In the setting of secure multiparty computation (MPC), a set of mutually distrusting parties wish to jointly compute a function, while guaranteeing the privacy of their inputs and the correctness of the output. An MPC protocol is called \emph{fully secure} if no adversary can prevent the honest parties from obtaining their outputs. A protocol is called \emph{fair} if an adversary can prematurely abort the computation, however, only before learning any new information. We present highly efficient transformations from fair computations to fully secure computations, assuming the fraction of honest parties is constant (e.g., $1\%$ of the parties are honest). Compared to previous transformations that require linear invocations (in the number of parties) of the fair computation, our transformations require super-logarithmic, and sometimes even super-constant, such invocations. The main idea is to delegate the computation to chosen random committees that invoke the fair computation. Apart from the benefit of uplifting security, the reduction in the number of parties is also useful, since only committee members are required to work, whereas the remaining parties simply "listen" to the computation over a broadcast channel.

翻译：在确定安全的多党计算(MPC)时,一组互不信任的当事方希望共同计算一个功能,同时保证其投入的隐私和产出的正确性。如果没有任何对手能够阻止诚实的当事方获得其产出,那么MPC协议就被称为 emph{fulsecurt}。如果对手只能在了解任何新信息之前提前中止计算,协议就被称为 emph{fair}。我们展示了从公平计算到完全安全的计算高度高效的转换,假设诚实的当事方的比例是不变的(例如,一方的1 ⁇ $是诚实的)。与以往要求公平计算线性引用(在当事方数目中)的转换相比,我们的转换需要超对数,有时甚至是超级一致的,这样的引用。主要想法是将计算委托给选择的随机委员会,援引公平计算。除了提高安全性的好处外,减少政党的数量也是有用的,因为只需要委员会成员来工作,而其余的当事方只需在广播频道上进行计算。