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 $\mathbb{F}_{2^n}$ 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.

Metadata
Available format(s)
PDF PS
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Vectorial Boolean functionS-boxNonlinearityDifferential uniformityAlmost perfect nonlinearAlmost bentAffine equivalenceCCZ-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
Creative Commons Attribution
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}
}
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