Perfectly Reliable and Secure Communication Tolerating Static and Mobile Mixed Adversary

In the problem of perfectly reliable message transmission (PRMT), a sender S and a receiver R are connected by n bidirectional synchronous channels. A mixed adversary A(tb,tf ,tp) with infinite computing power controls tb, tf and tp channels in Byzantine, failstop and passive fashion respectively. Inspite of the presence of A(tb,tf ,tp), S wants to reliably send a message m to R, using some protocol, without sharing any key with R beforehand. After interacting in phases as per the protocol, R should output m′ = m, without any error. In the problem of perfectly secure message transmission (PSMT), there is an additional constraint that A(tb,tf ,tp) should not know any information about m in information theoretic sense. 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 when the channels are controlled by a static/mobile Byzantine adversary. However, when the channels are controlled by mixed adversary A(tb,tf ,tp) , we encounter several surprising consequences. In this paper, we study the problem of PRMT and PSMT tolerating ”static/mobile mixed adversary”. 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 mobile mixed adversary is more than its static mixed counterpart. This is interesting because against only ”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, mobile mixed adversary is more powerful than its ∗Work supported by project No. CSE/05-06/076/DITX/CPAN on Protocols for Secure Communication and Computation sponsored by Department of Information Technology, Govt. of India. A phase is a send from S to R or vice-versa A static adversary corrupts the same set of channels in each phase of the protocol. The choice of the channel to corrupt is decided before the beginning of the protocol. A mobile adversary can corrupt different set of channels in different phases of the protocol.