  Energy dependence of $\gamma^*p$ total cross section is considered. It is
known from the HERA data that the cross section grows with energy, and the rate
of growth is an increasing function of the virtuality $Q^2$ of the photon
$\gamma^*$. This dependence can be explained in a simple and generic way by the
Froissart bound. To implement this mechanism quantitatively a theory satisfying
$s$-channel unitarity is required. This is achieved by computing the total
cross section from the optical theorem, and the forward elastic amplitude from
the phase shifts in the impact-parameter representation. A recipe to do so in
perturbative QCD is discussed, together with an expose of the advantage to
calculate the elastic amplitude via phase shift, rather than direct sum of all
Feynman diagrams. A two-loop computation of phase shift and total cross section
is presented, and compared with the HERA data with good agreements.
