Existing Byzantine fault-tolerant (BFT) state-machine replication (SMR) protocols in the standard (bounded) synchrony and weak synchrony models rely on equivocation detection to ensure safety. To perform a commit (or output a transaction block), this detection inherently requires $O(n^2)$ communication overhead among $n$ nodes and waiting for $O(Delta)$ time, where $Delta$ is the worst-case network delay. The quadratic communication overhead limits scalability. Moreover, as the typical network latency $delta$ tends to be much smaller than $Delta$, $51%$ honest-majority (and hence synchronous or weakly synchronous) solutions become slow as compared to $67%$ honest-majority asynchronous protocols working at network speed.

The observation that SMR commits do not have to be treated separately motivates
this work. We propose UCC (Unique Chain Commit) rule, a novel yet simple
rule for hash chains where extending a block by including its hash is treated as
a vote for the block and all its direct and indirect parents. When a block
obtains $f+1$ such votes, where $f$ is the maximum number of faulty nodes in the
system, we commit the block and its parents. We use this UCC rule to design
Apollo, an SMR protocol with rotating leaders which has a linear
communication complexity. Apollo proposes and commits a block every $delta$
time units with every block having a latency of $(f+1)delta$. When compared
to existing works which use equivocation detection, we improve the optimistic
commit latency when $(f+1)delta

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