  We introduce Mysticeti-C, the first DAG-based Byzantine consensus protocol to
achieve the lower bounds of latency of 3 message rounds. Since Mysticeti-C is
built over DAGs it also achieves high resource efficiency and censorship
resistance. Mysticeti-C achieves this latency improvement by avoiding explicit
certification of the DAG blocks and by proposing a novel commit rule such that
every block can be committed without delays, resulting in optimal latency in
the steady state and under crash failures. We further extend Mysticeti-C to
Mysticeti-FPC, which incorporates a fast commit path that achieves even lower
latency for transferring assets. Unlike prior fast commit path protocols,
Mysticeti-FPC minimizes the number of signatures and messages by weaving the
fast path transactions into the DAG. This frees up resources, which
subsequently result in better performance. We prove the safety and liveness in
a Byzantine context. We evaluate both Mysticeti protocols and compare them with
state-of-the-art consensus and fast path protocols to demonstrate their low
latency and resource efficiency, as well as their more graceful degradation
under crash failures. Mysticeti-C is the first Byzantine consensus protocol to
achieve WAN latency of 0.5s for consensus commit while simultaneously
maintaining state-of-the-art throughput of over 200k TPS. Finally, we report on
integrating Mysticeti-C as the consensus protocol into the Sui blockchain,
resulting in over 4x latency reduction.
