The goal of secure computation is for nodes in a network to compute and output
(potentially randomized) functions of their inputs in such a way that subsets of
nodes may not infer anything more about other nodes' inputs and outputs than
what their own inputs and outputs reveal. Such problems arise in a variety of
settings such as privacy-preserving data mining, online auctions, games etc.

A special class of such problems, which includes the familiar secret key
generation problem, is secure sampling. The question of how to perform secure
sampling efficiently (in stochastic resources consumed) remains open in general.
In this talk, we will present impossibility results for the two node setting and
and its generalization to the multi-node case based on a family of monotone
functions.