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Paper: On the hash function of ODH

Authors:
Xianhui Lu
Xuejia Lai
Dake He
Guomin Li
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URL: http://eprint.iacr.org/2007/468
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Abstract: M. Abdalla, M. Bellare and P. Rogaway proposed a variation of Diffie-Hellman assumption named as oracle Diffie-Hellman(ODH) assumption. They recommend to use a one-way cryptographic hash function for the ODH assumption. We notice that if the hash function is just one-way then there will be an attack. We show that if the the hash function is non-malleable then the computational version of ODH assumption can be reduced to the computational Diffie-Hellman(CDH) assumption. But we can not reduce the ODH assumption to the decisional Diffie-Hellman(DDH) even if the hash function is non-malleable. It seems that we need a random oracle hash function to reduce the ODH assumption to the DDH assumption.
BibTeX
@misc{eprint-2007-13748,
  title={On the hash function of ODH},
  booktitle={IACR Eprint archive},
  keywords={ODH, hash, one-way, non-malleable},
  url={http://eprint.iacr.org/2007/468},
  note={ luxianhui@gmail.com 13861 received 14 Dec 2007},
  author={Xianhui Lu and Xuejia Lai and Dake He and Guomin Li},
  year=2007
}