In the setting of multiparty computation, a set of parties wish to jointly compute a function of their inputs, while preserving security in the case that some subset of them are corrupted. The typical security properties considered are privacy, correctness, independence of inputs, guaranteed output delivery and fairness. Until now, all works in this area either considered the case that the corrupted subset of parties constitutes a strict minority, or the case that a half or more of the parties are corrupted. Secure protocols for the case of an honest majority achieve full security and thus output delivery and fairness are guaranteed. However, the security of these protocols is completely compromised if there is no honest majority. In contrast, protocols for the case of no honest majority do not guarantee output delivery, but do provide privacy, correctness and independence of inputs for any number of corrupted parties. Unfortunately, an adversary controlling only a single party can dis...