Function to generate pseudo ramdom sequence

Lets assume an ordered finite sequence of integers A = {0,1,2, ... k}. Im looking for a (seeded) function f: A -> A where the image of f seems to be ramdom, but every element is hit exactly once (bijective).

It's importatant that someone who has access to some results of f should neither be able to estimate if he's looking at direkt neighbours f(n), f(n+1) nor should he be able to guess the next result.

One idea would be to map a range(1, k) on a shuffle(range(1, k)). But this seems very low in performance (for large k) and does miss the basic idea of a generator. The first element in the sequece should be as expensive to calculate as the n-th element.