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Breaking Instance II of New TTM Cryptosystems

Xuyun Nie School of Computer Science and Engineering, University of Electronic Science and Technology, Chengdu, China Xin Jiang State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing, China Lei Hu State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing, China Jintai Ding Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, USA Zhiguang Qin School of Computer Science and Engineering, University of Electronic Science and Technology, Chengdu, China

TBD mathscidoc:2207.43036

IIH-MSP 2008, 1332-1335, 2008.8
TTM (tame transformation method) is a type of multivariate public key cryptosystem. In 2007, the inventor of TTM proposed two new instances of TTM to resist the existing attacks, in particular, the Nie et al attack. The two instances are claimed to achieve a security of 2109 against Nie et al attack. Through computation, we found that the instance II satisfied First Order Linearization Equations. After finding all linearization equations, we can perform a ciphertext-only attack to break it.
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@inproceedings{xuyun2008breaking,
  title={Breaking Instance II of New TTM Cryptosystems},
  author={Xuyun Nie, Xin Jiang, Lei Hu, Jintai Ding, and Zhiguang Qin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220712101000743134613},
  booktitle={IIH-MSP 2008},
  pages={1332-1335},
  year={2008},
}
Xuyun Nie, Xin Jiang, Lei Hu, Jintai Ding, and Zhiguang Qin. Breaking Instance II of New TTM Cryptosystems. 2008. In IIH-MSP 2008. pp.1332-1335. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220712101000743134613.
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