Collision Resistant Hashing from One-Way Functions? In general, can we construct a collision resistant hash function from a one-way function?
Simon [Sim98] showed that is not possible to build a collision-resistant hash function from a one-way permutation (which is a stronger statement) in a black-box manner . 

The main idea is to use the so-called oracle-separation technique. You can read more about it either here or in this survey.  

[Sim98]: Daniel Simon. Finding collisions on a one-way street: Can secure hash functions be based on general assumptions? Eurocrypt'98.