Cryptology ePrint Archive: Report 2019/852

Weak-Key Distinguishers for AES

Lorenzo Grassi and Gregor Leander and Christian Rechberger and Cihangir Tezcan and Friedrich Wiemer

Abstract: In this paper, we analyze the security of AES in the case in which the whitening key is a weak key.

After a systematization of the classes of weak-keys of AES, we perform an extensive analysis of weak-key distinguishers (in the single-key setting) for AES instantiated with the original key-schedule and with the new key-schedule proposed at ToSC/FSE'18 (which is faster than the standard key schedule and ensures a higher number of active S-Boxes). As one of the main results, we show that (almost) all the secret-key distinguishers for round-reduced AES currently present in the literature can be set up for a higher number of rounds of AES if the whitening key is a weak-key.

Using these results as starting point, we describe a property for 9-round AES-128 and 12-round AES-256 in the chosen-key setting with complexity 264 without requiring related keys. These new chosen-key distinguishers -- set up by exploiting a variant of the multiple-of-8 property introduced at Eurocrypt'17 -- improve all the AES chosen-key distinguishers in the single-key setting.

The entire analysis has been performed using a new framework that we introduce here -- called "weak-key subspace trails", which is obtained by combining invariant subspaces (Crypto'11) and subspace trails (FSE'17) into a new, more powerful, attack. Weak-key subspace trails are defined by extending the invariant subspace approach to allow for different subspaces in every round, something that so far only the subspace trail approach and a generalization for invariant subspace and invariant set attacks (Asiacrypt'18) were able to do. For an easier detection, we also provide an algorithm which finds these weak-key subspace trails.

Category / Keywords: secret-key cryptography / AES, Key Schedule, Weak-Keys, Invariant Subspaces, Chosen-Key Distinguisher

Original Publication (with minor differences): SAC 2020

Date: received 22 Jul 2019, last revised 16 Dec 2020

Contact author: lgrassi at science ru nl

Available format(s): PDF | BibTeX Citation

Note: - Minor mistakes have been corrected. - Acknowledgment has been updated.

Version: 20201216:115102 (All versions of this report)

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