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Polkadot Consensus

Why do we need Consensus?

Consensus is a method for coming to agreement over a shared state. In order for the state of the blockchain to continue to build and move forward, all nodes in the network must agree and come to consensus. It is the way that the nodes in a decentralized network are able to stay synced with each other. Without consensus for the decentralized network of nodes in a blockchain, there is no way to ensure that the state one node believes is true will be shared by the other nodes. Consensus aims to provide the objective view of the state amid participants who each have their own subjective views of the network. It is the process by which these nodes communicate and come to agreement, and are able to build new blocks.

What are PoW and PoS?

Proof of Work (PoW) and Proof of Stake (PoS) have been inaccurately used as short hand to refer to consensus mechanisms of blockchains, but that does not capture the full picture. PoW is the method for agreeing on a block author and part of the fuller Nakamoto consensus that also encompasses a chain selection algorithm (longest chain rule in Bitcoin). Similarly, PoS is a set of rules for selecting the validator set and does not specify a chain selection rule or how a chain might reach finality. PoS algorithms have traditionally been paired with an algorithm for coming to Byzantine agreement between nodes. For example, Tendermint is a practical Byzantine fault tolerant algorithm that uses PoS as its validator set selection method.

Why not Proof of Work?

Although simple and effective in coming to a decentralized consensus on the next block producer, proof of work with Nakamoto consensus consumes an incredible amount of energy, has no economic or provable finality, and has no effective strategy in resisting cartels.

Nominated Proof of Stake

In traditional PoS systems, block production participation is dependant on token holdings as opposed to computational power. While PoS developers usually have a proponent for equitable participation in a decentralized manner, most projects end up proposing some level of centralized operation, where the number of validators with full participation rights is limited. These validators are often seen to be the most wealthy, and, as a result, influence the PoS network as they are the most staked. Usually, the number of candidates to maintain the network with the necessary knowledge (and equipment) is limited; this can directly increase operational costs as well. Systems with a large number of validators tend to form pools to decrease the variance of their revenue and profit from economies of scale. These pools are often off-chain.

A way to alleviate this is to implement pool formation on-chain and allow token holders to vote [with their stake] for validators to represent them.

Polkadot uses NPoS (Nominated Proof-of-Stake) as its mechanism for selecting the validator set. It is designed with the roles of validators and nominators, to maximize chain security. Actors who are interested in maintaining the network can run a validator node.

Validators assume the role of producing new blocks in BABE, validating parachain blocks, and guaranteeing finality. Nominators can choose to back select validators with their stake. Nominators can approve candidates that they trust and back them with their tokens.

Probabilistic vs. Provable Finality

A pure Nakamoto consensus blockchain that runs PoW is only able to achieve the notion of probabilistic finality and reach eventual consensus. Probabilistic finality means that under some assumptions about the network and participants, if we see a few blocks building on a given block, we can estimate the probability that it is final. Eventual consensus means that at some point in the future, all nodes will agree on the truthfulness of one set of data. This eventual consensus may take a long time and will not be able to be determined how long it will take ahead of time. However, finality gadgets such as GRANDPA (GHOST-based Recursive ANcestor Deriving Prefix Agreement) or Ethereum's Casper FFG (the Friendly Finality Gadget) are designed to give stronger and quicker guarantees on the finality of blocks - specifically, that they can never be reverted after some process of Byzantine agreements has taken place. The notion of irreversible consensus is known as provable finality.

In the GRANDPA paper, it is phrased in this way:

We say an oracle A in a protocol is eventually consistent if it returns the same value to all participants after some unspecified time.

Hybrid Consensus

There are two protocols we use when we talk about the consensus protocol of Polkadot, GRANDPA and BABE (Blind Assignment for Blockchain Extension). We talk about both of these because Polkadot uses what is known as hybrid consensus. Hybrid consensus splits up the finality gadget from the block production mechanism.

This is a way of getting the benefits of probabilistic finality (the ability to always produce new blocks) and provable finality (having a universal agreement on the canonical chain with no chance for reversion) in Polkadot. It also avoids the corresponding drawbacks of each mechanism (the chance of unknowingly following the wrong fork in probabilistic finality, and a chance for "stalling" - not being able to produce new blocks - in provable finality). By combining these two mechanisms, Polkadot allows for blocks to be rapidly produced, and the slower finality mechanism to run in a separate process to finalize blocks without risking slower transaction processing or stalling.

