  The Fermi-LAT collaboration has recently reported the detection of angular
power above the photon noise level in the diffuse gamma-ray background between
1 and 50 GeV. Such signal can be used to constrain a possible contribution from
Dark-Matter-induced photons. We estimate the intensity and features of the
angular power spectrum (APS) of this potential Dark Matter (DM) signal, for
both decaying and annihilating DM candidates, by constructing template all-sky
gamma-ray maps for the emission produced in the galactic halo and its
substructures, as well as in extragalactic (sub)halos. The DM distribution is
given by state-of-the-art N-body simulations of cosmic structure formation,
namely Millennium-II for extragalactic (sub)halos, and Aquarius for the
galactic halo and its subhalos. We use a hybrid method of extrapolation to
account for (sub)structures that are below the resolution limit of the
simulations, allowing us to estimate the total emission all the way down to the
minimal self-bound halo mass. We describe in detail the features appearing in
the APS of our template maps and we estimate the effect of various
uncertainties such as the value of the minimal halo mass, the fraction of
substructures hosted in a halo and the shape of the DM density profile. Our
results indicate that the fluctuation APS of the DM-induced emission is of the
same order as the Fermi-LAT APS, suggesting that one can constrain this
hypothetical emission from the comparison with the measured anisotropy. We also
quantify the uncertainties affecting our results, finding "theoretical error
bands" spanning more than two orders of magnitude and dominated (for a given
particle physics model) by our lack of knowledge of the abundance of low-mass
(sub)halos.
