On the primitivity of the AES-128 key-schedule

2021/03/10 by Aragona, Riccardo, Civino, Roberto, Volta, Francesca Dalla
#20B15 #20B35 #94A60 #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2103.06169

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 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.

Related

• Primitivity of the group of a cipher involving the action of the key-schedule
• Imprimitive permutations groups generated by the round functions of key-alternating block ciphers and truncated differential cryptanalysis
• Public-key cryptography and invariant theory
• Algebraic properties of generalized Rijndael-like ciphers
• Key-agreement based on automaton groups