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Blockchain is a tool that allowed for the first time ever to organize and store information in a decentralized way. 



Rather than be managed by a third party, the data in a blockchain is distributed across numerous independent computers - network nodes that run the [tooltip content=" set of rules or procedures that govern the transfer of data between devices"] blockchain protocol [/tooltip]. This constantly updated data composes the so-called distributed ledger - the history of all transactions that have ever taken place on a particular network. The ledger, as well as the rules that determine transaction processing, are stored within network participants’ computers, making sure that neither the ledger, nor the rules cannot be changed centrally. 



Such unique structure allows, also for the first time, to transfer digital assets from one owner to another in a decentralized fashion and without creating copies of the asset along the way. 



It is called a blockchain because ledger updates (or transactions) are combined in a data structure called a block. Each block is timestamped and cryptographically bound to its predecessor, thus creating an immutable chain of blocks.&nbsp;



<h2><a href="https://d.center/explore/blockchain-underlying-technologies" class="ek-link">Underlying technologies</a></h2>



 Blockchain functioning relies on a set of concepts and technologies from different domains, notably mathematics (such as algorithm complexity, one-way functions, elliptic curves and discrete logarithm problem), cryptography (asymmetric cryptography, digital signatures, cryptographic hash functions, digital linked time stamping and zero-knowledge proofs) and distributed computing (P2P). 



<h2><a href="https://d.center/explore/consensus-protocol" class="ek-link">Consensus</a></h2>



New transactions, i.e. ledger updates, are gathered in blocks and added to the blockchain according to a mechanism called consensus (meaning that all network nodes agree with these updates). Network nodes who add new blocks to the blockchain are remunerated in newly created coins and/or transaction fees as an incentive to keep the blockchain going.



<h2><a href="https://d.center/explore/blockchain-functions" class="ek-link">Blockchain functions&nbsp;</a></h2>



The main role of a blockchain is to serve as a transactions recording ledger. Bitcoin blockchain was the first blockchain ever and it is a public record of Bitcoin transactions in a chronological order. Over time, however, more and more applications appeared, allowing the execution of more complex conditions directly on the blockchain via smart contracts, for example by issuing additional cryptoassets other than the native coins - tokens.



<h2><a href="https://d.center/explore/blockchain-governance" class="ek-link">Blockchain governance</a></h2>



Blockchain is a new and constantly evolving technology, therefore it has to deal with constant upgrades and mutations. The way these upgrades are agreed upon by the network nodes, users and the larger cryptocurrency community is called the governance. It plays an important role in blockchain's vitality and often sparkles fervent debates.

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Consensus is a key element in a decentralized system and its choice (PoW, PoS, PBFT…) is determined largely by the blockchain’s purpose. 



The blockchain works thanks to a network of independent computers who execute its protocol: it is the first concrete realization of the distributed ledger technology, or DLT. Such an organization assures that blockchain (ledger) keeping is independent from any central authority. However this independence has a particular condition attached: all network computers must store an identical blockchain and agree on every update to it. The mechanism allowing this result is called a consensus. 



A distributed system is a group of independent and spatially separate computers (nodes) that work together on a shared task. These independence and remoteness make it much harder to achieve consensus and numerous studies on distributed ledgers (a subsection of distributed informatics) put this problem at the heart of the research. 



<h2>Understanding a distributed system </h2>



A consensus must take into consideration the characteristics of a distributed system, as well as its actors. 



Distributed system characteristics: 



📌 Competition - nodes work independently and simultaneously



📌 A global clock not always available - difficult to date and order the events 



📌 Message transfer - every consensus relies on message transfer between the nodes. Depending on a type of such transfer there are two classes of distributed systems:



 ➡️ Synchronous system: messages are delivered within a defined period



 ➡️ Asynchronous system: messages can be retarded for an undefined period



📌 Network partition - a part of the network does not communicate with another part







Distributed system’s actors are the nodes that can be: 



<ul>
<li>Simply faulty - nodes experiencing technical problems</li>



<li>Byzantine - nodes having incoherent or malicious behavior</li>



<li>Altruist - nodes who are always honest and work in the interest of the network</li>



<li>Rational - nodes acting in their best interest</li>
</ul>



The theory of distributed systems assimilates a blockchain to a replicated state machine -&nbsp;



a group of equal nodes&nbsp;allowing to transition after the reception of data (transaction) from one state to another (transition)&nbsp;according to the common rules&nbsp;and keeping a historical record of all these states (blockchain). 



