### 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.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Part of this work was presented at SETA'08
Keywords
Commutative semifieldEquivalence of functionsPerfect nonlinearPlanar function
Contact author(s)
Lilya Budaghyan @ ii uib no
History
Short URL
https://ia.cr/2009/053

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},
note = {\url{https://eprint.iacr.org/2009/053}},
url = {https://eprint.iacr.org/2009/053}
}

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