Cryptanalysis of the Lifted Unbalanced Oil Vinegar Signature Scheme

Jintai Ding University of Cincinnati, Cincinnati, OH, USA Joshua Deaton University of Cincinnati, Cincinnati, OH, USA Kurt Schmidt University of Cincinnati, Cincinnati, OH, USA Vishakha University of Cincinnati, Cincinnati, OH, USA Zheng Zhang University of Cincinnati, Cincinnati, OH, USA

TBD mathscidoc:2207.43092

CRYPTO 2020, 279–298, 2020.8
In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar (LUOV) [4], a signature scheme based on the famous multivariate public key cryptosystem (MPKC) called Unbalanced Oil and Vinegar (UOV), to NIST for the competition for post-quantum public key scheme standardization. The defining feature of LUOV is that, though the public key P works in the extension field of degree r of F_2, the coefficients of P come from F_2. This is done to significantly reduce the size of P. The LUOV scheme is now in the second round of the NIST PQC standardization process. In this paper we introduce a new attack on LUOV. It exploits the “lifted” structure of LUOV to reduce direct attacks on it to those over a subfield. We show that this reduces the complexity below the targeted security for the NIST post-quantum standardization competition.
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@inproceedings{jintai2020cryptanalysis,
  title={Cryptanalysis of the Lifted Unbalanced Oil Vinegar Signature Scheme},
  author={Jintai Ding, Joshua Deaton, Kurt Schmidt, Vishakha, and Zheng Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220715110636705238671},
  booktitle={CRYPTO 2020},
  pages={279–298},
  year={2020},
}
Jintai Ding, Joshua Deaton, Kurt Schmidt, Vishakha, and Zheng Zhang. Cryptanalysis of the Lifted Unbalanced Oil Vinegar Signature Scheme. 2020. In CRYPTO 2020. pp.279–298. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220715110636705238671.
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