  We consider elastic quark-quark scattering at high energy and fixed
transferred momentum. Performing factorization of soft gluon exchanges into
Wilson line expectation value we find that there is one-to-one correspondence
between high energy asymptotics in QCD and renormalization properties of the so
called cross singularities of Wilson lines. Using this relation we show that
the asymptotic behavior of the quark-quark scattering amplitude is controlled
by a $2\times 2$ matrix of the cross anomalous dimensions. We evaluate the
matrix of cross anomalous dimension to two-loop order and study the properties
of the obtained expressions to higher loop order.
