Design Principles for HFEv- Based Multivariate Signature Schemes

Albrecht Petzoldt Technische Universität Darmstadt, Darmstadt, Germany Ming-Shing Chen Academia Sinica, Taipei, Taiwan; National Taiwan University, Taipei, Taiwan Bo-Yin Yang Academia Sinica, Taipei, Taiwan Chengdong Tao South China University of Technology, Guangzhou, China Jintai Ding ChongQing University, Chongqing, China; University of Cincinnati, Cincinnati, OH, USA

TBD mathscidoc:2207.43071

ASIACRYPT 2015, 311–334, 2015.12
The Hidden Field Equations (HFE) Cryptosystem as proposed by Patarin is one of the best known and most studied multivariate schemes. While the security of the basic scheme appeared to be very weak, the HFEv- variant seems to be a good candidate for digital signature schemes on the basis of multivariate polynomials. However, the currently existing scheme of this type, the QUARTZ signature scheme, is hardly used in practice because of its poor efficiency. In this paper we analyze recent results from Ding and Yang about the degree of regularity of HFEv- systems and derive from them design principles for signature schemes of the HFEv- type. Based on these results we propose the new HFEv- based signature scheme Gui, which is more than 100 times faster than QUARTZ and therefore highly comparable with classical signature schemes such as RSA and ECDSA.
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@inproceedings{albrecht2015design,
  title={Design Principles for HFEv- Based Multivariate Signature Schemes},
  author={Albrecht Petzoldt, Ming-Shing Chen, Bo-Yin Yang, Chengdong Tao, and Jintai Ding},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714144546906520649},
  booktitle={ASIACRYPT 2015},
  pages={311–334},
  year={2015},
}
Albrecht Petzoldt, Ming-Shing Chen, Bo-Yin Yang, Chengdong Tao, and Jintai Ding. Design Principles for HFEv- Based Multivariate Signature Schemes. 2015. In ASIACRYPT 2015. pp.311–334. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714144546906520649.
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