Is the output of hash function evenly distributed?

[btc_enigma]

I rephrase my question:

1) given arbitrary inputs, does the SHA-256 function really generate outputs that are evenly distributed?

2) given block headers** as inputs, does the SHA-256 function really generate outputs that are evenly distributed?

Yes, yes. If not, it would not be a good hash function and it would be open to attacks.

Good point. Collision resistance comes from the fact that its uniformly distributed. 

[arulbero]

Good point. Collision resistance comes from the fact that its uniformly distributed.  

good distribution --> collision resistance ? No, example: SuperFastHash

http://softwareengineering.stackexchange.com/questions/49550/which-hashing-algorithm-is-best-for-uniqueness-and-speed

I think the more important takeaway is that there are two classes of algorithms when it comes to collisions:

    collisions rare: FNV-1, FNV-1a, DJB2, DJB2a, SDBM
    collisions common: SuperFastHash, Loselose

And then there's the how evenly distributed the hashes are:

    outstanding distribution: Murmur2, FNV-1a, SuperFastHash
    excellent distribution: FNV-1
    good distribution: SDBM, DJB2, DJB2a
    horrible distribution: Loselose

collision resistance --> uniformity    but uniformity != random uniformity  

https://research.neustar.biz/2012/02/02/choosing-a-good-hash-function-part-3/

A hash function ought to distribute its keys uniformly across its output range.
Now, uniformity is different from random uniformity.