There are two excellent papers among many others: while Luby
and Rackoff's paper \cite{LR} treats pseudorandom
permutation generators focusing on complexity theory,
Maurer's paper \cite{M} is based on the relation between
probability and complexity theory. One of the Maurer's
result is that the famous Luby--Rackoff lemma can be assumed
as a purely probabilistic result. In this paper we compare
and generalize  both approaches. We show that for arbitrary
$n$, and given a general oracle circuit $C_{2n}$ it is not
possible to find Boolean function
$g:(\{0,1\}^{2n})^k\rightarrow\{0,1\}$ and
$x=(x_1,\dots,x_k), x_i\in\{0,1\}^{2n}$ such that for all
Boolean functions  $f:\{0,1\}^{2n}\rightarrow\{0,1\}^{2n}$
the relation $ C_{2n}(f)= g(f(x_1),\dots , f(x_k)) $ is
valid.

