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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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Proof of Stake (PoS) is a type of consensus protocol which selects block validating nodes depending on their stake in the network's base currency.&nbsp;



The idea of using a stake in cryptocurrency as a gauge of validator’s honesty was first proposed in a forum post in 2011, then&nbsp; described in details in August 2012 in the Peercoin white paper, presenting it as a faster and cheaper alternative to the PoW.



In PoS the nodes who wish to become validators lock up their coins into a deposit, and the probability of being given the right to add the new block depends on the size of such deposit (or stake). The stake works as a financial pledge of security: in case of a fraudulent transaction validation the validator will lose a portion of his stake (event known as slashing) and the right to validate other blocks for a certain period of time.



In a PoS-based blockchains there is no monetary creation associated with block validation (coins are often pre-mined during the blockchain's launch), so the nodes' main reward is transaction fees. Also, the blocks are said to be forged rather than mined.



In order to discourage oligarchic tendencies and maintain the necessary decentralization level, the validator selection process often includes other criteria than the stake, such as staking age or randomization.



Some versions of PoS have BFT particularities, e.g. when nodes are selected to propose the new block, but its validation is done through a multi-round voting process, the weight of a vote being proportional to the size of the stake (such model is supposed to be used in the Casper - the consensus for ETH 2.0).



<h2>PoS security</h2>



A PoS-based blockchain can face certain security issues: the classical 51% attack, and also several other specific problems like “nothing at stake”, “stake grinding” and “long range attack”.



<h3>51% attack&nbsp;</h3>



In order to control a PoS-based blockchain and be able to approve fraudulent transactions (for example in order to execute double spending) , an attacker would need to stake 51% of all the staking, which would be not only really expensive, but also illogical, as after the attack becomes public, the coins will quickly depreciate.



<h3>Nothing at stake</h3>



In the first PoS-based blockchains block validators had nothing to lose by proposing blocks on all existing forks and thus increasing their chances to be rewarded - they had nothing at stake and it was enough to just keep the native cryptocurrency in their wallets. Such behavior carried a risk of non-execution of a consensus and increased the double spending risk. That is why later PoS-based blockchains require a security deposit which is lost in case of validator’s deceitful behavior, notably when they simultaneously propose or validate blocks on different chains.&nbsp;



<h3>Stake grinding</h3>



The stake grinding consists of trying to influence the validators selection and thus determine who will propose the next block. This issue is dealt with by randomizing the validators selection process.



<h3>Long range attack</h3>



The long range attack consists of getting the keys of old addresses that contained in the past enough native coins to influence the validator selection process. An attacker starts then to rewrite the blockchain from an old block, in order to replace the existing one and execute a double spending. Blockchains can protect themselves against a long range attack by setting up “checkpoints”, i.e. by signalling specific blocks in the chain, all blocks before it being considered as definitive and impossible to modify.



<h2>PoS now</h2>



The main advantage of the PoS algorithm is energy efficiency, which helps maintain the network's decentralization (a greater number of users is encouraged to run nodes and there's no need for them to gather in pools). To further diversify the network, many PoS-based blockchains introduce staking incentives, where every user can earn dividends by holding the coins in a stakeable wallet. They still need, however, to mature and improve their security in order to compete in robustness with Bitcoin-tested Proof- of-Work.Among the most famous blockchains using PoS consensus we can name Cardano, Tezos, Polkadot and <a href="https://d.center/explore/ethereum" class="ek-link">Ethereum</a> 2.0 with Casper upgrade.