  The Feistel Boomerang Connectivity Table (FBCT) was proposed as the feistel
counterpart of the Boomerang Connectivity Table. The entries of the FBCT are
actually related to the second-order zero differential spectrum. Recently,
several results on the second-order zero differential uniformity of some
functions were introduced. However, almost all of them were focused on power
functions, and there are only few results on non-power functions. In this
paper, we investigate the second-order zero differential uniformity of the
swapped inverse functions, which are functions obtained from swapping two
points in the inverse function. We also present the second-order zero
differential spectrum of the swapped inverse functions for certain cases. In
particular, this paper is the first result to characterize classes of non-power
functions with the second-order zero differential uniformity equal to 4, in
even characteristic.
