Disperse integer function

[OAnimal]

Hi,

 

I would like to develop an integer function f (in form of a computer program) with the following properties:

 

a) x and f(x) should both be unsigned 32-bit integer numbers

b) f should be injective function and if you know f(x), it should be easy and fast to calculate x

c) for any x₁ and x₂ with Hamming distance not greater than 2, f(x1) and f(x2) should be as unrelated as possible

d) (actually extenstion of c)) for any relatively small group of values f(x₁), f(x₂), ... f(x_n) it should not be possible to predict what f(x_n+1) will be (unless one knows the program that calculates it, obviously). For example: if I tell you only the values of f(1), f(2), f(3) and f(4), you should not be able to guess what is f(5) or f(8).

 

I am a good computer programmer, so I am not asking for the actual code; instead, any ideas or links would be great.

Edited September 24, 2015 by OAnimal