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On CCA1-Security of Elgamal And Damg{\aa}rd Cryptosystems
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Abstract: | Denote by $X^{Y[i]}$ the assumption that the adversary, given a non-adaptive oracle access to the $Y$ oracle with $i$ free variables cannot break the assumption $X$. We show that Elgamal is CCA1-secure under the $DDH^{CCH[1]}$ assumption. We then give a simple proof that the Damg{\aa}rd cryptosystem is CCA1-secure under the $DDH^{DDH[2]}$ assumption, where the proof uses a recent trapdoor test trick by Cash, Kiltz and Shoup. |
BibTeX
@misc{eprint-2008-17911, title={On CCA1-Security of Elgamal And Damg{\aa}rd Cryptosystems}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / CCA1-security, Damg{\aa}rd cryptosystem, DDH, Elgamal cryptosystem.}, url={http://eprint.iacr.org/2008/234}, note={Manuscript h.lipmaa@cs.ucl.ac.uk 14025 received 22 May 2008, last revised 26 May 2008}, author={Helger Lipmaa}, year=2008 }