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Disperse integer function

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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(xn) it should not be possible to predict what f(xn+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 by OAnimal

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