We take the recent result from the CDMS collaboration as a hint that the dark matter has an elastic scattering cross section with the nucleon in the vicinity of 10^-7 pb. By crossing symmetry such a cross section implies annihilation of dark matter into hadrons inside the halo, resulting in an anti-proton flux that could be constrained by data from the PAMELA collaboration if one includes a large boost factor necessary to explain the PAMELA excess in the positron fraction. As an illustration, we present a model-independent analysis for a fermionic dark matter and study the upper bound on the boost factor using the PAMELA anti-proton flux.

4 pages, 4 figures. Version to appear in Phys. Lett. B