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A fundamental problem in distributed computing and multi-agent systems is to achieve overall system reliability in the presence of a number of faulty processes. This often requires coordinating processes to reach consensus , or agree on some data value that is needed during computation. Example applications of consensus include agreeing on what transactions to commit to a database in which order, state machine replication , and atomic broadcasts . Real-world applications often requiring consensus include cloud computing , clock synchronization , PageRank , opinion formation, smart power grids , state estimation , control of UAVs (and multiple robots/agents in general), load balancing , blockchain , and others.

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98-570: CoinDesk is a news site specializing in bitcoin and digital currencies . Founded by Shakil Khan, the firm also provides guides to bitcoin for those new to digital currencies. Seven years after being acquired by Digital Currency Group , it was purchased in November 2023 by Bullish. CoinDesk was founded by entrepreneur Shakil Khan and began publishing in May 2013. Khan is also an investor in BitPay ,

196-419: A decentralized system, bitcoin operates without a central authority or single administrator, so that anyone can create a new bitcoin address and transact without needing any approval. This is accomplished through a specialized distributed ledger called a blockchain that records bitcoin transactions. The blockchain is implemented as an ordered list of blocks . Each block contains a SHA-256 hash of

294-511: A distributed lock service library called Chubby . Chubby maintains lock information in small files which are stored in a replicated database to achieve high availability in the face of failures. The database is implemented on top of a fault-tolerant log layer which is based on the Paxos consensus algorithm . In this scheme, Chubby clients communicate with the Paxos master in order to access/update

392-422: A free market ideology, bitcoin was invented in 2008 by Satoshi Nakamoto , an unknown person. Use of bitcoin as a currency began in 2009, with the release of its open-source implementation . In 2021, El Salvador adopted it as legal tender . It is mostly seen as an investment and has been described by some scholars as an economic bubble . As bitcoin is pseudonymous , its use by criminals has attracted

490-635: A non-peer-reviewed study by the Cambridge Centre for Alternative Finance (CCAF) estimated that bitcoin mining represented 0.4% of global electricity consumption . Another 2022 non-peer-reviewed commentary published in Joule estimated that bitcoin mining was responsible for 0.2% of world greenhouse gas emissions. About half of the electricity used is generated through fossil fuels . Moreover, mining hardware's short lifespan results in electronic waste . The amount of electrical energy consumed, and

588-469: A payment system than as a currency. In 2014, economist Robert J. Shiller wrote that bitcoin has potential as a unit of account for measuring the relative value of goods, as with Chile's Unidad de Fomento , but that "Bitcoin in its present form... doesn't really solve any sensible economic problem". François R. Velde, Senior Economist at the Chicago Fed , described bitcoin as "an elegant solution to

686-574: A proof-of-work scheme for spam control in 1997. The first proposals for distributed digital scarcity-based cryptocurrencies came from cypherpunks Wei Dai (b-money) and Nick Szabo ( bit gold ) in 1998. In 2004, Hal Finney developed the first currency based on reusable proof of work. These various attempts were not successful: Chaum's concept required centralized control and no banks wanted to sign on, Hashcash had no protection against double-spending , while b-money and bit gold were not resistant to Sybil attacks . The domain name bitcoin.org

784-538: A stablecoin , and the Celsius Network , a cryptocurrency loan company. In 2023, ordinals— non-fungible tokens (NFTs)—on bitcoin, went live. In January 2024, the first 11 US spot bitcoin ETFs began trading, offering direct exposure to bitcoin for the first time on American stock exchanges. As of June 2023, River Financial estimated that bitcoin had 81.7 million users, about 1% of the global population. At

882-478: A store of value , a medium of exchange , and a unit of account . According to The Economist in 2014, bitcoin functions best as a medium of exchange. In 2015, The Economist noted that bitcoins had three qualities useful in a currency: they are "hard to earn, limited in supply and easy to verify". However, a 2018 assessment by The Economist stated that cryptocurrencies met none of these three criteria. Per some researchers, as of 2015 , bitcoin functions more as

980-557: A treasury reserve asset , Square, Inc. , $ 50 million, and MassMutual , $ 100 million. In November 2020, PayPal added support for bitcoin in the US. In February 2021, bitcoin's market capitalization reached $ 1 trillion for the first time. In November 2021, the Taproot soft-fork upgrade was activated, adding support for Schnorr signatures , improved functionality of smart contracts and Lightning Network . Before, bitcoin only used

