In a network of $n$ nodes (modeled as a digraph), the goal of a perfectly secret message transmission (PSMT) protocol is to replicate sender’s message $m$ at the receiver’s end without revealing any information about $m$ to a computationally unbounded adversary that eavesdrops on any $t$ nodes. The adversary may be mobile too that is, it may eavesdrop on a different set of $t$ nodes in different rounds. We prove a necessary and sufficient condition on the synchronous network for the existence of $r$ -round PSMT protocols, for any given $r > 0$ ; further, we show that round-optimality is achieved without trading-off the communication complexity; specifically, our protocols have an overall communication complexity of $O(n)$ elements of a finite field to perfectly transmit one field element. Apart from optimality/scalability, two interesting implications of our results are: 1) adversarial mobility does not affect its tolerability: PSMT tolerating a static $t$ -adversary is possible if and only if PSMT tolerating mobile $t$ -adversary is possible; and 2) mobility does not affect the round optimality: the fastest PSMT protocol tolerating a static $t$ -adversary is not faster than the one tolerating a mobile $t$ -adversary.