A New Family of Perfect Nonlinear Binomials

Zhengbang Zha; Gohar M.  Kyureghyan; Xueli Wang

Paper 2008/196

A New Family of Perfect Nonlinear Binomials

Zhengbang Zha, Gohar M. Kyureghyan, and Xueli Wang

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 $k$.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: perfect nonlinear functions almost perfect nonlinear functions
Contact author(s): gohar kyureghyan @ ovgu de
History: 2008-05-12: received
Short URL: https://ia.cr/2008/196
License: CC BY

BibTeX

@misc{cryptoeprint:2008/196,
      author = {Zhengbang Zha and Gohar M.  Kyureghyan and Xueli Wang},
      title = {A New Family of Perfect Nonlinear Binomials},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/196},
      year = {2008},
      url = {https://eprint.iacr.org/2008/196}
}