  Civino et al. have characterised diffusion layers that expose an SPN to
vulnerability from differential cryptanalysis when employing alternative
operations coming from groups isomorphic to the translation group on the
message space. In this study, we present a classification of diffusion layers
that exhibit linearity in parallel alternative operations for ciphers with
4-bit s-boxes, enabling the possibility of an alternative differential attack
simultaneously targeting all the s-boxes within the block. Furthermore, we
investigate the differential behaviour with respect to alternative operations
for all classes of optimal 4-bit s-boxes, as defined by Leander and Poschmann
(2007). Our examination reveals that certain classes contain weak permutations
w.r.t. alternative differential attacks, and we leverage these vulnerabilities
to execute a series of experiments.
