### 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 $n = 10$.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Boolean functionalmost perfect nonlinear (APN)partial APN
Contact author(s)
nikolay kaleyski @ uib no
History
Short URL
https://ia.cr/2020/557

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},
note = {\url{https://eprint.iacr.org/2020/557}},
url = {https://eprint.iacr.org/2020/557}
}

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