Post-Quantum Security of the Fujisaki-Okamoto and OAEP Transforms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9986)

Abstract

In this paper, we present a hybrid encryption scheme that is chosen ciphertext secure in the quantum random oracle model. Our scheme is a combination of an asymmetric and a symmetric encryption scheme that are secure in a weak sense. It is a slight modification of the Fujisaki-Okamoto transform that is secure against classical adversaries. In addition, we modify the OAEP-cryptosystem and prove its security in the quantum random oracle model based on the existence of a partial-domain one-way injective function secure against quantum adversaries.

Keywords

Quantum Random oracle Indistinguishability against chosen ciphertext attacks 

References

  1. 1.
    Alagic, G., Broadbent, A., Fefferman, B., Gagliardoni, T., Schaffner, C., Jules, M.S.: Computational security of quantum encryption. IACR ePrint 2016/424, April 2016Google Scholar
  2. 2.
    Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems (the hardness of quantum rewinding). In: FOCS 2014, pp. 474–483. IEEE, October 2014Google Scholar
  3. 3.
    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.) Proceedings of the 1st ACM Conference on Computer and Communications Security, CCS 1993, 3–5 November 1993, Fairfax, Virginia, USA, pp. 62–73. ACM (1993)Google Scholar
  4. 4.
    Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995). doi:10.1007/BFb0053428 Google Scholar
  5. 5.
    Ben-Or, M.: Probabilistic algorithms in finite fields. In: 22nd Annual Symposium on Foundations of Computer Science, 28–30 October 1981, Nashville, Tennessee, USA, pp. 394–398. IEEE Computer Society (1981)Google Scholar
  6. 6.
    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). doi:10.1007/978-3-642-25385-0_3 CrossRefGoogle Scholar
  7. 7.
    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). doi:10.1007/978-3-642-40084-1_21 CrossRefGoogle Scholar
  8. 8.
    Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999). doi:10.1007/3-540-48405-1_34 Google Scholar
  9. 9.
    Fujisaki, E., Okamoto, T., Pointcheval, D., Stern, J.: RSA-OAEP is secure under the RSA assumption. J. Cryptology 17(2), 81–104 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001). doi:10.1007/3-540-44647-8_15 CrossRefGoogle Scholar
  12. 12.
    Targhi, E.E., Tabia, G.N., Unruh, D.: Quantum collision-resistance of non-uniformly distributed functions. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 79–85. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29360-8_6 CrossRefGoogle Scholar
  13. 13.
    Unruh, D.: Quantum position verification in the random oracle model. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 1–18. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44381-1_1 CrossRefGoogle Scholar
  14. 14.
    Unruh, D.: Revocable quantum timed-release encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 129–146. Springer, Heidelberg (2014). doi:10.1007/978-3-642-55220-5_8 CrossRefGoogle Scholar
  15. 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). doi:10.1007/978-3-662-46803-6_25 Google Scholar
  16. 16.
    Yuen, H.: A quantum lower bound for distinguishing random functions from random permutations. Quantum Inf. Comput. 14(13–14), 1089–1097 (2014)MathSciNetGoogle Scholar
  17. 17.
    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). doi:10.1007/978-3-642-32009-5_44 CrossRefGoogle Scholar
  18. 18.
    Zhandry, M.: A note on the quantum collision and set equality problems. Quantum Inf. Comput. 15(7&8), 557–567 (2015)MathSciNetGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.University of TartuTartuEstonia

Personalised recommendations