  We compute the onium-onium scattering amplitude at fixed impact parameter in
the framework of the perturbative QCD dipole model. Relying on the conformal
properties of the dipole cascade and of the elementary dipole-dipole scattering
amplitude, we obtain an exact result for this onium-onium scattering amplitude,
which is proved to be identical to the BFKL result, and which is frame
invariant. The asymptotic expression for this amplitude at fixed impact
parameter agrees with previous numerical simulations.