The goal of a consensus is to make sure the nodes agree on transitions (output value) and the record, while taking into account the characteristics of a system and its actors. It comes as no surprise that such a task can quickly become problematic and that its conception depends on particular conditions in which a network evolves. 



<h2>Consensus theory </h2>



An algorithm can allow achieving consensus if it can satisfy two conditions: 



<ul>
<li>Agreement / safety - all non faulty nodes give the same output value</li>



<li>Termination / liveness - all non faulty nodes end up deciding on an output value</li>
</ul>







Achieving a consensus in a synchronous system is much easier than in an asynchronous one, notably when it comes to the liveness condition. However in reality many systems evolve in an asynchronous environment, which presents additional challenges. 



According to a study by Fisher, Lynch and Paterson a deterministic consensus in a distributed asynchronous system is impossible if at least one node is simply faulty (FLP impossibility result). Deterministic means that once the nodes agree on a new state, it could not be changed. 



This study leads to a conclusion that in order to circumvent the impossibility and achieve a consensus one must either evolve in a partially synchronous system, or choose a non-deterministic consensus. 



<h2>Consensus in a partially synchronous system: PFBT </h2>



In a partially synchronous system and in the absence of [tooltip content="nodes having incoherent or malicious behavior "] Byzantine nodes [/tooltip] algorithms such as Paxos or RAFT allow achieving consensus. 



In the presence of Byzantine nodes, the fundamental theoretical contribution is a study by Leslie Lamport, Robert Shostak and Marshall Pease called The Byzantin generals problem. This study shows that a system with n Byzantine nodes must have at least (3n+1) nodes. In other words, in order to achieve consensus a system must have less than a third of Byzantine nodes. 



The methodology of the study applies only to the synchronous systems, however other researches have been conducted under conditions of partial synchronicity.&nbsp; The consensus based on these studies are generally called BFT, or Byzantine Fault Tolerant consensus. 



One algorithm in particular has shown itself very useful: called PBFT (Practical Byzantin Fault Tolerant), it was proposed in 1999 by Miguel Castro et Barbara Liskov. Numerous blockchains today, such as Stellar, Ripple, Hyperledger and Tendermint are inspired by the PBFT. 



The PBFT algorithm and its variants necessitate partial synchronicity, and their implementation requires numerous messages circulating between the nodes. There’s designing a leader who proposes a new state, information rounds, votes… it is considered that the number of messages increases exponentially to the number to nodes. Hence these algorithms are not quite adapted to public blockchains with a big number of nodes, they are rather used in case of few nodes or in private blockchains. 



To summarize, the consensus like PBFT that circumvent the FLP impossibility by partial synchronicity are quite adapted to certain types of blockchains, but are still difficult to implement. Numerous researches in this field are being conducted in order to improve the algorithm or to adapt it to different conditions. 



<h2>Non-deterministic consensus: Pow and PoS </h2>



Bitcoin is the first blockchain ever created and thus the first one to implement a consensus algorithm in a blockchain. Bitcoin being public and having numerous nodes, the FLP impossibility was circumvented using a non-deterministic approach. 



Bitcoin’s innovation is called the <a href="https://d.center/explore/proof-of-work" class="ek-link">Proof of Work</a> (PoW), which, instead of electing a leader, gives an opportunity for anyone providing a PoW (solving a cryptographic puzzle) to propose a new state - a new block - to the blockchain (see <a href="https://d.center/explore/mining-and-consensus" class="ek-link">Bitcoin: consensus and mining</a>). 



The PoW consensus is non-deterministic, because it can happen that different blocks (states) are proposed at the same time and that one part of the network agrees on a state A, and another part of the network agrees on a state B, thus adding two different blocks to the blockchain at the same height. 



As a consensus the PoW assures the liveness (all non-faulty nodes end up giving an output value), but not the safety (all non-faulty nodes give the same output value). This can seem contradictory to the notion of consensus, for there’s no safety, but this situation does not last: before long the network converges to the same blockchain by choosing the one that has produced the biggest amount of work. Here the safety is probabilistic, meaning that the more a block is followed by other blocks, i.e. the more time passes, the bigger is the probability that block is definitive.  



The PoW consensus does not treat the problem of Byzantine nodes in a classic way (Byzantine nodes must be fewer than one third of the network nodes), but circumvents it by making Byzantine nodes’ acts more expensive and more random with respect to their goals. As in the case of safety, the result cannot be proven mathematically, but there’s a strong probability to achieve it. 