1078-662: A "pure bubble" as its intrinsic value is zero. According to him, some bubbles are long-lasting such as gold and fiat currencies, and it's impossible to predict whether bitcoin will collapse like other financial bubbles or become the new gold. According to research published in the International Review of Financial Analysis in 2018, bitcoin as an asset is highly volatile and does not behave like any other conventional asset. According to one 2022 analysis published in The Journal of Alternative Investments , bitcoin

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1176-447: A 'proof of stake' over a 'proof of work' system, is the high energy consumption demanded by the latter. As an example, bitcoin mining (2018) is estimated to consume non-renewable energy sources at an amount similar to the entire nations of Czech Republic or Jordan, while the total energy consumption of Ethereum, the largest proof of stake network, is just under that of 205 average US households. Some cryptocurrencies, such as Ripple, use

1274-461: A 2024 Nashville Bitcoin conference, Republican presidential candidate Donald J. Trump announced he was an energetic supporter of the industry and would make the country a "crypto capital of the planet". The unit of account of the bitcoin system is the bitcoin . It is most commonly represented with the symbol ₿ and the currency code BTC. However, the BTC code does not conform to ISO 4217 as BT

1372-457: A Byzantine consensus algorithm, simply by creating enough virtual participants to overwhelm the fault tolerance threshold. A permissionless consensus protocol, in contrast, allows anyone in the network to join dynamically and participate without prior permission, but instead imposes a different form of artificial cost or barrier to entry to mitigate the Sybil attack threat. Bitcoin introduced

1470-661: A bitcoin payment processor. At the start of 2016, CoinDesk was acquired by Digital Currency Group for an estimated US$ 500,000–600,000 . The next year, in 2017, the company acquired blockchain data and research platform Lawnmower. In 2021 the company acquired cryptocurrency data analytics firm TradeBlock. In December 2017, CoinDesk established CoinDesk Korea in collaboration with the 22nd Century Media Co., subsidiary of Hankyoreh Co., Ltd. to provide blockchain news service in South Korea. In November 2022, CoinDesk reported that FTX 's partner firm Alameda Research held

1568-492: A collective delusion ". A 2014 World Bank report also concluded that bitcoin was not a deliberate Ponzi scheme. Consensus (computer science) The consensus problem requires agreement among a number of processes (or agents) on a single data value. Some of the processes (agents) may fail or be unreliable in other ways, so consensus protocols must be fault-tolerant or resilient. The processes must put forth their candidate values, communicate with one another, and agree on

1666-619: A custom elliptic curve with the ECDSA algorithm to produce signatures . In September 2021, bitcoin became legal tender in El Salvador , alongside the US dollar. In October 2021, the first bitcoin futures exchange-traded fund (ETF), called BITO, from ProShares was approved by the SEC and listed on the CME . In May and June 2022, the bitcoin price fell following the collapses of TerraUSD ,

1764-428: A difficulty adjustment function and a reorganization function to achieve permissionless consensus in its open peer-to-peer network. To extend bitcoin's blockchain or distributed ledger , miners attempt to solve a cryptographic puzzle, where probability of finding a solution is proportional to the computational effort expended in hashes per second. The node that first solves such a puzzle has their proposed version of

1862-476: A full copy of the blockchain to check the validity of mined blocks, or lightweight clients, just to send and receive transactions without a local copy of the entire blockchain. Third-party internet services called online wallets store users' credentials on their servers, making them susceptible of hacks. Cold storage protects bitcoins from such hacks by keeping private keys offline, either through specialized hardware wallets or paper printouts. Nakamoto limited

1960-600: A growing use of bitcoin, alongside cash and cards, was reported in restaurant business. In September 2021, the Bitcoin Law made bitcoin legal tender in El Salvador , alongside the US dollar. The adoption has been criticized both internationally and within El Salvador. In particular, in 2022, the International Monetary Fund (IMF) urged El Salvador to reverse its decision. As of 2022 ,

2058-544: A lengthy delay. Of the two types of failures, Byzantine failures are far more disruptive. Thus, a consensus protocol tolerating Byzantine failures must be resilient to every possible error that can occur. A stronger version of consensus tolerating Byzantine failures is given by strengthening the Integrity constraint: The consensus problem may be considered in the case of asynchronous or synchronous systems. While real world communications are often inherently asynchronous, it

