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    On the sensitivity of some APN permutations to swapping points

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    We define a set called the pAPN-spectrum of an (n,n)(n,n)-function FF, which measures how close FF is to being an APN function, and investigate how the size of the pAPN-spectrum changes when two of the outputs of a given FF are swapped. We completely characterize the behavior of the pAPN-spectrum under swapping outputs when F(x)=x2nβˆ’2F(x) = x^{2^n-2} is the inverse function over F2n\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=10n = 10
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