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Paper 2008/196
A New Family of Perfect Nonlinear Binomials
Zhengbang Zha and 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
-
CC BY