Cryptology ePrint Archive: Report 2007/320

On the Big Gap Between $|p|$ and $|q|$ in DSA

Zhengjun Cao

Abstract: We introduce a message attack against DSA and show that the security of DSA is indeed reduced to the following problem, i.e., find $\theta\in \mathbb{Z}_q^*$ such that\\ \centerline{$z=(\hat g^{\theta} \,\mbox{mod}\, p)\, \mbox{mod}\, q $}\\ where $\mbox{Ord}_p(\hat g)=q$ and $z\in \mathbb{Z}_q^*$ is randomly chosen by the adversary. Compared with the common key-only attack, i.e., find $x\in \mathbb{Z}_q^*$ such that\\ \centerline{$ y= g^x \,\mbox{mod}\, p$}\\ the message attack is more effective because of the big gap between $|p|$ (1024-bit) and $|q|$ (160-bit).

Category / Keywords: DSA, Schnorr's signature, message attack

Date: received 15 Aug 2007, last revised 16 Aug 2007

Contact author: caozhj at shu edu cn

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Version: 20070816:122127 (All versions of this report)

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