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Polkadot's Consensus Protocols

In traditional PoS systems, block production participation is dependent on token holdings as opposed to computational power. While PoS developers usually have a proponent for equitable participation in a decentralized manner, most projects propose 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 also increase operational costs. 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.

Nominated Proof of Stake​

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, validating parachain blocks, and guaranteeing finality. Nominators can choose to backselect validators with their stake. Nominators can approve candidates that they trust and back them with their tokens.

Hybrid Consensus​

Polkadot uses a hybrid consensus composed by the finality gadget (GRANDPA) and the block production mechanism (BABE).

This is a way of getting the benefits of probabilistic finality (the ability always to produce new blocks) and provable finality (having a universal agreement on the canonical chain with no chance for reversion). 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). The combination of these two mechanisms 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 relay chain's randomness cycle. The chain’s runtime is required to provide the BABE authority list and randomness to the host via a consensus message in the header of the first block of each epoch.

BABE execution happens in sequential non-overlapping phases known as epochs. Each epoch is divided into a predefined number of slots. All slots in each epoch are sequentially indexed starting from 0 (slot number). At the beginning of each epoch, the BABE node needs to run the Block-Production-Lottery algorithm to find out in which slots it should produce a block and gossip to the other block producers.

Validators participate in a lottery for every slot, which will inform whether or not they are the block producer candidate for that slot. Slots are discrete units of time of approximately 6 seconds in length. Because the mechanism of allocating slots to validators is based on a randomized design, 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. Polkadot protocol runs a secondary validator selection algorithm in the background. The validators selected through this predictable algorithm always produce blocks. These secondary blocks are ignored if the same slot has a primary block produced 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.

Finality Gadget: GRANDPA​

GRANDPA (GHOST-based Recursive ANcestor Deriving Prefix Agreement) is the finality gadget that is implemented for the relay chain.

The Polkadot Host uses the GRANDPA Finality protocol to finalize blocks. Finality is obtained by consecutive rounds of voting by the validator nodes. Validators execute the GRANDPA finality process in parallel to Block Production as an independent service.

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 particular block, all blocks leading up to that one are finalized at once.

GRANDPA description and implementation

Please refer to the GRANDPA paper for a full description of the protocol. GRANDPA is implemented as a module of the Substrate Frame System.

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 determine 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:

note

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

Fork Choice​

Bringing BABE and GRANDPA together, the fork choice of the relay chain becomes clear. BABE must always build on the chain that GRANDPA has finalized. BABE provides probabilistic finality when there are forks after the finalized head 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

Bridging: BEEFY​

The BEEFY (Bridge Efficiency Enabling Finality Yielder) is a secondary protocol to GRANDPA to support efficient bridging between relay chains (Polkadot and Kusama) and remote, segregated blockchains, such as Ethereum, which were not built with the Polkadot native interoperability in mind. The protocol allows participants of the remote network to efficiently verify finality proofs created by validators on the relay chain, i.e. clients in the Ethereum network can verify that the Polkadot network is at a specific state.

Storing all the information necessary to verify the state of the remote chain, such as the block headers, is too expensive. In BEEFY, all honest validators sign on a GRANDPA finalized block. This reduces the efforts on the light client side, as tracking forks, GRANDPA justifications, etc., is no longer necessary. Moreover, BEEFY utilizes Merkle Mountain Ranges (MMR) as an efficient data structure for storing and transmitting block headers and signatures to light clients and the ECDSA signature schemes (more efficiently verifiable on EVM). Light clients now only have to check if the block has a super-majority of BEEFY votes by validators.

Overall, BEEFY addresses the limitations of GRANDPA finality for bridges to chains like Ethereum by providing a more lightweight and efficient finality solution.

For additional implementation details about BEEFY, see the Polkadot Specification.

Resources​

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