What are the other data that can be retrieved from comparing hash values of two files?

Question

I understand that hash functions like md5 can be used to tell if two files(or sets of data) are similar or not. Even changing a single bit changes the hash value of any file. Apart from this information is there any other information when comparing two hash function like to what degree are the two files different or the location of the changes. Are there any hash functions that can used to get these information

Answer 1

None if the hash function is cryptographically secure.

If you are presented with two hashes coming from two files, the only thing you can tell is if the files are exactly, bit for bit, identical (same hash) or not.

Some properties of a hash function is that any final bit of the hash depends on multiple bits of the message, and that a change in a single bit in the message will result in a completely different hash, to the extent that this second hash cannot be distinguished from any other possible hash.

Even with a somewhat vulnerable hash function like md5, the main thing an attacker could do is create a second document hashing to the same final hash (a collision). Not really infer the relatedness of two documents. For this to be possible, the hash function would have to be quite weak.