New candidates for multivariate trapdoor functions

Jaiberth Porras Universidad Nacional de Colombia, Medell´ın, Colombia John B. Baena Universidad Nacional de Colombia, Medell´ın, Colombia Jintai Ding University of Cincinnati, Cincinnati, OH, USA

TBD mathscidoc:2207.43115

IACR Cryptol. ePrint Arch., 2014.5
We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with such a pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is GF(2) and showed that these new trapdoor functions have high degrees of regularity, and therefore they are secure against the direct algebraic attack. We also give theoretical arguments to show that these new trapdoor functions over GF(2) are secure against the MinRank attack as well.
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@inproceedings{jaiberth2014new,
  title={New candidates for multivariate trapdoor functions},
  author={Jaiberth Porras, John B. Baena, and Jintai Ding},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722161507132115697},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2014},
}
Jaiberth Porras, John B. Baena, and Jintai Ding. New candidates for multivariate trapdoor functions. 2014. In IACR Cryptol. ePrint Arch.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722161507132115697.
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