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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]

We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of -bit S-Boxes, with or , we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation-based ciphers, such as the PRESENT cipher, generate the alternating group. [ABSTRACT FROM AUTHOR]