Another class of quadratic APN binomials over $\F_{2^n}$: the case $n$ divisible by 4

Lilya Budaghyan; Claude Carlet; Gregor Leander

Paper 2006/428

Another class of quadratic APN binomials over $\F_{2^n}$: the case $n$ divisible by 4

Lilya Budaghyan, Claude Carlet, and Gregor Leander

Abstract

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^{n}}$ to $\mathbb{F}_{2^{n}}$ with $n=4k$ and $k$ odd. We prove that these functions are CCZ-inequivalent to known APN power functions when $k\ne 1$. In particular it means that for $n=12,20,28$, they are CCZ-inequivalent to any power function.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Affine equivalence Almost bent Almost perfect nonlinear CCZ-equivalence Differential uniformity Nonlinearity S-box Vectorial Boolean function.
Contact author(s): lilya @ science unitn it
History: 2006-11-27: revised; 2006-11-19: received; See all versions
Short URL: https://ia.cr/2006/428
License: CC BY

BibTeX

@misc{cryptoeprint:2006/428,
      author = {Lilya Budaghyan and Claude Carlet and Gregor Leander},
      title = {Another class of quadratic {APN} binomials over $\F_{2^n}$: the case $n$ divisible by 4},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/428},
      year = {2006},
      url = {https://eprint.iacr.org/2006/428}
}