Different modeling assumptions under which we construct BFT protocols often make it hard to compare two protocols and understand their relative contributions. In this post we discuss synchronous protocols in the authenticated model (assuming a PKI).

A protocol runs in the synchronous model if it assumes a bounded message delay, i.e., all messages will arrive within a bounded delay of $\Delta$. A common strengthening of synchronous model is lock-step synchrony, i.e., replicas execute the protocol in rounds in a synchronized manner. A message sent at the start of a round arrives by the end of the round.

### Is the synchronous model practical?

The short answer is, it’s hard to say. For practitioners, the synchrony assumption may seem strong for several reasons. First, if the bounded-message delay assumption does not hold even for a single message between honest parties, then we may have a safety violation. Second, lock-step execution may be hard to implement in practice. Finally, waiting for multiple rounds/$\Delta$’s implies a high latency to commit. On the other hand, research in the synchronous setting has been improving all of these aspects to bring synchrony closer to practice.

### The advantage of synchrony: tolerating a minority corruption

The DLS lower bound implies that we can tolerate at most one-third corruption with weaker assumptions such as partial synchrony/asynchrony. The synchronous model, together with digital signatures or PoW, can tolerate up to minority corruption.

### Comparing authenticated synchronous BFT protocols

To evaluate and compare authenticated synchronous protocols we analyze them in the following dimensions:

1. Consensus definition. Whether the protocol was intended to solve Byzantine Broadcast (BB), Byzantine Agreement (BA), or State Machine Replication (SMR).
2. Lock-step vs bounded-message delay. Whether the protocol requires a lock-step execution of replicas, or can they rely only on bounded-message delay.
3. Latency to commit. For protocols with lock-step execution, the (expected) latency is measured in the number of #rounds to commit. For protocols which only assume bounded-message delay, the (expected) latency in measured in terms of $\Delta$. For protocols in SMR that use the steady-state-and-view-change paradigm, we mention the latency as a tuple of (steady state time to commit, expected time to arrive at the next steady state through view changes).
4. Communication complexity. The (expected) number of signatures sent by honest parties. Wherever applicable, the message complexity is described assuming the presence of threshold signatures.
5. Optimistic responsiveness (OR). Some protocols can commit in time independent of $\Delta$ when certain optimistic conditions hold. e.g., the actual number of Byzantine behaving parties is less than $n/4$. We will discuss this further in a separate post.
Defn Lock-step? Latency Communication complexity OR? Adaptive?
LSP [1982] BB/BA Y $O(n)$ rounds $O(2^n)$ N Y
Dolev-Strong [1982] BB Y $O(n)$ rounds $O(n^2f)$ N Y
Katz-Koo [2006] BA Y $29$ rounds $O(n^2)$ N Y
Micali-Vaikuntanathan [2017]* BB Y $\kappa$ rounds $O(\kappa n^3)$ N Y
Abraham et al. [2017] BB/BA Y $16$ rounds $O(n^2)$ N Y
XFT [2016] SMR N ($O(\delta)$, $O({n \choose f} \Delta)$ ) ($O(n)$, $O{n \choose f}$) Y N
Dfinity [2018] SMR N $9\Delta$ $O(n^2)$ N N
PiLi [2018]** SMR Y $65\Delta$ $O(n^2)$ Y N
Sync HotStuff [2019]** SMR N $(2\Delta, O(\Delta))$ $(O(n^2), O(n^2))$ Y N

* The protocol by Micali and Vaikuntanathan requires $\kappa$ rounds where $\kappa$ is a statistical security parameter and obtains a “player replaceability” notion of adaptive security.

** PiLi and Sync HotStuff also handle a weaker synchrony model with mobile sluggish faults.

Lock-step execution vs. bounded-message delay. As can be seen in the latency column, lock-step protocols express latency in terms of #rounds, whereas non-lock-step protocols in terms of $\Delta$. This distinction is minor in theory (or asymptotically) because one can obtain lock-step execution from a bounded message delay assumption, by merely using a clock synchronization protocol such as Dolev et al. and Abraham et al.. Specifically, these protocols have $O(n^2)$ message complexity and can synchronize honest parties’ clocks within $\Delta$ time. Thus, using rounds of duration $2\Delta$ suffices to implement lock-step execution. However, state-of-art non-lock-step protocols can achieve lower latency by avoiding such transformations.

Remark. All protocols derived from Nakamoto consensus rely on synchrony. We will discuss them separately here.