Perfectly Reliable and Secure Communication Tolerating Static and Mobile Mixed Adversary

Abstract

In this paper, we study the problem of perfectly reliable message transmission (PRMT) and perfectly secure message transmission (PSMT) between a sender S and a receiver R in an undirected synchronous network, tolerating a mixed adversary, where the adversary can be either static or mobile. The connectivity requirement, phase complexity and communication complexity are three important parameters of any interactive PRMT/PSMT protocol and are well studied in the literature in the presence of a static/mobile Byzantine adversary. However, in the presence of a mixed adversary, we encounter several surprising consequences. In this paper, we prove that even though the connectivity requirement for PRMT is same against both static and mobile mixed adversary, the lower bound on communication complexity for PRMT tolerating a mobile mixed adversary is more than its static mixed counterpart. This is interesting because against a ”Byzantine adversary”, the connectivity requirement and the lower bound on the communication complexity of PRMT protocols are same for both static and mobile case. Thus our result shows that for PRMT, a mobile mixed adversary is more powerful than its static counterpart. As our second contribution, we design a four phase communication optimal PSMT protocol tolerating a ”static mixed adversary”. Comparing this with the existing three phase communication optimal PSMT protocol against a ”static Byzantine adversary”, we find that additional one phase is enough to design communication optimal protocol against a static mixed adversary. Finally, we show that the connectivity requirement and lower bound on communication complexity of any PSMT protocol is same against both static and mobile mixed adversary, thus proving that mobility of the adversary has no effect on PSMT. To show that our bound is tight, we also present a worst case nine phase communication optimal PSMT protocol tolerating a mobile mixed adversary which is first of it’s kind. This also shows that the mobility of the adversary does not hinder to design constant phase communication optimal PSMT protocol. In our protocols, we have used new techniques which can be effectively used against both static and mobile mixed adversary and are of independent interest.