Hybrid consensus has been proposed in the past. Notably, it was proposed (now defunct) as a step in Ethereum's transition to proof of stake in EIP 1011, which specified Casper FFG.

Block Production: BABE

BABE (Blind Assignment for Blockchain Extension) is the block production mechanism that runs between the validator nodes and determines the authors of new blocks. BABE is comparable as an algorithm to Ouroboros Praos, with some key differences in chain selection rule and slot time adjustments. BABE assigns block production slots to validators according to stake and using the Polkadot randomness cycle.

Validators in Polkadot will participate in a lottery in every slot that will tell them whether or not they are the block producer candidate for that slot. Slots are discrete units of time, nominally 6 seconds in length. Because of this randomness mechanism, multiple validators could be candidates for the same slot. Other times, a slot could be empty, resulting in inconsistent block time.

Multiple Validators per Slot

When multiple validators are block producer candidates in a given slot, all will produce a block and broadcast it to the network. At that point, it's a race. The validator whose block reaches most of the network first wins. Depending on network topology and latency, both chains will continue to build in some capacity, until finalization kicks in and amputates a fork. See Fork Choice below for how that works.

No Validators in Slot

When no validators have rolled low enough in the randomness lottery to qualify for block production, a slot can remain seemingly blockless. We avoid this by running a secondary, round-robin style validator selection algorithm in the background. The validators selected to produce blocks through this algorithm always produce blocks, but these secondary blocks are ignored if the same slot also produces a primary block from a VRF-selected validator. Thus, a slot can have either a primary or a secondary block, and no slots are ever skipped.

For more details on BABE, please see the BABE paper.

BADASS BABE: SASSAFRAS

SASSAFRAS (Semi Anonymous Sortition of Staked Assignees For Fixed-time Rhythmic Assignment of Slots) (aka SASSY BABE or BADASS BABE), is an extension of BABE and acts as a constant-time block production protocol. This approach tries to address the shortcomings of BABE by ensuring that exactly one block is produced with time-constant intervals. The protocol utilizes zk-SNARKs to construct a ring-VRF and is a work in progress. This section will be updated as progress ensues.

Finality Gadget: GRANDPA

GRANDPA (GHOST-based Recursive ANcestor Deriving Prefix Agreement) is the finality gadget that is implemented for the Polkadot Relay Chain.

It works in a partially synchronous network model as long as 2/3 of nodes are honest and can cope with 1/5 Byzantine nodes in an asynchronous setting.

A notable distinction is that GRANDPA reaches agreements on chains rather than blocks, greatly speeding up the finalization process, even after long-term network partitioning or other networking failures.

In other words, as soon as more than 2/3 of validators attest to a chain containing a certain block, all blocks leading up to that one are finalized at once.

Protocol

Please refer to the GRANDPA paper for a full description of the protocol.

Implementation

The Substrate implementation of GRANDPA is part of Substrate Frame.

Fork Choice

Bringing BABE and GRANDPA together, the fork choice of Polkadot becomes clear. BABE must always build on the chain that has been finalized by GRANDPA. When there are forks after the finalized head, BABE provides probabilistic finality by building on the chain with the most primary blocks.

Best chain choice

In the above image, the black blocks are finalized, and the yellow blocks are not. Blocks marked with a "1" are primary blocks; those marked with a "2" are secondary blocks. Even though the topmost chain is the longest chain on the latest finalized block, it does not qualify because it has fewer primaries at the time of evaluation than the one below it.

Comparisons

Nakamoto consensus

Nakamoto consensus consists of the longest chain rule using proof of work as its sybil resistance mechanism and leader election.

Nakamoto consensus only gives us probabilistic finality. Probabilistic finality states that a block in the past is only as safe as the number of confirmations it has, or the number of blocks that have been built on top of it. As more blocks are built on top of a specific block in a Proof of Work chain, more computational work has been expended behind this particular chain. However, it does not guarantee that the chain containing the block will always remain the agreed-upon chain, since an actor with unlimited resources could potentially build a competing chain and expend enough computational resources to create a chain that did not contain a specific block. In such a situation, the longest chain rule employed in Bitcoin and other proof of work chains would move to this new chain as the canonical one.

PBFT / Tendermint

Please see the relevant section in the Cosmos comparison article.

Casper FFG

The two main differences between GRANDPA and Casper FFG are:

  • in GRANDPA, different voters can cast votes simultaneously for blocks at different heights
  • GRANDPA only depends on finalized blocks to affect the fork-choice rule of the underlying block production mechanism

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