Meet-in-The-middle preimage attacks on hash modes of generalized feistel and misty schemes with SP round function

We assume that the domain extender is the Merkle- Damgård (MD) scheme and he message is padded by a '1', and minimum number of '0' s, followed by a fixed size length information so that the length of padded message is multiple of block length. Under this assumption, we analyze securities of the hash mode when the compression function follows the Davies-Meyer (DM) scheme and the underlying block cipher is one of the plain Feistel or Misty scheme or the generalized Feistel or Misty schemes with Substitution-Permutation (SP) round function. We do this work based on Meet-in-The-Middle (MitM) preimage attack techniques, and develop several useful initial structures.