**An infinite class of quadratic APN functions which are not equivalent to power mappings**

*L. Budaghyan and C. Carlet and P. Felke and G. Leander*

**Abstract: **We exhibit an infinite class of almost
perfect nonlinear quadratic polynomials from $\mathbb{F}_{2^n}$ to
$\mathbb{F}_{2^n}$ ($n\geq 12$, $n$ divisible by 3 but not by 9).
We prove that these functions are EA-inequivalent to any power
function. In the forthcoming version of the present paper we will
proof that these functions are CCZ-inequivalent to any Gold
function and to any Kasami function, in particular for $n=12$,
they are therefore CCZ-inequivalent to power functions.

**Category / Keywords: **foundations / Vectorial Boolean function, S-box, Nonlinearity, Differential uniformity, Almost perfect nonlinear, Almost bent, Affine equivalence, CCZ-equivalence

**Date: **received 6 Oct 2005, last revised 17 Oct 2005

**Contact author: **Gregor Leander at rub de

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20051017:152710 (All versions of this report)

**Short URL: **ia.cr/2005/359

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