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In this paper, we study the problem of Perfectly Reliable Message Transmission(PRMT) and Perfectly Secure Message Transmission(PSMT) between two nodes Sand Rin an undirected synchronous network, a part of which is under the influence of an all powerful mobile Byzantineadversary. We design a threephase bit optimalPSMT protocol tolerating mobile adversary, whose communication complexity matches the existing lower bound on the communication complexity of any multi phase PSMT protocol, tolerating mobile adversary. This significantly reduces the phase complexity of the existing O(t) phase bit optimal PSMT protocol tolerating mobile adversary, where tdenotes the number of nodes corrupted by the mobile adversary. Furthermore, we design a three phase bit optimalPRMT protocol which achieves reliability with constant factoroverhead against a mobile adversary. These are the firstever constant phase bit optimalPRMT and PSMT protocols against mobile Byzantine adversary. We also characterize PSMT protocols in directednetworks tolerating mobile adversary. Finally, we derive tight bound on the number of rounds required to achieve reliable communication from Sto Rtolerating a mobile adversary with arbitrary roaming speed.Finally, we show how our constant phase PRMT and PSMT protocols can be adapted to design round optimaland bit optimalPRMT and PSMT protocols, provided the network is given as collection of vertex disjoint paths.