In question about associative pseudo-random permutation the definition uses:
$f(k_1, f(k_2, m)) = f(f(k_1, k_2), m)$
What is defined by that? No luck with google so far.
As far as I know a permutation is defined by item number at a certain index. If $f$ is a table the item number count would be higher than the number of columns/rows which would result in invalid indices. Or is it a permutation in each row and column? Number of rows and columns need to be equal then. Would be some kind of Latin-square matrix. If that's the case the definition would result in a symmetric matrix which would be the same permutation in each direction.