Bias Cancellation of MixColumns

At COSADE'2020, Carre et al. established a novel biascancelling property of the AES MixColumns matrix that effectively corrects any skewed output distribution of a state byte due to a faulty substitution box. Consequently, any effected byte is rendered uniform upon passing through the MixColumns layer. In this work in progress paper, we revisit and generalize this result and in the process identify a large class of matrices that exhibit this bias cancellation phenomenon and conclude with a foray into how this property is advantageous in the design of countermeasures against Persistent Fault Injections.