  We provide a new property, called Non-Type-Preserving, for a mixing layer
which guarantees protection against algebraic attacks based on the
imprimitivity of the group generated by the round functions. Our main result is
to present necessary and sufficient conditions on the structure of the binary
matrix associated to the mixing layer, so that it has this property. 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 a power
of 2 as key mixing function is primitive if its mixing layer satisfies this
property. Moreover we generalise the definition of a GOST-like cipher using a
Non-Type-Preserving matrix as mixing layer and we show, under the only
assumption of invertibility of the S-Boxes, that the corresponding group is
primitive.
