Abstract
The AES block cipher is today the most important and analyzed symmetric algorithm. While all versions of the AES are known to be secure in the single-key setting, this is not the case in the related-key scenario. In this article we try to answer the question whether the AES would resist better differential-like related-key attacks if the key schedule was different. For this, we search for alternative permutation-based key schedules by extending the work of Khoo et al. at ToSC 2017 and Derbez et al. at SAC 2018. We first show that the model of Derbez et al. was flawed. Then, we develop different approaches together with MILP-based tools to find good permutations that could be used as the key schedule for AES-128, AES-192 and AES-256. Our methods permitted to find permutations that outperform the permutation exhibited by Khoo et al. for AES-128. Moreover, our new approach based on two MILP models that call one another allowed us to handle a larger search space and thus to search for alternative key schedules for the two bigger versions of AES. This method permitted us to find permutations for AES-192 and AES-256 that provide better resistance to related-key differential attacks. Most importantly, we showed that these variants can resist full-round boomerang attacks.
All authors were partially supported by the French Agence Nationale de la Recherche through the OREO project under Contract ANR-22-CE39-0015.
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Notes
- 1.
We contacted the authors of [9] to let them know about our findings and after verification they confirmed there is indeed a problem with their CP model and that the results of this paper should be considered as flawed.
- 2.
Note that the bounds are computed assuming the master key is filled into the first round keys. Shifting the round keys does slightly modify some of the bounds.
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Boura, C., Derbez, P., Funk, M. (2024). Alternative Key Schedules for the AES. In: Pöpper, C., Batina, L. (eds) Applied Cryptography and Network Security. ACNS 2024. Lecture Notes in Computer Science, vol 14584. Springer, Cham. https://doi.org/10.1007/978-3-031-54773-7_19
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