  Several string or GUT constructions motivate the existence of a dark U(1)_D
gauge boson which interacts with the Standard Model only through its kinetic
mixing. We compute the dark matter abundance in such scenario and the
constraints in the light of the recent data from CoGENT, CDMSII and XENON100.
We show in particular that a region with relatively light WIMPS, M_{Z_D}< 40
GeV and a kinetic mixing 10^-4 < delta < 10^-3 is not yet excluded by the last
experimental data and seems to give promising signals in a near future. We also
compute the value of the kinetic mixing needed to explain the
DAMA/CoGENT/CRESST excesses and find that for M_{Z_D}< 30 GeV, delta ~ 10^-3 is
sufficient to fit with the data.