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2156-400: A limited number of faulty processes . These protocols must satisfy several requirements to be useful. For instance, a trivial protocol could have all processes output binary value 1. This is not useful; thus, the requirement is modified such that the production must depend on the input. That is, the output value of a consensus protocol must be the input value of some process. Another requirement

2254-749: A man attempting to use them to buy illegal substances. This marked the first time a government agency had seized bitcoins. The FBI seized about ₿30,000 in October 2013 from Silk Road, following the arrest of its founder Ross Ulbricht . In December 2013, the People's Bank of China prohibited Chinese financial institutions from using bitcoin. After the announcement, the value of bitcoin dropped, and Baidu no longer accepted bitcoins for certain services. Buying real-world goods with any virtual currency had been illegal in China since at least 2009. Research produced by

2352-570: A new address for each transaction. In the bitcoin network, each bitcoin is treated equally, ensuring basic fungibility . However, users and applications can choose to differentiate between bitcoins. While wallets and software treat all bitcoins the same, each bitcoin's transaction history is recorded on the blockchain. This public record allows for chain analysis , where users can identify and potentially reject bitcoins from controversial sources. For example, in 2012, Mt. Gox froze accounts containing bitcoins identified as stolen. Bitcoin wallets were

2450-507: A new block can collect transaction fees from the included transactions and a set reward in bitcoins. To claim this reward, a special transaction called a coinbase is included in the block, with the miner as the payee. All bitcoins in existence have been created through this type of transaction. This reward is halved every 210,000 blocks until ₿21 million, with new bitcoin issuance slated to end around 2140. Afterward, miners will only earn from transaction fees. These fees are determined by

2548-472: A polynomial time binary consensus protocol that tolerates Byzantine failures is the Phase King algorithm by Garay and Berman. The algorithm solves consensus in a synchronous message passing model with n processes and up to f failures, provided n > 4 f . In the phase king algorithm, there are f + 1 phases, with 2 rounds per phase. Each process keeps track of its preferred output (initially equal to

2646-410: A previous unspent output in the blockchain. Using multiple inputs is similar to using multiple coins in a cash transaction. As in a cash transaction, the sum of inputs can exceed the intended sum of payments. In such a case, an additional output can return the change back to the payer. Unallocated input satoshis in the transaction become the transaction fee. Losing a private key means losing access to

2744-460: A process may undergo, a crash failure or a Byzantine failure . A crash failure occurs when a process abruptly stops and does not resume. Byzantine failure s are failures in which absolutely no conditions are imposed. For example, they may occur as a result of the malicious actions of an adversary. A process that experiences a Byzantine failure may send contradictory or conflicting data to other processes, or it may sleep and then resume activity after

2842-561: A public value and generate a consensus vector with the following requirements: It can be shown that variations of these problems are equivalent in that the solution for a problem in one type of model may be the solution for another problem in another type of model. For example, a solution to the Weak Byzantine General problem in a synchronous authenticated message passing model leads to a solution for Weak Interactive Consistency. An interactive consistency algorithm can solve

2940-426: A random private key and then computing the corresponding address. This process is almost instant, but the reverse (finding the private key for a given address) is nearly impossible. Publishing a bitcoin address does not risk its private key, and it is extremely unlikely to accidentally generate a used key with funds. To use bitcoins, owners need their private key to digitally sign transactions, which are verified by

3038-670: A significant portion of its assets in FTX's native token FTT. The news led to a bank run and liquidity crisis at FTX, culminating in FTX filing for bankruptcy protection . In November 2023, CoinDesk was acquired by Bullish Global, run by Tom Farley , a former New York Stock Exchange president. It operates a cryptocurrency exchange. CoinDesk TV is an online video channel which produce live news program everyday. The channel produces daily and weekly shows including "First Mover", "The Hash", "All About Bitcoin", "Word On The Block" and so on. Consensus

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3136-540: A single consensus value. The consensus problem is a fundamental problem in controlling multi-agent systems. One approach to generating consensus is for all processes (agents) to agree on a majority value. In this context, a majority requires at least one more than half of the available votes (where each process is given a vote). However, one or more faulty processes may skew the resultant outcome such that consensus may not be reached or may be reached incorrectly. Protocols that solve consensus problems are designed to deal with

