Growth of the Ideal Generated by a Quadratic Boolean Function

Jintai Ding 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 Victoria Kruglov Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025 USA

TBD mathscidoc:2207.43049

PQCrypto 2010, 13–27, 2010.5
We give exact formulas for the growth of the ideal Aλ for λ a quadratic element of the algebra of Boolean functions over the Galois field GF(2). That is, we calculate dim A_k λ where A_k is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made in the article of Yang, Chen and Courtois [22,23] concerning the efficiency of the XL algorithm.
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@inproceedings{jintai2010growth,
  title={Growth of the Ideal Generated by a Quadratic Boolean Function},
  author={Jintai Ding, Timothy J. Hodges, and Victoria Kruglov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714131150215944626},
  booktitle={PQCrypto 2010},
  pages={13–27},
  year={2010},
}
Jintai Ding, Timothy J. Hodges, and Victoria Kruglov. Growth of the Ideal Generated by a Quadratic Boolean Function. 2010. In PQCrypto 2010. pp.13–27. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714131150215944626.
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