Abstract
A design of secure and efficient public key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as the ElGamal-type encryption is concerned, some variants of the original ElGamal encryption scheme whose security depends on weaker computational assumption have been proposed: Although the security of the original ElGamal encryption is based on the decisional Diffie-Hellman assumption (DDH-A), the security of a recent scheme, such as Pointcheval’s ElGamal encryption variant, is based on the weaker assumption, the computational Diffie-Hellman assumption (CDH-A). In this paper, we propose a length-saving ElGamal encryption variant whose security is based on CDH-A and analyze its security in the random oracle model. The proposed scheme is length-efficient which provides a shorter ciphertext than that of Pointcheval’s scheme and provably secure against the chosen-ciphertext attack.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdalla, M., Bellare, M., Rogaway, P.: DHAES: An Encryption Scheme Based on Diffie-Hellman Problem. IEEE P1363a Submission (1998), Available at http://grouper.ieee.org/groups/1363/addendum.html
Bellare, M.: Practice-Oriented Provable-Security. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396. Springer, Heidelberg (1998)
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. ACM Conference on Computer and Communications Security, 62–73 (1993)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Canetti, R., Goldreich, O., Halevi, S.: The Random Oracle Methodology, Revisited. In: Proceedings of the 30th Annual Symposium on the Theory of Computing. ACM, New York (1998)
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)
Dolev, D., Dwork, C., Naor, M.: Non-Malleable Cryptography. In: Proceedings of 23rd STOC. ACM Press, New York (1991)
Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)
ElGamal, T.: A Public Key Cryptosystems and a Signature Schems 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)
Goldwasser, S., Micali, S.: A Probabilistic Encryption. Journal of Computer and System Sciences 28, 270–299 (1984)
Pointcheval, D.: Chosen-Ciphertext Security for any One-Way Cryptosystem. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 129–146. Springer, Heidelberg (2000)
Tsiounis, Y., Yung, M.: On the Security of ElGamal Based Encryption. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 117–134. Springer, Heidelberg (1998)
Zheng, Y., Seberry, J.: Practical Approaches to Attaining Security Against Adaptively Chosen Ciphertext Attacks. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 292–304. Springer, Heidelberg (1993)
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
Baek, J., Lee, B., Kim, K. (2000). Secure Length-Saving ElGamal Encryption under the Computational Diffie-Hellman Assumption. In: Dawson, E.P., Clark, A., Boyd, C. (eds) Information Security and Privacy. ACISP 2000. Lecture Notes in Computer Science, vol 1841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10718964_5
Download citation
DOI: https://doi.org/10.1007/10718964_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67742-0
Online ISBN: 978-3-540-45030-6
eBook Packages: Springer Book Archive