**On the sensitivity of some APN permutations to swapping points**

*Lilya Budaghyan and Nikolay Kaleyski and 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 $n = 10$.

**Category / Keywords: **foundations / Boolean function, almost perfect nonlinear (APN), partial APN

**Date: **received 12 May 2020

**Contact author: **nikolay kaleyski at uib no

**Available format(s): **PDF | BibTeX Citation

**Version: **20200515:095538 (All versions of this report)

**Short URL: **ia.cr/2020/557

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