Abstract--We consider resource-constrained broadcast authentication for n receivers in a static, known network topology. There are only two known broadcast authentication protocols that do not use asymmetric cryptography, one-time signatures, multi-receiver MACs, or time synchronization [1], [2]. Both these protocols require three passes of a message front traversing the network. We investigate whether this amount of interaction can be improved efficiently for specific common topology classes, namely, linear topologies, tree topologies and fully connected topologies. We show modifications to the protocols allowing them to complete in just two passes in the linear and fully connected cases with a small constant factor increase in per-node communication overhead, and a further optimization that achieves the equivalent of just a single pass in the linear case with O(log n) increase in per-node communication overhead. We also prove new lower bounds for round complexity, or the maximum numb...