In the multiparty secure function evaluation problem, a group of communicating players want to compute some function on privately held inputs, but in a way that maximally protects the privacy of these inputs. We craft careful definitions for what it means to achieve this goal, and then exhibit a protocol for the task. The protocol demonstrates that secure function evaluation can be achieved using polynomial local computation and a constant number of rounds of interaction. We assume pairwise private communication and broadcast, the existence of a one-way function, and that the majority of the participants to the protocol behave correctly.