  We consider elastic quark-quark scattering at high energy and fixed
transferred momentum. Performing factorization of soft gluon exchanges into
Wilson lines vacuum expectation values and studying their properties, we find
that the asymptotics of the scattering amplitude is controlled by the
renormalization properties of the so called cross singularities of Wilson
loops. Using this fact, we evaluate the scattering amplitude and show that its
asymptotics is determined by the properties of the $2\times 2$ matrix of
anomalous dimensions which appears after one renormalizes the cross
singularities of Wilson loops. A generalization to the case of quark-antiquark
and gluon-gluon elastic scattering is discussed.
