chosen-ciphertext attacks (IND-qCCA security) of key-encapsulation mechanisms (KEMs) in quantum random oracle model (QROM). We show that the SXY conversion proposed by Saito, Yamakawa, and Xagawa (EUROCRYPT 2018) and the HU conversion proposed by Jiang, Zhang, and Ma (PKC 2019) turn a weakly-secure deterministic public-key encryption scheme into an IND-qCCA-secure KEM scheme in the QROM. The proofs are very similar to that for the IND-CCA security in the QROM, easy to understand, and as tight as the original proofs.

Keywords

Tight security Quantum chosen-ciphertext security Post-quantum cryptography KEM 

Notes

Acknowledgments

We would like to thank Haodong Jiang and anonymous reviewers of PQCrypto 2019 for insightful comments.

References

  1. [ARU14]
    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 2014Google Scholar
  2. [ATTU16]
    Anand, M.V., Targhi, E.E., Tabia, G.N., Unruh, D.: Post-quantum security of the CBC, CFB, OFB, CTR, and XTS modes of operation. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 44–63. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-29360-8_4CrossRefzbMATHGoogle Scholar
  3. [BCHK07]
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)MathSciNetCrossRefGoogle Scholar
  4. [BDF+11]
    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_3CrossRefzbMATHGoogle Scholar
  5. [BZ13a]
    Boneh, D., Zhandry, M.: Quantum-secure message authentication codes. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 592–608. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_35CrossRefGoogle Scholar
  6. [BZ13b]
    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_21CrossRefzbMATHGoogle Scholar
  7. [CJL+16]
    Chen, L., et al.: Report on post-quantum cryptography. Technical report, National Institute of Standards and Technology (NIST) (2016)Google Scholar
  8. [DFNS14]
    Damgård, I., Funder, J., Nielsen, J.B., Salvail, L.: Superposition attacks on cryptographic protocols. In: Padró, C. (ed.) ICITS 2013. LNCS, vol. 8317, pp. 142–161. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-04268-8_9CrossRefGoogle Scholar
  9. [FO13]
    Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. J. Cryptol. 26(1), 80–101 (2013)MathSciNetCrossRefGoogle Scholar
  10. [GHS16]
    Gagliardoni, T., Hülsing, A., Schaffner, C.: Semantic security and indistinguishability in the quantum world. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 60–89. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_3CrossRefzbMATHGoogle Scholar
  11. [Gro96]
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th ACM STOC, pp. 212–219. ACM Press, May 1996Google Scholar
  12. [HHK17]
    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_12CrossRefzbMATHGoogle Scholar
  13. [HRS16]
    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_15CrossRefGoogle Scholar
  14. [JZC+18]
    Jiang, H., Zhang, Z., Chen, L., Wang, H., Ma, Z.: IND-CCA-secure key encapsulation mechanism in the quantum random oracle model, revisited. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 96–125. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96878-0_4CrossRefGoogle Scholar
  15. [JZM19]
    Jiang, H., Zhang, Z., Ma, Z.: Key encapsulation mechanism with explicit rejection in the quantum random oracle model. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 618–645. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-17259-6_21CrossRefGoogle Scholar
  16. [KLLN16]
    Kaplan, M., Leurent, G., Leverrier, A.,  Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 207–237. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53008-5_8CrossRefGoogle Scholar
  17. [KLS18]
    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_18CrossRefzbMATHGoogle Scholar
  18. [KM12]
    Kuwakado, H., Morii, M.: Security on the quantum-type even-mansour cipher. In: Proceedings of the International Symposium on Information Theory and its Applications, ISITA 2012, Honolulu, HI, USA, 28–31 October 2012, pp. 312–316. IEEE (2012)Google Scholar
  19. [NC00]
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  20. [Sho97]
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefGoogle Scholar
  21. [Sim97]
    Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)MathSciNetCrossRefGoogle Scholar
  22. [SXY18]
    Saito, T., Xagawa, K., Yamakawa, T.: Tightly-secure key-encapsulation mechanism in the quantum random oracle model. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 520–551. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78372-7_17CrossRefzbMATHGoogle Scholar
  23. [Zha12]
    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_44CrossRefzbMATHGoogle Scholar
  24. [Zha18]
    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

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesMusashino-shiJapan

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