Improved (Pseudo) Preimage Attack and Second Preimage Attack on Round-Reduced Grostl Hash Function

The Grøstl hash function is one of the five finalists in the third round of SHA-3 competition hosted by NIST. In this paper, we propose some improved (pseudo) preimage attacks on the Grøstl hash function by using some techniques, such as subspace preimage attack and the guess-and-determine technique. We present the improved pseudo preimage attacks on 5-round Grøstl-256 hash function and 8-round Grøstl-512 hash function, and the complexities of these attacks are (2, 2) (in time and memory) and (2, 2), respectively. We also extend the pseudo preimage from 5 rounds to 6 rounds for Grøstl-256 hash function, besides the biclique attack. Furthermore, we propose the pseudo second preimage attack on 6-round Grøstl-256 hash function. The complexities of our 6-round (pseudo) preimage and second preimage attacks are (2, 2) and (2, 2), respectively. As far as we know, these are the best known preimage attacks on round-reduced Grøstl hash function.