On the primitivity of the AES key-schedule

03/10/2021

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by   Riccardo Aragona, et al.

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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 proper and non-trivial subspace can be invariant under its action.