3234-556: A stronger, transferable form of authentication, where each message is signed by the sender, so that a receiver knows not just the immediate source of every message, but the participant that initially created the message. This stronger type of authentication is achieved by digital signatures, and when this stronger form of authentication is available, protocols can tolerate a larger number of faults. The two different authentication models are often called oral communication and written communication models. In an oral communication model,

3332-931: A system of validating nodes to validate the ledger. This system used by Ripple, called Ripple Protocol Consensus Algorithm (RPCA), works in rounds: Other participation rules used in permissionless consensus protocols to impose barriers to entry and resist sybil attacks include proof of authority , proof of space , proof of burn, or proof of elapsed time. Contrasting with the above permissionless participation rules, all of which reward participants in proportion to amount of investment in some action or resource, proof of personhood protocols aim to give each real human participant exactly one unit of voting power in permissionless consensus, regardless of economic investment. Proposed approaches to achieving one-per-person distribution of consensus power for proof of personhood include physical pseudonym parties, social networks, pseudonymized government-issued identities, and biometrics. To solve

3430-455: A transaction committed to a database. A special case of the single-value consensus problem, called binary consensus , restricts the input, and hence the output domain, to a single binary digit {0,1}. While not highly useful by themselves, binary consensus protocols are often useful as building blocks in more general consensus protocols, especially for asynchronous consensus. In multi-valued consensus protocols such as Multi-Paxos and Raft ,

3528-410: A value v {\displaystyle v} to all processes such that: It is also known as The General's Problem. Formal requirements for a consensus protocol may include: For n processes in a partially synchronous system (the system alternates between good and bad periods of synchrony), each process chooses a private value. The processes communicate with each other by rounds to determine

3626-657: Is CoinDesk's annual crypto summit. It started in 2015. It has been held in New York City from 2017 to 2019, virtually in 2020 and 2021, and in Austin, Texas since 2022. The CoinDesk Bitcoin Price Index (CoinDesk BPI) was launched in September 2013. The Bitcoin Price Index is an average of bitcoin prices across bitcoin exchanges, and began by using price data from Bitstamp , BTC-e and CampBX. Although Mt. Gox data

3724-421: Is allowed, whereas in others processes are completely anonymous. Shared memory models in which processes communicate by accessing objects in shared memory are also an important area of research. In most models of communication protocol participants communicate through authenticated channels. This means that messages are not anonymous, and receivers know the source of every message they receive. Some models assume

3822-435: Is difficult. However, the use of bitcoin can be criminalized, and shutting down exchanges and the peer-to-peer economy in a given country would constitute a de facto ban. The use of bitcoin by criminals has attracted the attention of financial regulators, legislative bodies, and law enforcement. Nobel-prize winning economist Joseph Stiglitz says that bitcoin's anonymity encourages money laundering and other crimes. This

3920-589: Is given in Big O notation in the number of rounds of message exchange as a function of some input parameters (typically the number of processes and/or the size of the input domain). Message complexity refers to the amount of message traffic that is generated by the protocol. Other factors may include memory usage and the size of messages. Varying models of computation may define a "consensus problem". Some models may deal with fully connected graphs, while others may deal with rings and trees. In some models message authentication

4018-430: Is more practical and often easier to model synchronous systems, given that asynchronous systems naturally involve more issues than synchronous ones. In synchronous systems, it is assumed that all communications proceed in rounds . In one round, a process may send all the messages it requires, while receiving all messages from other processes. In this manner, no message from one round may influence any messages sent within

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4116-550: Is no consensus solution that can tolerate one or more crash failures even when only requiring the non triviality property. This result is sometimes called the FLP impossibility proof named after the authors Michael J. Fischer , Nancy Lynch , and Mike Paterson who were awarded a Dijkstra Prize for this significant work. The FLP result has been mechanically verified to hold even under fairness assumptions . However, FLP does not state that consensus can never be reached: merely that under

4214-406: Is that a process may decide upon an output value only once, and this decision is irrevocable. A method is correct in an execution if it does not experience a failure. A consensus protocol tolerating halting failures must satisfy the following properties. Variations on the definition of integrity may be appropriate, according to the application. For example, a weaker type of integrity would be for

