Consensus algorithm may refer to one of several proposed protocols for solving the consensus problem. In case of blockchain, consensus algorithm is a protocol through which all the parties of the blockchain network come to a common agreement (consensus) on the present data state of the ledger and be able to trust unknown peers in a distributed computing environment.
There are more than a dozen consensus algorithms but some very famous ones are below:
Proof of Work: use case = Bitcoin
This explanation will focus on proof of work as it functions in the bitcoin network. The way that users detect tampering in practice is through hashes, long strings of numbers that serve as proof of work. Put a given set of data through a hash function (bitcoin uses SHA-256), and it will only ever generate one hash. Due to the "avalanche effect," however, even a tiny change to any portion of the original data will result in a totally unrecognizable hash. Whatever the size of the original data set, the hash generated by a given function will be the same length. The hash is a one-way function: it cannot be used to obtain the original data, only to check that the data that generated the hash matches the original data.
Generating just any hash for a set of bitcoin transactions would be trivial for a modern computer, so in order to turn the process into "work," the bitcoin network sets a certain level of "difficulty." This setting is adjusted so that a new block is "mined" – added to the blockchain by generating a valid hash – approximately every 10 minutes. Setting difficulty is accomplished by establishing a "target" for the hash: the lower the target, the smaller the set of valid hashes, and the harder it is to generate one. Since a given set of data can only generate one hash, how do miners make sure they generate a hash below the target? They alter the input by adding an integer, called a nonce ("number used once"). Once a valid hash is found, it is broadcast to the network, and the block is added to the blockchain.
Mining is a competitive process, but it is more of a lottery than a race. On average, someone will generate acceptable proof of work every ten minutes, but who it will be is anyone's guess. Miners pool together to increase their chances of mining blocks, which generates transaction fees and, for a limited time, a reward of newly-created bitcoins.
Proof of work makes it extremely difficult to alter any aspect of the blockchain since such an alteration would require re-mining all subsequent blocks. It also makes it difficult for a user or pool of users to monopolize the network's computing power, since the machinery and power required to complete the hash functions are expensive.
Proof of Stake: use case = Ethereum Casper
Proof of stake is a type of consensus algorithm by which a cryptocurrency blockchain network aims to achieve distributed consensus. A person can mine or validate block transactions according to how many coins he or she holds. This means that the more Bitcoin or altcoin owned by a miner, the more mining power he or she has. The proof of stake (PoS) seeks to address this issue by attributing mining power to the proportion of coins held by a miner.
This way, instead of utilizing energy to answer PoW puzzles, a PoS miner is limited to mining a percentage of transactions that is reflective of his or her ownership stake. For instance, a miner who owns 3% of the Bitcoin available can theoretically mine only 3% of the blocks.
Practical Byzantine Fault Tolerance: use case = Hyperledger
Byzantine Fault Tolerance(BFT) is the feature of a distributed network to reach consensus(agreement on the same value) even when some of the nodes in the network fail to respond or respond with incorrect information. The objective of a BFT mechanism is to safeguard against the system failures by employing collective decision making(both – correct and faulty nodes) which aims to reduce to influence of the faulty nodes. BFT is derived from Byzantine Generals’ Problem.
pBFT tries to provide a practical Byzantine state machine replication that can work even when malicious nodes are operating in the system.
Nodes in a pBFT enabled distributed system are sequentially ordered with one node being the primary(or the leader node) and others referred to as secondary(or the backup nodes). Note here that any eligible node in the system can become the primary by transitioning from secondary to primary(typically, in the case of primary node failure). The goal is that all honest nodes help in reaching a consensus regarding the state of the system using the majority rule.
A practical Byzantine Fault Tolerant system can function on the condition that the maximum number of malicious nodes must not be greater than or equal to one-third of all the nodes in the system. As the number of nodes increase, the system becomes more secure.
Federated Byzantine Agreement: use case = Ripple
Similar to pBFT but with one change, users can vote for a group to provide consensus. The group can be dynamically changed according to the policies. Example users can code the top 10% stakeholders of the network to provide consensus to the rest 90%
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