Paper 2007/320 Original: eprint.iacr.org/2007/320 ↗
On the Big Gap Between $|p|$ and $|q|$ in DSA
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).
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2007-08-16: last updated
- 2007-08-16: published
- Short URL
- https://ia.cr/2007/320
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2007/320,
author = {Zhengjun Cao},
title = {On the Big Gap Between $|p|$ and $|q|$ in DSA},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/320},
year = {2007},
url = {https://eprint.iacr.org/2007/320}
}