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On The Security of The ElGamal Encryption Scheme and Damgards Variant
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| Abstract: | In this paper, we discuss the security of the ElGamal encryption scheme and its variant by Damgard. For the ElGamal encryption, we show that (1) under the generalized knowledge-of-exponent assumption and the one-more discrete log assumption, ElGamal encryption is one-way under nonadaptive chosen cipher attacks; (2) one-wayness of ElGamal encryption under non-adaptive chosen cipher attacks is equivalent to the hardness of one-more computational Diffie-Hellman problem. For a variant of ElGamal encryption proposed by Damgard (DEG), we give a new proof that DEG is semantically secure against non-adaptive chosen ciphertext attacks under the one-more decisional Diffie-Hellman assumption (although the same result for DEG security has been presented in the literature before, our proof is simpler). We also give a new security proof for DEG based on the decisional Diffie- Hellman assumption (DDHA) and a weaker version of the knowledge-of-exponent assumption (KEA), and note that KEA is stronger than necessary in the security proof of DEG, for which KEA was originally proposed. |
BibTeX
@misc{eprint-2008-17877,
title={On The Security of The ElGamal Encryption Scheme and Damgards Variant},
booktitle={IACR Eprint archive},
keywords={public-key cryptography /},
url={http://eprint.iacr.org/2008/200},
note={ j32wu@cs.uwaterloo.ca 14006 received 7 May 2008},
author={J. Wu and D.R. Stinson},
year=2008
}