Abstract
For two years, public key encryption has become an essential topic in cryptography, namely with security against chosen-ciphertext attacks. This paper presents a generic technique to make a highly secure cryptosystem from any partially trapdoor one-way function, in the random oracle model. More concretely, any suitable problem providing a one-way cryptosystem can be efficiently derived into a chosen-ciphertext secure encryption scheme. Indeed, the overhead only consists of two hashing and a XOR. As application, we provide the most efficient El Gamal encryption variant, therefore secure relative to the computational Diffie-Hellman problem. Furthermore, we present the first scheme whose security is relative to the factorization of large integers, with a perfect reduction (factorization is performed within the same time and with identical probability of success as the security break).
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdalla, M., Bellare, M., Rogaway, P.: DHAES: An Encryption Scheme Based on the Diffie-Hellman Problem. IEEE P1363a Submission (September 1998), Available from http://grouper.ieee.org/groups/1363/addendum.html
Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among Notions of Security for Public-Key Encryption Schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)
Bellare, M., Rogaway, P.: Random Oracles Are Practical: a Paradigm for Designing Efficient Protocols. In: Proc. of the 1st CCS, pp. 62–73. ACM Press, New York (1993)
Bellare, M., Rogaway, P.: Optimal Asymmetric Encryption – How to Encrypt with RSA. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures – How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)
Bellare, M., Sahai, A.: Non-Malleable Encryption: Equivalence between Two Notions, and an Indistinguishability-Based Characterization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 519–536. Springer, Heidelberg (1999)
Cohen, J.D. (Benaloh): Improving Privacy in Cryptographic Elections. Technical Report TR-454, Yale University (February 1986)
Cohen, J.D. (Benaloh): Improving Privacy in Cryptographic Elections. PhD thesis, Yale University (September 1987); Also available as technical report TR-561
Bleichenbacher, D.: A Chosen Ciphertext Attack 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)
Coppersmith, D., Halevi, S., Jutla, C.S.: ISO 9796 and the New Forgery Strategy. Working Draft presented at the Rump Session of Crypto 1999 (1999)
Coron, S., Naccache, D., Stern, J.P.: On the Security of RSA Padding. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 1–18. Springer, Heidelberg (1999)
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)
Diffie, W., Hellman, M.E.: New Directions in Cryptography. IEEE Transactions on Information Theory IT–22(6), 644–654 (1976)
Dolev, D., Dwork, C., Naor, M.: Non-Malleable Cryptography. In: Proc. of the 23rd STOC. ACM Press, New York (1991)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory IT–31(4), 469–472 (1985)
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)
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)
Goldwasser, S., Micali, S.: Probabilistic Encryption. Journal of Computer and System Sciences 28, 270–299 (1984)
SET Secure Electronic Transaction LLC. SET Secure Electronic Transaction Specification Book 3: Formal Protocol Definition (May 1997), Available from http://www.setco.org/
Maurer, U.M.: Diffie Hellman Oracles. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 268–282. Springer, Heidelberg (1996)
Naccache, D., Stern, J.: A New Cryptosystem based on Higher Residues. In: Proc. of the 5th CCS, pp. 59–66. ACM Press, New York (1998)
Naor, M., Yung, M.: Public-Key Cryptosystems Provably Secure against Chosen Ciphertext Attacks. In: Proc. of the 22nd STOC, pp. 427–437. ACM Press, New York (1990)
Ohta, K., Okamoto, T.: On Concrete Security Treatment of Signatures Derived from Identification. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 354–369. Springer, Heidelberg (1998)
Okamoto, T., Uchiyama, S.: A New Public Key Cryptosystem as Secure as Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
Okamoto, T., Uchiyama, S., Fujisaki, E.: EPOC: Efficient Probabilistic Public-Key Encryption. Submission to IEEE P1363a (November 1998), Available from http://grouper.ieee.org/groups/1363/addendum.html
Paillier, P.: A Trapdoor Permutation Equivalent to Factoring. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 219–222. Springer, Heidelberg (1999)
Paillier, P.: Public-Key Cryptosystems Based on Discrete Logarithms Residues. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Paillier, P., Pointcheval, D.: Efficient Public-Key Cryptosystems Provably Secure against Active Adversaries. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 165–179. Springer, Heidelberg (1999)
Pointcheval, D.: New Public Key Cryptosystems based on the Dependent-RSA Problems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 239–254. Springer, Heidelberg (1999)
Pointcheval, D.: HD–RSA: Hybrid Dependent RSA - a New Public Key Encryption Scheme. Submission to IEEE P1363a (October 1999), Available from http://grouper.ieee.org/groups/1363/addendum.html
Pointcheval, D., Stern, J.: Security Arguments for Digital Signatures and Blind Signatures. Journal of Cryptology (1999), Available from http://www.di.ens.fr/~pointche
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)
Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
RSA Data Security, Inc. Public Key Cryptography Standards – PKCS., Available from http://www.rsa.com/rsalabs/pubs/PKCS/
Schnorr, C.P.: Efficient Signature Generation by Smart Cards. Journal of Cryptology 4(3), 161–174 (1991)
Shoup, V.: Lower Bounds for Discrete Logarithms and Related Problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)
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)
Tsiounis, Y., Yung, M.: On the Security of El Gamal based Encryption. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, p. 117. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pointcheval, D. (2000). Chosen-Ciphertext Security for Any One-Way Cryptosystem. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 2000. Lecture Notes in Computer Science, vol 1751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46588-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-46588-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66967-8
Online ISBN: 978-3-540-46588-1
eBook Packages: Springer Book Archive