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 functionsalmost perfect nonlinear functions
Contact author(s)
gohar kyureghyan @ ovgu de
History
2008-05-12: received
Short URL
https://ia.cr/2008/196
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2008/196}},
      url = {https://eprint.iacr.org/2008/196}
}
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