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The key-scheduling algorithm in the AES is the component responsible for selecting from the master key the sequence of round keys to be xor-ed to the partially encrypted state at each iteration. We consider here the group Γ generated by the action of the AES-128 key-scheduling operation, and we prove that the smallest group containing Γ and all the translations of the message space is primitive. As a consequence, we obtain that no linear partition of the message space can be invariant under its action. [ABSTRACT FROM AUTHOR]

A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps on a small vector space. We show that this cannot happen for the AES. More precisely, we prove that if the AES round transformations can be embedded into a linear cipher acting on a vector space, then this space is huge-dimensional and so this embedding is infeasible in practice. We present two elementary proofs. [ABSTRACT FROM AUTHOR]