It's a neat result in cryptography that you can build a secure hash function given a secure signature scheme, and you can build a secure signature scheme given a secure hash function. However, far from the theory, in the real world, lots of signatures today depend on SHA-1, which is looking increasingly less like a secure hash function.
There are lots of properties by which one can evaluate a hash function, but the most important are preimage resistance (if I give you a hash, can you find an input with that hash value?), second preimage resistance (if I give you a message, can you find another that hashes to the same value?) and collision resistance (can you find two messages with the same hash?). Of those, the third appears to be much harder to meet than the first two, based on historical results against hash functions.
more here...........https://www.imperialviolet.org/2014/05/14/sha256.html
There are lots of properties by which one can evaluate a hash function, but the most important are preimage resistance (if I give you a hash, can you find an input with that hash value?), second preimage resistance (if I give you a message, can you find another that hashes to the same value?) and collision resistance (can you find two messages with the same hash?). Of those, the third appears to be much harder to meet than the first two, based on historical results against hash functions.
more here...........https://www.imperialviolet.org/2014/05/14/sha256.html