Collision resistance implies second-preimage resistance, but second-preimage resistance does not imply collision resistance. Some care is needed with the defin

Collision resistance implies second-preimage resistance, but second-preimage resistance does not imply collision resistance. Some care is needed with the definitions. For any hash function, the adversary can compute a bunch of hashes, and those outputs obviously have known first preimages. And a hash function with a known collision has a known second preimage given one of the colliding inputs.