New commutative semifields defined by PN multinomials

Lilya Budaghyan; Tor Helleseth

Paper 2009/053

New commutative semifields defined by PN multinomials

Lilya Budaghyan and Tor Helleseth

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.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. Part of this work was presented at SETA'08
Keywords: Commutative semifield Equivalence of functions Perfect nonlinear Planar function
Contact author(s): Lilya Budaghyan @ ii uib no
History: 2009-02-03: received
Short URL: https://ia.cr/2009/053
License: CC BY

BibTeX

@misc{cryptoeprint:2009/053,
      author = {Lilya Budaghyan and Tor Helleseth},
      title = {New commutative semifields defined by {PN} multinomials},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/053},
      year = {2009},
      url = {https://eprint.iacr.org/2009/053}
}