The PoW consensus has proven its worth and Bitcoin blockchain works under the condition of asynchronicity with numerous nodes and possible Byzantine actors. Many other blockchains have also adopted it. However, while PoW success is obvious, it has its set of disadvantages: slow speed, not immediate block finality, energy consumption, concentration of miners (nodes that provide PoW)... 



In order to address these concerns other consensus types were born, also non-deterministic and based on the idea of providing something in return for the right to propose a new block to the blockchain The most famous is the <a href="https://d.center/explore/proof-of-stake" class="ek-link">Proof of Stake</a><a href="https://d.center/explore/proof-of-stake" class="ek-link"> </a>(PoS) and its variant the Delegated Proof of Stake (DPoS).&nbsp; 



Instead of providing a proof of work that necessitates high energy spending, the PoS requires having native blockchain coins. The chances of submitting a block are linked more or less directly to the number of native coins a node possesses, in other words its stake in the blockchain. 



<h2>A perfect consensus?&nbsp; </h2>



Every consensus has its advantages and disadvantages and can be targeted by a specific type of attack. The criteria of a suitable consensus depend on a particular blockchain’s characteristics, notably:



📌 number of nodes



📌 public or private



📌 need or does not need an immediate finality



📌 network security



📌 speed



📌 capacity (number of transactions per second)



As of today the majority of blockchain consensus are inspired by the PoW, PoS, DPoS or PBFT. They can also mix them or create new ones, while the search of a perfect consensus continues and numerous developments are underway.

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Designed for the Bitcoin blockchain, Proof of Work (PoW) was the first Consensus protocol that allowed blockchain nodes to agree upon ledger updates.&nbsp;



Basically the PoW consensus requires from the nodes that want to propose a new block (miners) to find a piece of data that necessitates significant computational power to produce, but is easy for others to verify. The nature of this task makes the “brute force” the only possible way to proceed, thus obliging nodes to invest into sophisticated equipment and pay heavy electricity bills. These expenses are, in a way, a gauge of node’s good intentions, as they make it economically stupid/ not worthwhile/ to sabotage the system. (see <a href="https://d.center/explore/bitcoin-consensus-and-mining" class="ek-link">Bitcoin consensus and mining</a>)



As used in Bitcoin, the PoW consensus has another particularity: it manages bitcoin emission rhythm. The node that adds its block to the blockchain receives a reward of newly created bitcoins.



<h2>The PoW mechanism</h2>



The PoW puzzle exploits a particularity of Hash function – a math function taking an input of any length and giving an output of a fixed length. The only way to find the input data of a hash function's output is to attempt a brute-force search of possible inputs to see if they produce a match, which makes it practically impossible. To get a PoW a node must hash the block information until the result starts with a certain number of 0s. However, since a particular piece of information will always have the same hash, nodes are adding a variable piece of data (nonce and extra nonce for Bitcoin) in order to achieve the needed result.



The difficulty of this work is adjusted so as to limit the rate at which new blocks can be generated by the network.



Once a node finds a proof-of-work, it broadcasts the timestamped block to other nodes that verify it and add it to the blockchain if it’s a correct block as specified by the protocol.



This method does not assure the immediate agreement (safety) on block, since two nodes can provide their PoW almost at the same time and propose two different blocks to the network. In this case and if the two blocks are valid they are both accepted by different parts of the network, thus creating two different chains.This problem, however, is resolved with time, as the nodes always converge to the chain with the biggest amount of work.



<h2>Attacks on a PoW blockchain</h2>



The most obvious way of cheating in a PoW-based blockchain is Double Spending - a method allowing to spend a certain amount of cryptocurrency (and to receive a goods/service in return), then create a parallel chain of blocks without the transaction of spending that amount. If the quantity of work in the parallel chain is bigger than in the first chain, the network will automatically switch to the parallel one. In this case the attacker ends up having both the goods/service and the money.



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In order to be sure to double spend on a PoW network a potential attacker (a 
 Byzantine node 
 node having incoherent or malicious behavior 
 in consensus theory) must gather more than 50% of the network's computing power (also called the hash rate, or the quantity of hashes per second executed while attempting to find the hash with a requested amount of 0s) and keep it for a certain time needed to add several blocks.



This is called the 51% attack and its probability decreases as the network gets bigger.



In summary, the PoW consensus born with Bitcoin has shown its robustness and up to this day is considered as the most secure one. Its critics however note its important energy consumption and its difficulty to increase its scalability (number of transactions per second).