Differential experiments using parallel alternative operations

The use of alternative operations in differential cryptanalysis, or alternative notions of differentials, is lately receiving increasing attention. Recently, Civino et al. managed to design a block cipher that is secure with respect to the classical differential cryptanalysis performed using XOR-differentials, but weaker with respect to the attack based on an alternative difference operation acting on the first s-box of the block. We extend this result to parallel alternative operations, i.e. acting on each s-box of the block. First, we recall the mathematical framework needed to define and use such operations. After that, we perform some differential experiments against a toy cipher and compare the effectiveness of the attack with respect to the one that uses XOR-differentials.