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Inoculating Multivariate Schemes Against Differential Attacks

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

TBD mathscidoc:2207.43013

Public Key Cryptography - PKC 2006, 290–301, 2006.4
We demonstrate how to prevent differential attacks on multivariate public key cryptosystems using the Plus (+) method of external perturbation. In particular, we prescribe adding as few as 10 Plus polynomials to the Perturbed Matsumoto-Imai (PMI) cryptosystem when g=1 and r=6, where θ is the Matsumoto-Imai exponent, n is the message length, g = gcd(θ,n), and r is the internal perturbation dimension; or as few as g+10 when g ≠ 1. The external perturbation does not significantly decrease the efficiency of the system, and in fact has the additional benefit of resolving the problem of finding the true plaintext among several preimages of a given ciphertext. We call this new scheme the Perturbed Matsumoto-Imai-Plus (PMI+) cryptosystem.
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@inproceedings{jintai2006inoculating,
  title={Inoculating Multivariate Schemes Against Differential Attacks},
  author={Jintai Ding, and Jason E. Gower},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220708163730018177590},
  booktitle={Public Key Cryptography - PKC 2006},
  pages={290–301},
  year={2006},
}
Jintai Ding, and Jason E. Gower. Inoculating Multivariate Schemes Against Differential Attacks. 2006. In Public Key Cryptography - PKC 2006. pp.290–301. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220708163730018177590.
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