Against all odds, the Nakamoto coefficient was not mentioned by the creator of Bitcoin. It was published in 2017 by Balaji S. Srinivasan, former CTO (Chief Technical Officer) of Coinbase and associate (General Partner) of the famous fund Andreessen Horowitz (known as a16z). This coefficient is important because users and developers of a blockchain must be certain that any valid transactions they send on the network will be included in a block and then confirmed by consensus. If a group of consensus nodes (validators on the network) is compromised or acts in a malicious and coordinated way, it can attempt to modify or prevent the network from reaching consensus on new blocks. The Nakamoto coefficient is a way to measure the resilience of a blockchain to such behavior. In other words, it allows you to estimate your vulnerability to the risk of malicious consent.
Put simply, this 3.0-style coefficient represents the number of nodes (validators on a network) that must intentionally want to prevent a blockchain from functioning properly. The greater this coefficient with respect to the total number of validators, the lower the risk of corruption and, therefore, the network becomes increasingly decentralized. It is calculated by 6 indicators:
- Extraction (per reward)
- Client (per code base)
- Developers (for software commitments)
- Knots (by number)
- Trade (by trade volume)
- Property (by address)
The level of risk varies depending on the underlying consensus model (proof of stake or proof of work) of the blockchain network under study.
Nakamoto coefficient – Proof-of-Work (PoW)
In the context of Bitcoin, and globally in all blockchains operating under the proof of work consensus, any person or group of people with 51% of the computing power (hash rate) of the network can control it at will. In other words, that person or group will be able to double their spending and alter the course of the chain. For example, on Bitcoin, three mining pools (grouping multiple miners to combine computing power) alone concentrate 55% of the computing power.
Distribution of the hash rate on Bitcoin
We can have different interpretations regarding the Nakamoto coefficient on Bitcoin. We could say that if Foundry USA Pool, AntPool and F2Pool (graph above) teamed up to coordinate a network attack, they would have the computing power to corrupt Bitcoin. However, behind each of these pools, there are miners, individuals like you and me, who have decided to contribute to the system by pooling their computing power to have a better chance of validating a block and therefore being rewarded in bitcoin. If they validate a block together, they share the reward in proportion to each one’s contribution.
This pooling is made possible thanks to a feature built into the Bitcoin client software that allows a mining group to exploit blocks in cooperation by pooling the computing power of a group of miners.
We could imagine this, to popularize this system, as if you connect to a server using a username, password and payment address and then start making your machine work so that it solves the calculations with other machines. other users on this same server. Once the algorithmic equation of the block is found together, the compensation is divided among the different machines according to the amount of work provided (per proof of work).
Let’s go back to the Nakamoto coefficient. As mentioned above, we could estimate that this coefficient is 3 by assembling Foundry USA Pool, Antpool and F2Pool which together hold 55% of the total computing power. That is, it would be enough for three actors to join together to be able to corrupt the network. But since miners are free to leave the pools, they have the ability, at any time, not to follow the will of other miners within these pools who would like to corrupt the system. For this reason, the coefficient, in the context of Bitcoin, is usually calculated from the number of individual nodes. That’s just over 13,000 at the time of this writing.
Number of nodes on the Bitcoin network
The coefficient is therefore generally estimated at 51% of the total number of nodes in the network, or 6807. On the other hand, this number is to be taken with a grain of salt, since each node does not have exactly the same computing power depending on the number and the quality of the machines accumulated by the miners behind these nodes. In other words, a miner A with 2 mining machines with its own node will have much less computing power than a pool B miner set with 100 machines. Taking the nodes with the greatest computing power would then reduce the number to 6807, as this number is initially calculated as if each node had the same computing power. However, even with this significant subtlety in mind, Bitcoin remains by far the most decentralized network.
Here we are interested in the Nakamoto coefficient for a proof of work blockchain, but the functioning is very different for those operating in proof of stake.
Nakamoto coefficient – Proof-of-Stake (PoS)
In proof of stake blockchain networks, the Nakamoto coefficient not to be exceeded is different from that seen previously in proof of work.
For the proof-of-stake network to function properly, a node must not contain more than 33.4%, or one third, (versus 51% for proof-of-work) of the supply blocked on the network, otherwise it could on its own corrupt the chain. Therefore, preventing a node from holding more than 33.4% of the voting rights is critical to keeping the network running and ensuring its resistance to censorship. On the other hand, with the same process as the proof of work, nodes can mutualise their “participation” to hold together more than 33.4% of the voting rights.
Note: It is important to emphasize that an attacker or group of attackers does not need to hold a third of the total supply in circulation, but rather a third of the active stake (staking or “staking” on the network). Most investors, in fact, buy and store their cryptocurrencies (which operate on a PoS blockchain) in their wallets without detaching them on the network (thus blocking them) in order to become a validator and obtain returns.
Example : imagine that only 25% of the total supply is stacked / staking, so the amount required to corrupt the network is only 1/12 of the total supply, or ⅓ x 25%.
We understand here that the voting “weight” or “power” of a validator is proportional to the amount of participation associated with it. Therefore, validators that have more stakes (therefore more cryptocurrencies in staking) can have a greater influence on the outcome of the consensus process and block the production, securing and validation of validators with less stakes.
Let’s make some concrete examples:
Nakamoto coefficient of various PoS blockchains
Typically, looking at the graph above, we can see that the Nakamoto coefficient is 31 for the Solana network. This means that the minimum number of validators that should agree to censor the network is 31. In other words, the 31 addresses holding the most staked SOLs on the network would have to agree and join together to reach 33.4% of the total detached supply and then be able to censor the network. We may have the same intellectual path for the Avalanche, Binance, Polygon network, but with their associated coefficient (see graph above).
An increase in this coefficient over time is a sign of good health for the decentralization of the network. Vice versa downwards.
Note: the validators of a network have no interest in coming together to own 33.4% of the network. Indeed, this could lead to a total loss of investor confidence in it and therefore also in the associated underlying cryptocurrency. This could create huge selling waves and bring the price of the asset down dramatically. Therefore, validators would continue to own 33.4% of the network (through holding the supply of cryptocurrency in staking), but its economic value would automatically go zero.
Ultimately, the Nakamoto coefficient allows us to appreciate the decentralized nature of a blockchain network. Such an important character in the eyes of the creator of Bitcoin. On the other hand, the crypto-blockchain initiatives that have quickly returned in the wake of Satoshi’s libertarian philosophy are entrepreneurial approaches. More than 20,000 cryptocurrencies have been added to bitcoin over 10 years, promising decentralization, social revolution and a new economic paradigm without trust. A 3.0 marketing veneer that in most cases has been cleverly and dishonestly introduced in crypto-blockchain project white papers leaving beginners hungry for quick money to get rid of with non-fungible sauce. From now on, we can at least, thanks to the Nakamoto coefficient, quickly appreciate the decentralized character of a blockchain, even if it is necessary to appreciate other elements to ensure the reliability of a distributed network. Other “on-chain” analysis tools can be found very quickly in Zonebourse’s columns.