Differential Attacks: Using Alternative Operations

Is it possible that a block cipher apparently immune to classical differential cryptanalysis can be attacked considering a different operation on the message space? Recently Calderini and Sala showed how to effectively compute alternative operations on a vector space which can serve as message space for a block cipher such that the resulting structure is still a vector space. The latter were used to mount a linearisation attack against a toy cipher. Here we investigate the possibility to design a block cipher which appears to be secure w.r.t. classical differential cryptanalysis, but weaker with respect to our attack which make use of alternative operations. Furthermore we compare the success probabilities of a distinguishing attack.