Constructing new APN functions from known ones

Lilya Budaghyan; Claude Carlet; Gregor Leander

Paper 2007/063

Constructing new APN functions from known ones

Lilya Budaghyan, Claude Carlet, and Gregor Leander

Abstract

We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function $x^3+\tr(x^9)$ over $\F_{2^n}$. It is proven that in general this function is CCZ-inequivalent to the Gold functions (and therefore EA-inequivalent to power functions), to the inverse and Dobbertin mappings, and in the case $n=7$ it is CCZ-inequivalent to all power mappings.

Note: In this version we add new results.

Metadata

Available format(s): PDF PS
Publication info: Published elsewhere. submitted to FFA
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: 2007-05-23: revised; 2007-02-20: received; See all versions
Short URL: https://ia.cr/2007/063
License: CC BY

BibTeX

@misc{cryptoeprint:2007/063,
      author = {Lilya Budaghyan and Claude Carlet and Gregor Leander},
      title = {Constructing new {APN} functions from known ones},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/063},
      year = {2007},
      url = {https://eprint.iacr.org/2007/063}
}