4312-449: Is the country code of Bhutan, and ISO 4217 requires the first letter used in global commodities to be 'X'. XBT, a code that conforms to ISO 4217 though not officially part of it, is used by Bloomberg L.P. No uniform capitalization convention exists; some sources use Bitcoin , capitalized, to refer to the technology and network , and bitcoin , lowercase, for the unit of account. The Cambridge Advanced Learner's Dictionary and

4410-513: Is the first decentralized cryptocurrency . Nodes in the peer-to-peer bitcoin network verify transactions through cryptography and record them in a public distributed ledger , called a blockchain , without central oversight. Consensus between nodes is achieved using a computationally intensive process based on proof of work , called mining , that secures the bitcoin blockchain. Mining consumes large quantities of electricity and has been criticized for its environmental impact . Based on

4508-580: Is the main justification behind bitcoin bans. As of November 2021 , nine countries applied an absolute ban (Algeria, Bangladesh, China, Egypt, Iraq, Morocco, Nepal, Qatar, and Tunisia) while another 42 countries had an implicit ban. Bitcoin is only legal tender in El Salvador . As of 2018 , bitcoin is rarely used in transactions with merchants, but it is popular to purchase illegal goods online. Prices are not usually quoted in bitcoin and trades involve conversions into fiat currencies. Commonly cited reasons for not using bitcoin include high costs,

4606-416: Is the number of failures and n {\displaystyle n} is the number of processes. For systems with n {\displaystyle n} processors, of which f {\displaystyle f} are Byzantine, it has been shown that there exists no algorithm that solves the consensus problem for n ≤ 3 f {\displaystyle n\leq 3f} in

4704-608: The Journal of Monetary Economics concluded that price manipulation occurred during the Mt. Gox bitcoin theft and that the market remained vulnerable to manipulation. Research published in The Journal of Finance also suggested that trading associated with increases in the amount of the Tether cryptocurrency and associated trading at the Bitfinex exchange accounted for about half of

4802-510: The Oxford Advanced Learner's Dictionary use the capitalized and lowercase variants without distinction. One bitcoin is divisible to eight decimal places. Units for smaller amounts of bitcoin are the millibitcoin (mBTC), equal to 1 ⁄ 1000 bitcoin, and the satoshi (sat), representing 1 ⁄ 100 000 000 (one hundred millionth) bitcoin, the smallest amount possible. 100,000 satoshis are one mBTC. As

4900-510: The Central Bank of Iran , allowing the central bank to use it for imports. Some constituent states also accept tax payments in bitcoin, including Colorado ( US ) and Zug ( Switzerland ). As of 2023, the US government owned more than $ 5 billion worth of seized bitcoin. As of 2018 , the overwhelming majority of bitcoin transactions took place on cryptocurrency exchanges . Since 2014, regulated bitcoin funds also allow exposure to

4998-538: The European Central Bank , the decentralization of money offered by bitcoin has its theoretical roots in the Austrian school of economics , especially with Friedrich Hayek 's The Denationalisation of Money , in which he advocates a complete free market in the production, distribution and management of money to end the monopoly of central banks . Sociologist Nigel Dodd argues that the essence of

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5096-698: The University of Cambridge estimated that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet , most of them using bitcoin. In August 2017, the SegWit software upgrade was activated. Segwit was intended to support the Lightning Network as well as improve scalability . SegWit opponents, who supported larger blocks as a scalability solution, forked to create Bitcoin Cash , one of many forks of bitcoin . In December 2017,

5194-429: The hashing power , it would allow them to censor transactions and double-spend coins. In 2014, mining pool Ghash.io reached 51% mining power, causing safety concerns, but later voluntarily capped its power at 39.99% for the benefit of the whole network. A few entities also dominate other parts of the ecosystem such as the client software, online wallets, and simplified payment verification (SPV) clients. According to

5292-413: The oral-messages model . The proof is constructed by first showing the impossibility for the three-node case n = 3 {\displaystyle n=3} and using this result to argue about partitions of processors. In the written-messages model there are protocols that can tolerate n = f + 1 {\displaystyle n=f+1} . In a fully asynchronous system there

