Round-Efficient Broadcast Authentication Protocols for Fixed Topology Classes

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 number of consecutive interactions in a protocol. We show that protocols with efficient per-node communication overhead (polylogarithmic in $n$) must require at least $2log n$ rounds in any topology; this implies that our two-pass protocol in the fully-connected topology requires the fewest possible passes, and this bound is asymptotically tight for the full-duplex communication model. Furthermore, we show that communication-efficient protocols must take asymptotically more than $2log n$ rounds on trees; this implies that that there are some tree topologies for which two passes do not suffice and the existing three-pass algorithms may be optimal.