Secure Communication in Multicast Channels: The Answer to Franklin and Wright's Question

Abstract

Problems of secure communication and computation have been studied extensively in network models. Goldreich et al., Franklin and Yung, and Franklin and Wright have initiated the study of secure communication and secure computation in multirecipient (multicast) models. A ``multicast channel'' (such as ethernet) enables one processor to send the same message--simultaneously and privately--to a fixed subset of processors. In their recent paper, Franklin and Wright have shown that if there are n multicast lines between a sender and a receiver and there are at most t malicious (Byzantine style) processors, then the condition n>t is necessary and sufficient for achieving efficient probabilistically reliable and probabilistically private communication. They also showed that if n> \lceil 3t/2\rceil , then there is an efficient protocol to achieve probabilistically reliable and perfectly private communication. They left open the question whether there exists an efficient protocol to achieve probabilistically reliable and perfectly private communication when \lceil 3t/2\rceil? n>t . In this paper, by using a different authentication scheme, we answer this question affirmatively and study related problems.