A Public Key Encryption Scheme Secure against Key Dependent Chosen Plaintext and Adaptive Chosen Ciphertext Attacks

  • Jan Camenisch
  • Nishanth Chandran
  • Victor Shoup
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5479)

Abstract

Recently, at Crypto 2008, Boneh, Halevi, Hamburg, and Ostrovsky (BHHO) solved the long-standing open problem of “circular encryption,” by presenting a public key encryption scheme and proving that it is semantically secure against key dependent chosen plaintext attack (KDM-CPA security) under standard assumptions (and without resorting to random oracles). However, they left as an open problem that of designing an encryption scheme that simultaneously provides security against both key dependent chosen plaintext and adaptive chosen ciphertext attack (KDM-CCA2 security). In this paper, we solve this problem. First, we show that by applying the Naor-Yung “double encryption” paradigm, one can combine any KDM-CPA secure scheme with any (ordinary) CCA2 secure scheme, along with an appropriate non-interactive zero-knowledge proof, to obtain a KDM-CCA2 secure scheme. Second, we give a concrete instantiation that makes use the above KDM-CPA secure scheme of BHHO, along with a generalization of the Cramer-Shoup CCA2 secure encryption scheme, and recently developed pairing-based NIZK proof systems. This instantiation increases the complexity of the BHHO scheme by just a small constant factor.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Backes, M., Pfitzmann, B., Scedrov, A.: Key-dependent message security under active attacks - BRSIM/UC-soundness of symbolic encryption with key cycles. In: CSF, pp. 112–124 (2007)Google Scholar
  3. 3.
    Bellare, M., Boldyreva, A., Micali, S.: Public-key encryption in a multi-user setting: Security proofs and improvements. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 259–274. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  5. 5.
    Black, J., Rogaway, P., Shrimpton, T.: Encryption-scheme security in the presence of key-dependent messages. In: Selected Areas in Cryptography, pp. 62–75 (2002)Google Scholar
  6. 6.
    Bleichenbacher, D.: Chosen ciphertext attacks against protocols based on the RSA encryption standard PKCS #1. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 1–12. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: STOC 1988, pp. 103–112 (1988)Google Scholar
  8. 8.
    Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Camenisch, J., Chandran, N., Shoup, V.: A public key encryption scheme secure against key dependent chosen plaintext and adaptive chosen ciphertext attacks. Cryptology ePrint Archive, Report 2008/375 (2008), http://eprint.iacr.org/
  11. 11.
    Camenisch, J.L., 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)CrossRefGoogle Scholar
  12. 12.
    Camenisch, J.L., Shoup, V.: Practical verifiable encryption and decryption of discrete logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    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, p. 45. Springer, Heidelberg (2002), http://eprint.iacr.org/2001/085 CrossRefGoogle Scholar
  15. 15.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: STOC 1991, pp. 542–552 (1991)Google Scholar
  16. 16.
    Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: FOCS 1990, pp. 308–317 (1990)Google Scholar
  17. 17.
    Goldwasser, S., Micali, S.: Probabilistic encryption and how to play mental poker keeping secret all partial information. In: STOC 1982, pp. 365–377 (1982)Google Scholar
  18. 18.
    Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  21. 21.
    Haitner, I., Holenstein, T.: On the (im)possibility of key dependent encryption. In: TCC 2009 (2009)Google Scholar
  22. 22.
    Halevi, S., Krawczyk, H.: Security under key-dependent inputs. In: CCS 2007: Proceedings of the 14th ACM conference on Computer and communications security, pp. 466–475. ACM, New York (2007)Google Scholar
  23. 23.
    Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 553–571. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Hofheinz, D., Unruh, D.: Towards key-dependent message security in the standard model. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 108–126. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  25. 25.
    IBM. IBM CCA Basic Services Reference and Guide for the IBM 4758 PCI and IBM 4764 PCI-X Cryptographic Coprocessors: Releases 2.53, 2.54, 3.20, 3.23, 3.24, 3.25, 3.27, and 3.30 (2008)Google Scholar
  26. 26.
    Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Kiltz, E.: Chosen-ciphertext secure key-encapsulation based on gap hashed diffie-hellman. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 282–297. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  28. 28.
    Lim, C.H., Lee, P.J.: Another method for attaining security against adaptively chosen ciphertext attacks. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 420–434. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  29. 29.
    MacKenzie, P.D., Reiter, M.K., Yang, K.: Alternatives to non-malleability: Definitions, constructions, and applications. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 171–190. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  30. 30.
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC 1990, pp. 427–437 (1990)Google Scholar
  31. 31.
    Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)Google Scholar
  32. 32.
    Rogaway, P., Shrimpton, T.: A provable-security treatment of the key-wrap problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 373–390. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  33. 33.
    RSA Laboratories. PKCS #11 v2.20: Cryptographic Token Interface Standard (2004)Google Scholar
  34. 34.
    Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS 1999, pp. 543–553 (1999)Google Scholar
  35. 35.
    De Santis, A., Di Crescenzo, G., Ostrovsky, R., Persiano, G., Sahai, A.: Robust non-interactive zero knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 566–598. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  36. 36.
    Shacham, H.: A Cramer-Shoup encryption scheme from the linear assumption and from progressively weaker linear variants. Cryptology ePrint Archive, Report 2007/074 (2007), http://eprint.iacr.org/
  37. 37.
    Shoup, V.: A proposal for an ISO standard for public key encryption, version 2.1 (2001), http://shoup.net/papers/
  38. 38.
    Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 1–16. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jan Camenisch
    • 1
  • Nishanth Chandran
    • 2
  • Victor Shoup
    • 3
  1. 1.IBM Research, work funded by the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 216483USA
  2. 2.UCLA, work done while visiting IBM ResearchUSA
  3. 3.NYU, work done while visiting IBM Research, supported by NSF award number CNS-0716690USA

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