Paper 2006/445
A class of quadratic APN binomials inequivalent to power functions
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 $\mathbb{F}_{2^n}$ ($n\geq 12$, $n$ divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for $n$ even they are CCZ-inequivalent to any known APN function, and in particular for $n=12,24$, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.
Metadata
- Available format(s)
-
PDF
PS
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Part of this paper was presented at ISIT 2006
- Keywords
- Affine equivalenceAlmost bentAlmost perfect nonlinearCCZ-equivalenceDifferential uniformityNonlinearityS-boxVectorial Boolean function
- Contact author(s)
- lilya @ science unitn it
- History
- 2006-12-04: received
- Short URL
- https://ia.cr/2006/445
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2006/445,
author = {Lilya Budaghyan and Claude Carlet and Gregor Leander},
title = {A class of quadratic {APN} binomials inequivalent to power functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2006/445},
year = {2006},
url = {https://eprint.iacr.org/2006/445}
}
