  In this work, we investigate the problem of private statistical analysis in
the distributed and semi-honest setting. In particular, we study properties of
Private Stream Aggregation schemes, first introduced by Shi et al. \cite{2}.
These are computationally secure protocols for the aggregation of data in a
network and have a very small communication cost. We show that such schemes can
be built upon any key-homomorphic \textit{weak} pseudo-random function. Thus,
in contrast to the aforementioned work, our security definition can be achieved
in the \textit{standard model}. In addition, we give a computationally
efficient instantiation of this protocol based on the Decisional Diffie-Hellman
problem. Moreover, we show that every mechanism which preserves
$(\epsilon,\delta)$-differential privacy provides \textit{computational}
$(\epsilon,\delta)$-differential privacy when it is executed through a Private
Stream Aggregation scheme. Finally, we introduce a novel perturbation mechanism
based on the \textit{Skellam distribution} that is suited for the distributed
setting, and compare its performances with those of previous solutions.
