For those who don't know, a bijective function is one for which each input yields one and only one output. A block cipher, for example, is guaranteed to be bijective or you could not decrypt.
When a hash function like SHA256 or SHA3 is used with an input the same length as its output, AFAIK this is not or at least should not be bijective. (Is that correct?)
If a hash is not bijective, does this mean that repeated hashing loses entropy?
Lets say you have 256 bits of entropy and you pass it through SHA256. Do you still have 256 bits of entropy? Lets say you SHA256 hash it a million times. What then?
It seems to me that the answer ought to be no, but then again wouldn't that create a problem for hash based cryptography?
Just a random question that popped into my head.