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

Authors:
L. Budaghyan
C. Carlet
P. Felke
G. Leander
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URL: http://eprint.iacr.org/2005/359
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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.
BibTeX
@misc{eprint-2005-12693,
  title={An infinite class of quadratic APN functions which are not equivalent to power mappings},
  booktitle={IACR Eprint archive},
  keywords={foundations / Vectorial Boolean function, S-box, Nonlinearity, Differential uniformity, Almost perfect nonlinear, Almost bent, Affine equivalence, CCZ-equivalence},
  url={http://eprint.iacr.org/2005/359},
  note={ Gregor.Leander@rub.de 13073 received 6 Oct 2005, last revised 17 Oct 2005},
  author={L. Budaghyan and C. Carlet and P. Felke and G. Leander},
  year=2005
}