Type-preserving matrices and security of block ciphers
Riccardo Aragona, Alessio Meneghetti · Advances in Mathematics of Communications · 2019
We introduce a new property for mixing layers which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Mixing layers satisfying this property are called non-type-preserving. Our main result is to characterize such mixing layers by providing a list of necessary and sufficient conditions on the structure of their underlying binary matrices. Then we show how several families of linear maps are non-type-preserving, including the mixing layers of AES, GOST and PRESENT. Finally we prove that the group generated by the round functions of an SPN cipher with addition modulo $ 2^n $ as key mixing function is primitive if its mixing layer satisfies this property.