## Cryptology ePrint Archive: Report 2020/557

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

Short URL: ia.cr/2020/557

[ Cryptology ePrint archive ]