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A New Family of Perfect Nonlinear Binomials

Authors:
Zhengbang Zha
Gohar M. Kyureghyan
Xueli Wang
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URL: http://eprint.iacr.org/2008/196
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Abstract: We prove that the binomials $x^{p^s+1}-\alpha x^{p^k+p^{2k+s}}$ define perfect nonlinear mappings in $GF(p^{3k})$ for an appropriate choice of the integer $s$ and $\alpha \in GF(p^{3k})$. We show that these binomials are inequivalent to known perfect nonlinear monomials. As a consequence we obtain new commutative semifields for $p\geq 5$ and odd $k$.
BibTeX
@misc{eprint-2008-17873,
  title={A New Family of Perfect Nonlinear Binomials},
  booktitle={IACR Eprint archive},
  keywords={foundations / perfect nonlinear functions,  almost perfect nonlinear functions},
  url={http://eprint.iacr.org/2008/196},
  note={ gohar.kyureghyan@ovgu.de 14005 received 6 May 2008},
  author={Zhengbang Zha and Gohar M. Kyureghyan and Xueli Wang},
  year=2008
}