Abstract
We provide a new security proof for a variant of ElGamal proposed by Damgård, showing that it is secure against non-adaptive chosen ciphertext attack. Unlike previous security proofs for this cryptosystem, which rely on somewhat problematic assumptions, our underlying problem is similar to accepted problems such the Gap and Decision Diffie-Hellman problems.
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.: 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.: The knowledge-of-exponent assumptions and 3-round zero-knowledge protocols. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 273–289. Springer, Heidelberg (2004)
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)
Boneh, D.: The Decision Diffie-Hellman problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998)
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)
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)
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)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory 22, 644–654 (1976)
Gjøsteen, K.: Symmetric subgroup membership problems. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 104–119. Springer, Heidelberg (2005)
Hada, S., Tanaka, T.: On the existence of 3-Round zero-knowledge protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998)
Okamoto, T., Pointcheval, D.: The gap-problems: A new class of problems for the security of cryptographic schemes. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 104–118. Springer, Heidelberg (2001)
Paillier, P.: Public-key cryptosystems based on composite degree residue classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gjøsteen, K. (2006). A New Security Proof for Damgård’s ElGamal. In: Pointcheval, D. (eds) Topics in Cryptology – CT-RSA 2006. CT-RSA 2006. Lecture Notes in Computer Science, vol 3860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605805_10
Download citation
DOI: https://doi.org/10.1007/11605805_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31033-4
Online ISBN: 978-3-540-32648-9
eBook Packages: Computer ScienceComputer Science (R0)