  We examine the combination of two directions in the field of privacy
concerning computations over distributed private inputs - secure function
evaluation (SFE) and differential privacy. While in both the goal is to
privately evaluate some function of the individual inputs, the privacy
requirements are significantly different. The general feasibility results for
SFE suggest a natural paradigm for implementing differentially private analyses
distributively: First choose what to compute, i.e., a differentially private
analysis; Then decide how to compute it, i.e., construct an SFE protocol for
this analysis.
  We initiate an examination whether there are advantages to a paradigm where
both decisions are made simultaneously. In particular, we investigate under
which accuracy requirements it is beneficial to adapt this paradigm for
computing a collection of functions including binary sum, gap threshold, and
approximate median queries. Our results imply that when computing the binary
sum of $n$ distributed inputs then:
  * When we require that the error is $o(\sqrt{n})$ and the number of rounds is
constant, there is no benefit in the new paradigm.
  * When we allow an error of $O(\sqrt{n})$, the new paradigm yields more
efficient protocols when we consider protocols that compute symmetric
functions.
  Our results also yield new separations between the local and global models of
computations for private data analysis.
