On the sensitivity of some APN permutations to swapping points
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 is the inverse function over F2n . 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.