Paper 2020/557
On the sensitivity of some APN permutations to swapping points
Lilya Budaghyan, Nikolay Kaleyski, Constanza Riera, and Pantelimon Stanica
Abstract
We define a set called the pAPN-spectrum of an $(n,n)$-function $F$, which measures how close $F$ is to being an APN function, and investigate how the size of the pAPN-spectrum changes when two of the outputs of a given $F$ are swapped. We completely characterize the behavior of the pAPN-spectrum under swapping outputs when $F(x) = x^{2^n-2}$ is the inverse function over $\mathbb{F}_{2^n}$. We also investigate this behavior for functions from the Gold and Welch monomial APN families, and experimentally determine the size of the pAPN-spectrum after swapping outputs for representatives from all infinite monomial APN families up to dimension $n = 10$.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean functionalmost perfect nonlinear (APN)partial APN
- Contact author(s)
- nikolay kaleyski @ uib no
- History
- 2020-05-15: received
- Short URL
- https://ia.cr/2020/557
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/557,
author = {Lilya Budaghyan and Nikolay Kaleyski and Constanza Riera and Pantelimon Stanica},
title = {On the sensitivity of some {APN} permutations to swapping points},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/557},
year = {2020},
url = {https://eprint.iacr.org/2020/557}
}
