  In this paper we prove that if G is a connected, simply-connected,
semi-simple algebraic group over an algebraically closed field of sufficiently
large characteristic, then all the blocks of the restricted enveloping algebra
(Ug)_0 of the Lie algebra g of G can be endowed with a Koszul grading
(extending results of Andersen, Jantzen and Soergel). We also give information
about the Koszul dual rings. Our main tool is the localization theory in
positive characteristic developed by Bezrukavnikov, Mirkovic and Rumynin.
