On the primitivity of the AES-128 key-schedule
This addresses a theoretical security property for cryptographers, but it is incremental as it builds on existing analysis of AES.
The paper tackled the problem of analyzing the group generated by the AES-128 key-scheduling operation, proving that the smallest group containing this and all translations is primitive, which implies no proper non-trivial subspace is invariant under its action.
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.