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New infinite families of APN functions from the switching construction in even dimension

ePrint Report: New infinite families of APN functions from the switching construction in even dimension Tor Helleseth, Nadiia Ichanska, Nikolay Kaleyski We present the first new infinite family of APN functions obtained by applying the switching construction to a known family since the introduction of the Budaghyan-Carlet-Leander family in 2009. Our construction is also the first example of an infinite APN family obtained via the switching construction from an infinite family of non-power functions. More generally, we study families of APN functions that can be obtained from the Budaghyan-Helleseth-Kaleyski family by the addition of carefully selected perturbation terms. We perturb the known family by combinations of Frobenius conjugates of the relative norm and obtain four constructions, naturally arranged into two switching pairs. One of these families is EA-equivalent to the Li-Zhou-Li-Qu family, for which our construction yields a new univariate representation. Switching it by a norm-derived Boolean term produces a second family that we prove to be APN in every dimension where the base family is defined, and we show that this family is CCZ-inequivalent to all previously known constructions. Furthermore, we investigate two other infinite families that can be switched to one another, conjecture that they are APN for infinitely many dimensions, and obtain conditions that can be used to characterize their APN-ness. The new infinite APN family and the two conjectured APN families generalize previously known sporadic APN instances in dimension 10.

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