5390-637: The US Financial Crimes Enforcement Network (FinCEN) established regulatory guidelines for "decentralized virtual currencies" such as bitcoin, classifying American bitcoin miners who sell their generated bitcoins as money services businesses , subject to registration and other legal obligations. In May 2013, US authorities seized the unregistered exchange Mt. Gox . In June 2013, the US Drug Enforcement Administration seized ₿11.02 from

5488-534: The asset or to futures as an investment. Bitcoin is used as a store of value : individuals and companies such as the Winklevoss twins and Elon Musk 's companies SpaceX and Tesla have massively invested in bitcoin. Bitcoin wealth is highly concentrated, with 0.01% holding 27% of in-circulation currency, as of 2021. As of September 2023 , El Salvador had $ 76.5 million worth of bitcoin in its international reserves . In 2018, research published in

5586-442: The attention of regulators, leading to its ban by several countries as of 2021 . Before bitcoin, several digital cash technologies were released, starting with David Chaum 's ecash in the 1980s. The idea that solutions to computational puzzles could have some value was first proposed by cryptographers Cynthia Dwork and Moni Naor in 1992. The concept was independently rediscovered by Adam Back who developed Hashcash ,

5684-440: The basis of bitcoin's consensus mechanism . The difficulty of generating a block is deterministically adjusted based on the mining power on the network by changing the difficulty target, which is recalibrated every 2,016 blocks (approximately two weeks) to maintain an average time of ten minutes between new blocks. The process requires significant computational power and specialized hardware . Miners who successfully find

5782-528: The bitcoin ideology is to remove money from social, as well as governmental, control. The Economist describes bitcoin as "a techno-anarchist project to create an online version of cash, a way for people to transact without the possibility of interference from malicious governments or banks". These philosophical ideas initially attracted libertarians and anarchists . Economist Paul Krugman argues that cryptocurrencies like bitcoin are only used by bank skeptics and criminals. Money serves three purposes:

5880-561: The bitcoins, with no other proof of ownership accepted by the protocol . For instance, in 2013, a user lost ₿7,500, valued at US$ 7.5 million, by accidentally discarding a hard drive with the private key. It is estimated that around 20% of all bitcoins are lost. The private key must also be kept secret as its exposure, such as through a data breach , can lead to theft of the associated bitcoins. As of December 2017 , approximately ₿980,000 had been stolen from cryptocurrency exchanges . The mining process in bitcoin involves maintaining

5978-423: The block size to one megabyte . The limited block size and frequency can lead to delayed processing of transactions, increased fees and a bitcoin scalability problem . The Lightning Network , second-layer routing network, is a potential scaling solution. Research shows a trend towards centralization in bitcoin as miners join pools for stable income. If a single miner or pool controls more than 50% of

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6076-402: The blockchain across all nodes without central oversight. This process tracks bitcoin spending, ensuring each bitcoin is spent only once . Unlike a traditional ledger that tracks physical currency, bitcoins exist digitally as unspent outputs of transactions . In the blockchain, bitcoins are linked to specific addresses that are hashes of a public key . Creating an address involves generating

6174-454: The blockchain through computer processing power . Miners group and broadcast new transactions into blocks, which are then verified by the network. Each block must contain a proof of work (PoW) to be accepted, involving finding a nonce number that, combined with the block content, produces a hash numerically smaller than the network's difficulty target . This PoW is simple to verify but hard to generate, requiring many attempts. PoW forms

6272-776: The chain, known as the genesis block . Embedded in this block was the text "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks ", which is the date and headline of an issue of The Times newspaper. Nine days later, Hal Finney received the first bitcoin transaction: ten bitcoins from Nakamoto. Wei Dai and Nick Szabo were also early supporters. On May 22, 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for ₿10,000, in what would later be celebrated as "Bitcoin Pizza Day". Blockchain analysts estimate that Nakamoto had mined about one million bitcoins before disappearing in 2010 when he handed

6370-579: The consensus problem by having each process choose the majority value in its consensus vector as its consensus value. There is a t-resilient anonymous synchronous protocol which solves the Byzantine Generals problem , if t n < 1 3 {\displaystyle {\tfrac {t}{n}}<{\tfrac {1}{3}}} and the Weak Byzantine Generals case where t {\displaystyle t}

6468-421: The consensus problem in a shared-memory system, concurrent objects must be introduced. A concurrent object, or shared object, is a data structure which helps concurrent processes communicate to reach an agreement. Traditional implementations using critical sections face the risk of crashing if some process dies inside the critical section or sleeps for an intolerably long time. Researchers defined wait-freedom as

