Practical Chosen Ciphertext Secure Encryption from Factoring

  • Dennis Hofheinz
  • Eike Kiltz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5479)

Abstract

We propose a practical public-key encryption scheme whose security against chosen-ciphertext attacks can be reduced in the standard model to the assumption that factoring is intractable.

Keywords

public-key encryption chosen-ciphertext security factoring 

References

  1. 1.
    Alexi, W., Chor, B., Goldreich, O., Schnorr, C.-P.: RSA and Rabin functions: Certain parts are as hard as the whole. SIAM Journal on Computing 17(2), 194–209 (1988)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press, New York (1993)Google Scholar
  3. 3.
    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
  4. 4.
    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
  5. 5.
    Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM Journal on Computing 15(2), 364–383 (1986)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Blum, M., Goldwasser, S.: An efficient probabilistic public-key encryption scheme which hides all partial information. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 289–302. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  7. 7.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudorandom bits. SIAM Journal on Computing 13(4), 850–864 (1984)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM Journal on Computing 36(5), 915–942 (2006)MathSciNetMATHGoogle Scholar
  10. 10.
    Boyen, X., Mei, Q., Waters, B.: Direct chosen ciphertext security from identity-based techniques. In: ACM CCS 2005, pp. 320–329. ACM Press, New York (2005)Google Scholar
  11. 11.
    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
  12. 12.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. Journal of the ACM 51(4), 557–594 (2004)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Cash, D.M., Kiltz, E., Shoup, V.: The twin diffie-hellman problem and applications. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 127–145. Springer, Heidelberg (2008)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, pp. 45–64. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM Journal on Computing 33(1), 167–226 (2003)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: 23rd ACM STOC, pp. 542–552. ACM Press, New York (1991)Google Scholar
  17. 17.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM Journal on Computing 30(2), 391–437 (2000)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Fischlin, R., Schnorr, C.-P.: Stronger security proofs for RSA and Rabin bits. Journal of Cryptology 13(2), 221–244 (2000)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. ACM Transactions on Information and System Security 9(2), 181–234 (2006)CrossRefMATHGoogle Scholar
  20. 20.
    Goldreich, O.: Foundations of Cryptography: Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)CrossRefMATHGoogle Scholar
  21. 21.
    Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st ACM STOC, pp. 25–32. ACM Press, New York (1989)Google Scholar
  22. 22.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Hanaoka, G., Kurosawa, K.: Efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, pp. 308–325. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    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
  26. 26.
    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
  27. 27.
    Kiltz, E., Pietrzak, K., Stam, M., Yung, M.: A new randomness extraction paradigm for hybrid encryption. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS. Springer, Heidelberg (2009)Google Scholar
  28. 28.
    Kurosawa, K., Desmedt, Y.G.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  29. 29.
    Lucks, S.: A variant of the cramer-shoup cryptosystem for groups of unknown order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 27–45. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  30. 30.
    Naor, M., Reingold, O., Rosen, A.: Pseudo-random functions and factoring. SIAM Journal on Computing 31(5), 1383–1404 (2002)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: 22nd ACM STOC. ACM Press, New York (1990)Google Scholar
  32. 32.
    Paillier, P., Villar, J.L.: Trading one-wayness against chosen-ciphertext security in factoring-based encryption. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 252–266. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  33. 33.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 187–196. ACM Press, New York (2008)Google Scholar
  34. 34.
    Phan, D.H., Pointcheval, D.: About the security of ciphers (Semantic security and pseudo-random permutations). In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 182–197. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  35. 35.
    Rabin, M.O.: Digital signatures and public key functions as intractable as factorization. Technical Report MIT/LCS/TR-212, Massachusetts Institute of Technology (January 1979)Google Scholar
  36. 36.
    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
  37. 37.
    Reyzin, L., Reyzin, N.: Better than BiBa: Short One-Time Signatures with Fast Signing and Verifying. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 144–154. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  38. 38.
    Williams, H.C.: A modification of the RSA public-key encryption procedure. IEEE Transactions on Information Theory 26(6), 726–729 (1980)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dennis Hofheinz
    • 1
  • Eike Kiltz
    • 1
  1. 1.Cryptology & Information Security GroupCWI AmsterdamThe Netherlands

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