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A New Family of Perfect Nonlinear Binomials
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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 }