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# HotStuff

Last updated Aug 9, 2022 Edit Source

A byzantine fault-tolerant state machine replication protocol for the partially synchronous system model. It can express other known protocols (e.g. PBFT, Tendermint, Casper FFG) in this common framework.

## # The Scaling Challenge

Original BFT SMR protocol were designed with a typical target system size of $n = 5$ or $n = 7$ for local-area deployments. As such, they don’t scale well to high $n$ as required by permissioned and permissionless blockchains.

HotStuff aims to overcome this by improving the bound of total number of authenticators communicated from $O(n^4)$ to $O(n^2)$

The first BFT SMR protocol with the following properties:

1. Linear view change: After GST, any correct leader, once designated, sends only $O(n)$ authenticators to drive a consensus decision in the best-case. In the worst-case, communication costs to reach consensus after GST is $O(n^2)$ authenticators in the worst case of cascading leader failures
2. Optimistic Responsiveness: : After GST, any correct leader, once designated, needs to wait just for the first $n − f$ responses to guarantee that it can create a proposal that will make progress

HotStuff does this by adding another phase to each view, with the assumption that the network delay is less than the $\Delta$ required to wait for GST. This solves the hidden QC problem.

If a leader doesn’t wait for the $\Delta$ expiration time of a round. Simply receiving $n-f$ replies from participants (up to $f$ of which may be Byzantine) is not sufficient to ensure that the leader gets to see the highest QC

Such an impatient leader may propose a lower QC value than what is accepted and this may lead to a liveness violation. In order not to wait the maximum Δ expiration time of a round, HotStuff introduces another round, Pre-commit, before the actual Commit round.

Both Casper and Tendermint wait the full $\Delta$ period instead of incurring the cost of a new round.

## # Cryptographic Primitives

Uses thresholded signatures with a threshold of $k = 2f+1$

## # Three-phase Protocol

HotStuff is a view-based protocol. Each view $v$ has a unique leader known to all. Each replicas has a tree of pending commands (as opposed to a list used by more classical BFT protocols).

During the protocol, a monotonically growing branch becomes committed. To become committed, the leader of a particular view proposing the branch must collect votes from a quorum of $(n − f)$ replicas (the QC) in three phases: prepare, pre-commit, and commit.

## # Chained HotStuff

Note that each of the three-phases have very similar structure and that the protocol isn’t doing “useful” work except collecting votes from replicas. To optimize this, we can pipeline the phases, similar to what Casper FFG does.

### # Commit Rule

HotStuff uses the concept of chains which maps nicely onto Chained HotStuff.

The decision when a block is considered committed rests purely on a simple graph structure, a three-chain.

The three-chain commit rule provides the following guarantee.

1. The first link (corresponding to prepare) in the chain QC|B' -> QC|B guarantees $n-f$ votes on a unique block B.
2. The second link (corresponding to pre-commit) in the chain QC|B'' -> QC|B' guarantees $n-f$ replicas have a QC on a unique block.
3. The last link (corresponding to commit) QC|B''' -> QC|B'' guarantees that $n-f$ replicas have the highest QC of any two-chain that has a vote.