1 Improved (Pseudo) Preimage Attack and Second Preimage Attack on Round-Reduced Grøstl 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 sub-space 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 (2239.90, 2240.40) (in time and memory) and (2499.50, 2499), respectively. We also extend the pseudo preimage from 5 rounds to 6 rounds for Grøstl-256 hash function, besides the biclique attack. Further-more, we propose the pseudo second preimage attack on 6-round Grøstl-256 hash func-tion. The complexities of our 6-round (pseudo) preimage and second preimage attacks are (2253.26, 2253.67) and (2251.0, 2252.0), respectively. As far as we know, these are the best known attacks on round-reduced Grøstl hash function