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Kipnis-Shamir Attack on HFE Revisited

Xin Jiang State Key Lab of Information Security, Chinese Academy of Sciences, Beijing, China Jintai Ding University of Cincinnati, USA; Technical University of Darmstadt, Germany Lei Hu State Key Lab of Information Security, Chinese Academy of Sciences, Beijing, China

TBD mathscidoc:2207.43028

Inscrypt 2007, 399-411, 2007.8
In this paper, we show the claims in the original Kipnis-Shamir attack on the HFE cryptosystems and the improved attack by Courtois that the complexity of the attacks is polynomial in terms of the number of variables are invalid. We present computer experiments and a theoretical argument using basic algebraic geometry to explain why it is so. Furthermore we show that even with the help of the powerful new Gröbner basis algorithm like F_4, the Kipnis-Shamir attack still should be exponential but not polynomial. This again is supported by our theoretical argument.
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@inproceedings{xin2007kipnis-shamir,
  title={Kipnis-Shamir Attack on HFE Revisited},
  author={Xin Jiang, Jintai Ding, and Lei Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220711125734946819605},
  booktitle={Inscrypt 2007},
  pages={399-411},
  year={2007},
}
Xin Jiang, Jintai Ding, and Lei Hu. Kipnis-Shamir Attack on HFE Revisited. 2007. In Inscrypt 2007. pp.399-411. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220711125734946819605.
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