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Small Odd Prime Field Multivariate PKCs

Anna Inn-Tung Chen School of EECS, National Taiwan University, Taipei, Taiwan Ming-Shing Chen Institute of Information Science, Academia Sinica, Taipei, Taiwan Tien-Ren Chen Institute of Information Science, Academia Sinica, Taipei, Taiwan Chen-Mou Cheng School of EECS, National Taiwan University, Taipei, Taiwan Jintai Ding Dept. of Math. Sciences, U. of Cincinnati, Cincinnati, Ohio, USA Eric Li-Hsiang Kuo Institute of Information Science, Academia Sinica, Taipei, Taiwan Frost Yu-Shuang Li School of EECS, National Taiwan University, Taipei, Taiwan Bo-Yin Yang Institute of Information Science, Academia Sinica, Taipei, Taiwan

TBD mathscidoc:2207.43104

IACR Cryptol. ePrint Arch., 2008.12
We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of 2^{80} under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than "traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity hardware, here embodied by SSE2 or more advanced special multimedia instructions on modern x86-compatible CPUs. We explain our implementation techniques and design choices in implementing our chosen MPKC instances modulo small a odd prime. The same techniques are also applicable in modern FPGAs which often contains a large number of multipliers.
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@inproceedings{anna2008small,
  title={Small Odd Prime Field Multivariate PKCs},
  author={Anna Inn-Tung Chen, Ming-Shing Chen, Tien-Ren Chen, Chen-Mou Cheng, Jintai Ding, Eric Li-Hsiang Kuo, Frost Yu-Shuang Li, and Bo-Yin Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721144237296135686},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2008},
}
Anna Inn-Tung Chen, Ming-Shing Chen, Tien-Ren Chen, Chen-Mou Cheng, Jintai Ding, Eric Li-Hsiang Kuo, Frost Yu-Shuang Li, and Bo-Yin Yang. Small Odd Prime Field Multivariate PKCs. 2008. In IACR Cryptol. ePrint Arch.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721144237296135686.
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