Weak-Key Distinguishers for AES

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\u2718 (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\u2717 -- 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\u2711) and subspace trails (FSE\u2717) 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\u2718) were able to do. For an easier detection, we also provide an algorithm which finds these weak-key subspace trails