EDIT: parent basically said "use a cryptographic hash".

You need some kind of random salt, too - it's not that hard to find a decent number of near-collisions even in cryptographic hashes. (E.g. if your hash table doubles in size whenever two keys end up in the same bucket, an attacker needs to spend O(2^n) operations to find two keys that agree in the first n bits, which will make you do O(2^n) operations and use O(2^n) memory.)

> No, using a slower cryptographic hash would produce better distribution

That absolutely isn't an intrinsic property of cryptographic hashes.

Using a faster cryptographic hash would be better.