New infinite classes of 0-APN power functions over 𝔽_2ⁿ

Abstract

Constructing new families of APN functions is an important and challenging topic. Up to now, only six infinite families of APN monomials have been found on finite fields of even characteristic. To study APN functions, partially APN functions have attracted plenty of researchers' particular interests recently. In this paper, we propose several new infinite classes of 0-APN power functions over 𝔽_2ⁿ by using the multivariate method and resultant elimination. Furthermore, we use Magma soft to show that these 0-APN power functions are CCZ-inequivalent to the known 0-APN power functions.