  We introduce a non-perturbative renormalization approach which identifies
stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of
rough surfaces. The usual limitations of real space methods to deal with
anisotropic (self-affine) scaling are overcome with an indirect functional
renormalization. The roughness exponent $\alpha$ is computed for dimensions
$d=1$ to 8 and it results to be in very good agreement with the available
simulations. No evidence is found for an upper critical dimension. We discuss
how the present approach can be extended to other self-affine problems.
