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The KDM-CCA Security of REACT

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Information Security Practice and Experience (ISPEC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10701))

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Abstract

In CT-RSA 2001, Okamoto and Pointcheval proposed a general conversion: Rapid enhanced-security asymmetric cryptosystem transform (REACT, for short), which achieves the CCA security in the random oracle from very weak building blocks and is (almost) optimal in terms of computational overload.

In this paper, we consider the key-dependent message (KDM) security of REACT and prove that it can be KDM-CCA secure under exactly the same assumptions on its building blocks as those used by Okamoto and Pointcheval. When presenting our proof, we mainly adopt the deferred-analysis technique proposed in [25] and the random-oracle-splitting technique which has been used in [17, 23] according to the roles of the random oracles in different phases.

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Notes

  1. 1.

    Note that \((r,\cdot )\in L_{G^*}\) if and only if \(((r,\cdot ,\cdot ,\cdot ),\cdot )\in L_{H^*}\).

References

  1. Applebaum, B.: Key-dependent message security: generic amplification and completeness. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 527–546. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_29

    Chapter  Google Scholar 

  2. Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_35

    Chapter  Google Scholar 

  3. Backes, M., Dürmuth, M., Unruh, D.: OAEP is secure under key-dependent messages. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 506–523. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_31

    Chapter  Google Scholar 

  4. Barak, B., Haitner, I., Hofheinz, D., Ishai, Y.: Bounded key-dependent message security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 423–444. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_22

    Chapter  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

    Google Scholar 

  6. Black, J., Rogaway, P., Shrimpton, T.: Encryption-scheme security in the presence of key-dependent messages. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_6

    Chapter  Google Scholar 

  7. Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-secure encryption from decision diffie-hellman. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 108–125. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_7

    Chapter  Google Scholar 

  8. Böhl, F., Davies, G.T., Hofheinz, D.: Encryption schemes secure under related-key and key-dependent message attacks. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 483–500. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_28

    Chapter  Google Scholar 

  9. Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_1

    Chapter  Google Scholar 

  10. Brakerski, Z., Goldwasser, S., Kalai, Y.T.: Black-box circular-secure encryption beyond affine functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 201–218. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_13

    Chapter  Google Scholar 

  11. Camenisch, J., Chandran, N., Shoup, V.: A public key encryption scheme secure against key dependent chosen plaintext and adaptive chosen ciphertext attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 351–368. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_20

    Chapter  Google Scholar 

  12. Camenisch, J., Lysyanskaya, A.: An efficient system for non-transferable anonymous credentials with optional anonymity revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93–118. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_7

    Chapter  Google Scholar 

  13. Cash, D., Green, M., Hohenberger, S.: New definitions and separations for circular security. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 540–557. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_32

    Chapter  Google Scholar 

  14. Chang, J., Dai, H., Xu, M., Xue, R.: Separations in circular security for arbitrary length key cycles, revisited. Secur. Commun. Netw. 9(18), 5392–5400 (2016)

    Article  Google Scholar 

  15. Chen, Y., Zhang, J., Deng, Y., Chang, J.: KDM security for identity-based encryption: construction and separations. IACR Cryptology ePrint Archive 2016: 1020

    Google Scholar 

  16. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  17. Davies, G.T., Stam, M.: KDM security in the hybrid framework. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 461–480. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04852-9_24

    Chapter  Google Scholar 

  18. Fujisaki, E., Okamoto, T.: How to enhance the security of public-key encryption at minimum cost. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 53–68. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49162-7_5

    Chapter  Google Scholar 

  19. 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). https://doi.org/10.1007/3-540-48405-1_34

    Google Scholar 

  20. Gentry, C.: A full homomorphic encryption scheme. PHD thesis, Standford University (2009). crypto.standford.edu/craig

  21. Han, S., Liu, S., Lyu, L.: Efficient KDM-CCA secure public-key encryption for polynomial functions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 307–338. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_11

    Chapter  Google Scholar 

  22. Haitner, I., Holenstein, T.: On the (Im)possibility of key dependent encryption. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 202–219. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00457-5_13

    Chapter  Google Scholar 

  23. Kitagawa, F., Matsuda, T., Hanaoka, G., Tanaka, K.: On the key dependent message security of the fujisaki-okamoto constructions. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 99–129. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_5

    Chapter  Google Scholar 

  24. Okamoto, T., Pointcheval, D.: REACT: rapid enhanced-security asymmetric cryptosystem transform. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 159–174. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45353-9_13

    Chapter  Google Scholar 

  25. Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. IACR Cryptology ePrint Archive 2004: 332

    Google Scholar 

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Acknowledgements

We are grateful to the anonymous reviewers for their helpful comments and suggestions. This research is supported by the National Natural Science Foundation of China (No. 61602061; No. 61672059; No. 61272499; No. 61472016; No.61472414; No.61402471) and China Postdoctoral Science Foundation (Grant No. 2017M610021).

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Authors and Affiliations

  1. School of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an, Shannxi, People’s Republic of China

    Jinyong Chang

  2. School of Mathematics, Peking University, Beijing, People’s Republic of China

    Jinyong Chang, Honglong Dai & Maozhi Xu

Authors
  1. Jinyong Chang
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  2. Honglong Dai
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Correspondence to Maozhi Xu .

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Editors and Affiliations

  1. Monash University, Clayton, Victoria, Australia

    Joseph K. Liu

  2. University of Milan, Milan, Italy

    Pierangela Samarati

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Chang, J., Dai, H., Xu, M. (2017). The KDM-CCA Security of REACT. In: Liu, J., Samarati, P. (eds) Information Security Practice and Experience. ISPEC 2017. Lecture Notes in Computer Science(), vol 10701. Springer, Cham. https://doi.org/10.1007/978-3-319-72359-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-72359-4_5

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