Given a block cipher, you want to produce a one-way hash function, where finding collisions should always be as hard as inverting the block cipher.
Use MDC-2, which is a construction that turns a block cipher into a hash function using two Matyas-Meyer-Oseas hashes and a bit of postprocessing.
Hash functions do not provide security in and of themselves! If you need to perform message integrity checking, use a MAC instead.
The MDC-2 message digest construction turns an arbitrary block cipher into a one-way hash function. It’s different from Davies-Meyer and Matyas-Meyer-Oseas in that the output of the hash function is twice the block length of the cipher. It is also protected by patent until August 28, 2004.
However, MDC-2 does use two instances of Matyas-Meyer-Oseas as components in its construction. Matyas-Meyer-Oseas hashes block by block and uses the internal state as a key used to encrypt each block of input. The resulting ciphertext is XOR’d with the block of input, and the output of that operation becomes the new internal state. The output of the hash function is the final internal state (though if the block size is not equal to the key size, it may need to be expanded, usually by repeating the value). The initial value of the internal state can be any arbitrary constant. See Figure 6-2 for a depiction of how one block of the message is treated.
Figure 6-2. The Mayas-Meyer-Oseas ...