International Association
for Cryptologic Research

Gr{\\o}stl 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 Gr{\\o}stl hash function, such

as subspace preimage attack and guess-and-determine technique. We

present improved pseudo preimage attacks on 5-round Gr{\\o}stl-256

and 8-round Gr{\\o}stl-512 respectively. The complexity of the above

two attacks are ($2^{239.90},2^{240.40}$) (in time and memory) and

($2^{499.50},2^{499}$) respectively. Furthermore, we propose pseudo

preimage attack and pseudo second preimage attack on 6-round

Gr{\\o}stl-256. The complexity of our 6-round pseudo preimage and

second preimage attack is ($2^{253.26},2^{253.67}$) and

($2^{251.0},2^{252.0}$) respectively. As far as we know, these are

the best known attacks on round-reduced Gr{\\o}stl hash function.