  Anti-proton and positron Galactic cosmic ray spectra are among the key
targets for indirect detection of dark matter. The boost factors, corresponding
to an enhancement of the signal and linked to the clumpiness properties of the
dark matter distribution, have been taken as high as thousands in the past. The
dramatic impact of these boost factors for indirect detection of antiparticles,
for instance with the PAMELA satellite or the coming AMS-02 experiment, asks
for their detailed calculation. We take into account the results of high
resolution N-body dark matter simulations to calculate the most likely energy
dependent boost factors linked to the cosmic ray propagation properties, for
anti-protons and positrons. Starting from the mass and space distributions of
sub-halos, the anti-proton and positron propagators are used to calculate the
mean value and the variance of the boost factor for the primary fluxes. We take
advantage of the statistical method introduced in Lavalle et al. (2007) and
cross-check the results with Monte Carlo computations. By spanning some extreme
configurations of sub-halo and propagation properties, we find that the average
contribution of the clumps is negligible compared to that of the smooth dark
matter component. Sub-halos do not lead to enhancement of the signals, unless
they are taken with some extreme (unexpected) properties. This result is
independent of the nature of the self-annihilating dark matter candidate
considered, and provides precise estimates of the theoretical and the
statistical uncertainties of the antimatter flux from dark matter
substructures. Spectral distortions can still be expected in antimatter flux
measurements, but scenarios invoking large and even mild clumpiness boost
factors are strongly disfavoured by our analysis.
