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

L.  Budaghyan; C.  Carlet; P.  Felke; G.  Leander

Paper 2005/359

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

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

Abstract

We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from $F_{2^{n}}$ to $F_{2^{n}}$ ( $n \geq 12$ , $n$ 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 , they are therefore CCZ-inequivalent to power functions.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: Vectorial Boolean function S-box Nonlinearity Differential uniformity Almost perfect nonlinear Almost bent Affine equivalence CCZ-equivalence
Contact author(s): Gregor Leander @ rub de
History: 2005-10-17: revised; 2005-10-09: received; See all versions
Short URL: https://ia.cr/2005/359
License: CC BY

BibTeX

@misc{cryptoeprint:2005/359,
      author = {L.  Budaghyan and C.  Carlet and P.  Felke and G.  Leander},
      title = {An infinite class of quadratic {APN} functions which are not equivalent to power mappings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/359},
      year = {2005},
      url = {https://eprint.iacr.org/2005/359}
}