In this paper, we present the pseudo-collision, pseudo-second-preimage and pseudo-preimage attacks on the SHA-3 candidate algorithm Luffa. The pseudocollisions and pseudo-second-preimages can be found easily by computing the inverse of the message injection function at the beginning of Luffa. We explain in details the pseudo-preimage attacks. For Luffa-224/256, given the hash value, only 2 iter...