[valarauca1]

      modulo will work fine as a hash function, but is obviously not one-way.

Modulo is a one way trap door operation.

Proof via arrogance:

       X % 100 = 50 
       Solve for X 
       Solution X = F(n) where F(n) = 100*n+50 (for all n > 1)

This does indeed meet the requirements of a hash functions. Modulu is a bad hash function because it is poorly distributed.

      Cryptographic Hashes should NEVER collide, on any inputs, ever, period.
      >This is obviously not possible

NIPS says if you observe 2 inputs of a cryptographic hash which compute to the same digest the hash is considered depreciated. So yes my definition is correct.

Obviously yes all cryptographic hashes aren't unique for every input. As they maybe N bytes long. And simply a logic will tell you there is more information in N bytes of data vs 64 bytes (512bits).

The real issue is, prove it. Testing even the 512bit address space will take you longer then the heat death of the universe, so good luck!

[dgacmu]

No - per the definition of a trapdoor function: "For any k ∈ K, without trapdoor tk, for any PPT algorithm, the probability to correctly invert fk (i.e., given fk(x), find a pre-image x' such that fk(x' ) = fk(x)) is negligible"

https://en.wikipedia.org/wiki/Trapdoor_function

Note that the definition is about a pre-image, not necessarily the input used to create it in the first place.

Second, that definition is absolutely not correct. "Never" would require that the size of the output of the hash function be equivalent to the size of the universe of possible inputs, which it obviously isn't. There's a very important difference between "never be observed in practice" and "never, period." You're not using the language precisely, and that's very dangerous when talking about hashing and cryptography.

[AstralStorm]

Pre-image is even simpler. A good cryptographic hash also prevents second pre-image attack e.g. pre-image based on multiple hashes.

None of those properties is needed for indexing into hash table. Good collision resistance is all that is required and salting for more paranoid cases.