6566-510: The decision value to equal a value that some correct process proposed – not necessarily all of them. There is also a condition known as validity in the literature which refers to the property that a message sent by a process must be delivered. A protocol that can correctly guarantee consensus amongst n processes of which at most t fail is said to be t-resilient . In evaluating the performance of consensus protocols two factors of interest are running time and message complexity . Running time

6664-402: The delta to their own game state and comparing the game state hashes. If the hashes do not agree then a vote is cast, and those players whose game state is in the minority are disconnected and removed from the game (known as a desync.) Another well-known approach is called MSR-type algorithms which have been used widely from computer science to control theory. Bitcoin uses proof of work ,

6762-635: The e-waste generated, is comparable to that of Greece and the Netherlands, respectively. Bitcoin is pseudonymous , with funds linked to addresses, not real-world identities. While the owners of these addresses are not directly identified, all transactions are public on the blockchain. Patterns of use, like spending coins from multiple inputs, can hint at a common owner. Public data can sometimes be matched with known address owners. Bitcoin exchanges might also need to collect personal data as per legal requirements. For enhanced privacy , users can generate

6860-578: The first cryptocurrency wallets , enabling users to store the information necessary to transact bitcoins. The first wallet program, simply named Bitcoin , and sometimes referred to as the Satoshi client , was released in 2009 by Nakamoto as open-source software . Bitcoin Core is among the best known clients . Forks of Bitcoin Core exist such as Bitcoin Unlimited . Wallets can be full clients, with

6958-748: The first futures on bitcoin was introduced by the Chicago Mercantile Exchange (CME). In February 2018, the price crashed after China imposed a complete ban on bitcoin trading. The percentage of bitcoin trading in the Chinese renminbi fell from over 90% in September 2017 to less than 1% in June 2018. During the same year, bitcoin prices were negatively affected by several hacks or thefts from cryptocurrency exchanges. In 2020, some major companies and institutions started to acquire bitcoin: MicroStrategy invested $ 250 million in bitcoin as

7056-957: The first permissionless consensus protocol using proof of work and a difficulty adjustment function, in which participants compete to solve cryptographic hash puzzles, and probabilistically earn the right to commit blocks and earn associated rewards in proportion to their invested computational effort. Motivated in part by the high energy cost of this approach, subsequent permissionless consensus protocols have proposed or adopted other alternative participation rules for Sybil attack protection, such as proof of stake , proof of space , and proof of authority . Three agreement problems of interest are as follows. A collection of n {\displaystyle n} processes, numbered from 0 {\displaystyle 0} to n − 1 , {\displaystyle n-1,} communicate by sending messages to one another. Process 0 {\displaystyle 0} must transmit

7154-406: The first round and serves as a tie breaker. Each process then updates its preferred value as follows. If the count of the majority value the process observed in the first round is greater than n /2 + f , the process changes its preference to that majority value; otherwise it uses the phase king's value. At the end of f + 1 phases the processes output their preferred values. Google has implemented

7252-439: The goal is to agree on not just a single value but a series of values over time, forming a progressively-growing history. While multi-valued consensus may be achieved naively by running multiple iterations of a single-valued consensus protocol in succession, many optimizations and other considerations such as reconfiguration support can make multi-valued consensus protocols more efficient in practice. There are two types of failures

7350-422: The greatest amount of effort to produce. To tamper or censor the ledger, one needs to control the majority of the global hashrate . The high cost required to reach this level of computational power secures the bitcoin blockchain. Bitcoin mining's environmental impact is controversial and has attracted the attention of regulators, leading to restrictions or incentives in various jurisdictions . As of 2022 ,

7448-487: The guarantee that the algorithm completes in a finite number of steps. The consensus number of a concurrent object is defined to be the maximum number of processes in the system which can reach consensus by the given object in a wait-free implementation. Objects with a consensus number of n {\displaystyle n} can implement any object with a consensus number of n {\displaystyle n} or lower, but cannot implement any objects with

7546-438: The immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message. In the most traditional single-value consensus protocols such as Paxos , cooperating nodes agree on a single value such as an integer, which may be of variable size so as to encode useful metadata such as

