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Paper 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 $n = 10$.
Metadata
- 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
- 2020-05-15: received
- Short URL
- https://ia.cr/2020/557
- License
-
CC BY