AES-based functions have attracted of a lot of analysis in the recent years,mainly due to the SHA-3 hash function competition. In particular, the rebound

attack allowed to break several proposals and many improvements/variants of

this method have been published. Yet, it remained an open question whether it

was possible to reach one more round with this type of technique compared to

the state-of-the-art. In this article, we close this open problem by providing

a further improvement over the original rebound attack and its variants, that

allows the attacker to control one more round in the middle of a differential

path for an AES-like permutation. Our algorithm is based on lists merging as

defined by Naya-Plasencia at CRYPTO 2011, and we generalized the concept to

non-full active truncated differential paths proposed by Sasaki et al. at

ASIACRYPT 2010.

As an illustration, we applied our method to the internal permutations used in

Grostl, one of the five finalist hash functions of the SHA-3 competition. When

entering this final phase, the designers tweaked the function so as to thwart

attacks proposed by Peyrin at CRYPTO 2010 that exploited relations between the

internal permutations. Until our results, no analysis was published on Grostl

and the best results reached 8 and 7 rounds for the 256-bit and 512-bit version

respectively. By applying our algorithm, we present new internal permutation

distinguishers on 9 and 10 rounds respectively.