Cryptology ePrint Archive: Report 2007/468

On the hash function of ODH assumption

Xianhui Lu, Xuejia Lai, Dake He, Guomin Li

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.

Category / Keywords: ODH, hash, one-way, non-malleable

Date: received 14 Dec 2007, last revised 6 Jan 2008, withdrawn 23 Oct 2009

Contact author: luxianhui at gmail com

Available format(s): (-- withdrawn --)

Version: 20091024:015039 (All versions of this report)

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