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Cryptanalysis of the TRMC-4 Public Key Cryptosystem

Xuyun Nie State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China Lei Hu State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China Jintai Ding Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45220, USA; Fachbereich Informatik, Technische Universit¨at Darmstadt, Germany Jianyu Li State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China John Wagner Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45220, USA

TBD mathscidoc:2207.43030

ACNS 2007, 104-115, 2007.6
In 2006, the inventors of TRMC public key cryptosystem proposed a new variant of TRMC, TRMC-4, which can resist the existing attack, in particular, the Joux et al attack. In this paper, we show that the new version is vulnerable to attack via the linearization equations (LE) method. For any given valid ciphertext and its corresponding TRMC-4 public key, we can derive the corresponding plaintext within 2^{24} F_{2^8}-operations, after performing once for the public key a computation of complexity less than 2^{34}. Our results are confirmed by computer experiments.
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@inproceedings{xuyun2007cryptanalysis,
  title={Cryptanalysis of the TRMC-4 Public Key Cryptosystem},
  author={Xuyun Nie, Lei Hu, Jintai Ding, Jianyu Li, and John Wagner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220711130400380655607},
  booktitle={ACNS 2007},
  pages={104-115},
  year={2007},
}
Xuyun Nie, Lei Hu, Jintai Ding, Jianyu Li, and John Wagner. Cryptanalysis of the TRMC-4 Public Key Cryptosystem. 2007. In ACNS 2007. pp.104-115. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220711130400380655607.
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