Consider the following proposal for a cryptographic hash function, that makes use of a block cipher E with block size k bits to produce k bit hash values. The message to be hashed is split into a sequence M₁ M₂ ..........M_n of K bit blocks. For simplicity, we ignore padding and consider only messages whose length is multiple of the block size. 

Hashing works as follows: 

h_o = IV 

h_i = E_mi (h_i – 1) for i = 1, 2, ............n. The hash of the message is h_n. Show that one can apply meet - in-the-middle attack (with birthday paradox) to find a preimage of the form all x Il y for a given hash value h_i.