Problems of secure communication and computation have been studied extensively in network models. Goldreich, Goldwasser, and Linial, Franklin and Yung, and Franklin and Wright have initiated the study of secure communication and secure computation in multi-recipient (broadcast) models. A “broadcast channel” (such as Ethernet) enables one processor to send the same message—simultaneously and privately— to a fixed subset of processors. Franklin and Wright, and Wang and Desmedt have shown that if there are at most k malicious (Byzantine style) processors, then there is an efficient protocol for achieving probabilisticly reliable and perfectly private communication in a strongly n