Abstract
In 1991, Damgård proposed a simple public-key cryptosystem that he proved CCA1-secure under the Diffie-Hellman Knowledge assumption. Only in 2006, Gjøsteen proved its CCA1-security under a more standard but still new and strong assumption. The known CCA2-secure public-key cryptosystems are considerably more complicated. We propose a hybrid variant of Damgård’s public-key cryptosystem and show that it is CCA1-secure if the used symmetric cryptosystem is CPA-secure, the used MAC is unforgeable, the used key-derivation function is secure, and the underlying group is a DDH group. The new cryptosystem is the most efficient known CCA1-secure hybrid cryptosystem based on standard assumptions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abdalla, M., Bellare, M., Rogaway, P.: The Oracle Diffie-Hellman Assumptions And An Analysis of DHIES. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 143–158. Springer, Heidelberg (2001)
Bellare, M., Palacio, A.: Towards Plaintext-Aware Public-Key Encryption Without Random Oracles. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 48–62. Springer, Heidelberg (2004)
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)
Cramer, R., Shoup, V.: Design And Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack. SIAM Journal of Computing 33(1), 167–226 (2004)
Damgård, I.: Towards Practical Public Key Systems Secure against Chosen Ciphertext Attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445–456. Springer, Heidelberg (1992)
Desmedt, Y., Phan, D.H.: A CCA Secure Hybrid Damgård’s ElGamal Encryption. In: Bao, F., Chen, K. (eds.) ProvSec 2008. LNCS, vol. 5324. Springer, Heidelberg (2008)
Elgamal, T.: A Public Key Cryptosystem And A Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory 31(4), 469–472 (1985)
Gjøsteen, K.: A New Security Proof for Damgård’s ElGamal. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 150–158. Springer, Heidelberg (2006)
Gennaro, R., Shoup, V.: A Note on An Encryption Scheme of Kurosawa And Desmedt. Technical Report 2004/194, International Association for Cryptologic Research (August 10, 2004) (last revision May 18 2005), http://eprint.iacr.org/2004/194
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)
Kurosawa, K., Desmedt, Y.: A New Paradigm of Hybrid Encryption Scheme. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004)
Kiltz, E., Pietrzak, K., Stam, M., Yung, M.: A New Randomness Extraction Paradigm for Hybrid Encryption. Technical Report 2008/304, International Association for Cryptologic Research (October 2008), http://eprint.iacr.org/2008/304
Lipmaa, H.: On CCA1-Security of Elgamal And Damgård Cryptosystems. Technical Report 2008/234, International Association for Cryptologic Research (October 2008), http://eprint.iacr.org/2008/234
Shoup, V.: Using Hash Functions as A Hedge against Chosen Ciphertext Attack. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 275–288. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Desmedt, Y., Lipmaa, H., Phan, D.H. (2008). Hybrid Damgård Is CCA1-Secure under the DDH Assumption. In: Franklin, M.K., Hui, L.C.K., Wong, D.S. (eds) Cryptology and Network Security. CANS 2008. Lecture Notes in Computer Science, vol 5339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89641-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-89641-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89640-1
Online ISBN: 978-3-540-89641-8
eBook Packages: Computer ScienceComputer Science (R0)