Given a positive integer:
$$\begin{align*} N \in \mathbb{Z}^+ \end{align*}$$
I would like a function:
$$\begin{align*} f : \mathbb{Z}^2 \rightarrow \mathbb{Z} \end{align*}$$
such that
$$\begin{align*} (f(N,0), f(N,1), f(N,2), \dots , f(N,N-1)) \end{align*}$$
is a deterministic but "pseudo-random" permutation of the identity N-vector:
$$\begin{align*} (0, 1, 2, \dots, N-1) \end{align*}$$
What is a simple closed form or algorithm for $f$?