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On CCA1-Security of Elgamal And Damg{\aa}rd Cryptosystems

Authors:
Helger Lipmaa
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URL: http://eprint.iacr.org/2008/234
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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
}