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 F generated by the action of the AES-128 key-scheduling operation, and we prove that the smallest group containing F 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.
Aragona, R., Civino, R., Dalla Volta, F. (2022). On the primitivity of the AES-128 key-schedule. JOURNAL OF ALGEBRA AND ITS APPLICATIONS [10.1142/S021949882350233X].
On the primitivity of the AES-128 key-schedule
Dalla Volta, F
2022
Abstract
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 F generated by the action of the AES-128 key-scheduling operation, and we prove that the smallest group containing F 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.
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Aragona-2023-JAA-AAM.pdf
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