Dimension of the Linearization Equations of the Matsumoto-Imai Cryptosystems

Adama Diene Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA Jintai Ding Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA Jason E. Gower Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA Timothy J. Hodges Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA Zhijun Yin Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA

TBD mathscidoc:2207.43014

WCC 2005, 242-251, 2005.3
The Matsumoto-Imai (MI) cryptosystem was the first multivariate public key cryptosystem proposed for practical use. Though MI is now considered insecure due to Patarin’s linearization attack, the core idea of MI has been used to construct many variants such as Sflash, which has recently been accepted for use in the New European Schemes for Signatures, Integrity, and Encryption project. Linearization attacks take advantage of the algebraic structure of MI to produce a set of equations that can be used to recover the plaintext from a given ciphertext. In our paper, we present a solution to the problem of finding the dimension of the space of linearization equations, a measure of how much work the attack will require.
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@inproceedings{adama2005dimension,
  title={Dimension of the Linearization Equations of the Matsumoto-Imai Cryptosystems},
  author={Adama Diene, Jintai Ding, Jason E. Gower, Timothy J. Hodges, and Zhijun Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220708164151352935591},
  booktitle={WCC 2005},
  pages={242-251},
  year={2005},
}
Adama Diene, Jintai Ding, Jason E. Gower, Timothy J. Hodges, and Zhijun Yin. Dimension of the Linearization Equations of the Matsumoto-Imai Cryptosystems. 2005. In WCC 2005. pp.242-251. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220708164151352935591.
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