Improved (Pseudo) Preimage Attack and Second Preimage Attack on Round-Reduced Grøstl

Abstract. Grøstl is one of the five finalists in the third round of SHA-3 competition hosted by NIST. In this paper, we use many techniques to improve the pseudo preimage attack on Grøstl hash function, such as subspace preimage attack and guess-and-determine technique. We present improved pseudo preimage attacks on 5-round Grøstl-256 and 8-round Grøstl-512 respectively. The complexity of the above two attacks are (2 , 2) (in time and memory) and (2 , 2) respectively. Furthermore, we propose pseudo preimage attack and pseudo second preimage attack on 6-round Grøstl-256. The complexity of our 6-round pseudo preimage and second preimage attack is (2 , 2) and (2, 2) respectively. As far as we know, these are the best known attacks on round-reduced Grøstl hash function.