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Paper: New commutative semifields defined by PN multinomials

Authors:
Lilya Budaghyan
Tor Helleseth
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URL: http://eprint.iacr.org/2009/053
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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
}