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New commutative semifields defined by PN multinomials
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Abstract: | We introduce infinite families of perfect nonlinear Dembowski-Ostrom multinomials over $F_{p^{2k}}$ where $p$ is any odd prime. We prove that for $k$ odd and $p\ne3$ these PN functions define new commutative semifields (in part by studying the nuclei of these semifields). This implies that these functions are CCZ-inequivalent to all previously known PN mappings. |
BibTeX
@misc{eprint-2009-18280, title={New commutative semifields defined by PN multinomials}, booktitle={IACR Eprint archive}, keywords={foundations / Commutative semifield, Equivalence of functions, Perfect nonlinear, Planar function}, url={http://eprint.iacr.org/2009/053}, note={Part of this work was presented at SETA'08 Lilya.Budaghyan@ii.uib.no 14277 received 2 Feb 2009}, author={Lilya Budaghyan and Tor Helleseth}, year=2009 }