Improved Differential Attacks for ECHO and Grøstl

We present improved cryptanalysis of two second-round SHA-3 candidates: the AESbased hash functions ECHO and Grøstl. We explain methods for building better differential trails for ECHO by increasing the granularity of the truncated differential paths previously considered. In the case of Grøstl, we describe a new technique, the internal differential attack, which shows that when using parallel computations designers should also consider the differential security between the parallel branches. Then, we exploit the recently introduced start-from-the-middle or SuperSbox attacks, that proved to be very efficient when attacking AES-like permutations, to achieve a very efficient utilization of the available freedom degrees. Finally, we obtain the best known attacks so far for both ECHO and Grøstl. In particular, we are able to mount a distinguishing attack for the full Grøstl-256 compression function.