7644-509: The inability to process chargebacks , high price volatility , long transaction times, and transaction fees (especially for small purchases). Bloomberg reported that bitcoin was being used for large-item purchases on the site Overstock.com and for cross-border payments to freelancers . As of 2015 , there was little sign of bitcoin use in international remittances despite high fees charged by banks and Western Union who compete in this market. Despite associated risks and costs, in 2022,

7742-642: The inclusion of Bitfinex price data, according to CoinDesk: "Since the decline of Mt. Gox, we have observed that Bitfinex has been able to sustain a dramatic increase in its share of the total volume of U.S. dollar-denominated bitcoins traded". Publications which have referenced the Bitcoin Price Index data or price include the BBC , The Wall Street Journal , Reuters , The New York Times , CNBC , and Bloomberg News . In February 2014, CoinDesk released its first 'State of Bitcoin' report. The aim of

7840-463: The model's assumptions, no algorithm can always reach consensus in bounded time. In practice it is highly unlikely to occur. The Paxos consensus algorithm by Leslie Lamport , and variants of it such as Raft , are used pervasively in widely deployed distributed and cloud computing systems. These algorithms are typically synchronous, dependent on an elected leader to make progress, and tolerate only crashes and not Byzantine failures. An example of

7938-733: The network alert key and control of the code repository over to Gavin Andresen . Andresen later became lead developer at the Bitcoin Foundation , an organization founded in September 2012 to promote bitcoin. After early " proof-of-concept " transactions, the first major users of bitcoin were black markets , such as the dark web Silk Road . During its 30 months of existence, beginning in February 2011, Silk Road exclusively accepted bitcoins as payment, transacting ₿9.9 million, worth about $ 214 million. In March 2013,

8036-402: The network using the public key, keeping the private key secret. Bitcoin transactions use a Forth -like scripting language , involving one or more inputs and outputs. When sending bitcoins, a user specifies the recipients' addresses and the amount for each output. This allows sending bitcoins to several recipients in a single transaction. To prevent double-spending, each input must refer to

8134-458: The network. Consensus algorithms traditionally assume that the set of participating nodes is fixed and given at the outset: that is, that some prior (manual or automatic) configuration process has permissioned a particular known group of participants who can authenticate each other as members of the group. In the absence of such a well-defined, closed group with authenticated members, a Sybil attack against an open consensus group can defeat even

8232-558: The network. In most normal situations, process scheduling has a degree of natural randomness. In an asynchronous model, some forms of failures can be handled by a synchronous consensus protocol. For instance, the loss of a communication link may be modeled as a process which has suffered a Byzantine failure. Randomized consensus algorithms can circumvent the FLP impossibility result by achieving both safety and liveness with overwhelming probability, even under worst-case scheduling scenarios such as an intelligent denial-of-service attacker in

8330-568: The next block of transactions added to the ledger and eventually accepted by all other nodes. As any node in the network can attempt to solve the proof-of-work problem, a Sybil attack is infeasible in principle unless the attacker has over 50% of the computational resources of the network. Other cryptocurrencies (e.g. Ethereum , NEO, STRATIS, ...) use proof of stake , in which nodes compete to append blocks and earn associated rewards in proportion to stake , or existing cryptocurrency allocated and locked or staked for some time period. One advantage of

8428-440: The previous block, chaining them in chronological order. The blockchain is maintained by a peer-to-peer network. Individual blocks, public addresses, and transactions within blocks are public information, and can be examined using a blockchain explorer. Nodes validate and broadcast transactions, each maintaining a copy of the blockchain for ownership verification. A new block is created every 10 minutes on average, updating

8526-601: The price increase in bitcoin in late 2017. Bitcoin, along with other cryptocurrencies, has been described as an economic bubble by several economists, including Nobel Prize in Economics laureates, such as Joseph Stiglitz , James Heckman , and Paul Krugman . Another recipient of the prize, Robert Shiller , argues that bitcoin is rather a fad that may become an asset class . He describes its price growth as an "epidemic", driven by contagious narratives . In 2024, Jean Tirole , also Nobel laureate, described bitcoin as

8624-646: The problem of creating a digital currency". David Andolfatto, Vice President at the Federal Reserve Bank of St. Louis , stated that bitcoin is a threat to the establishment, which he argues is a good thing for the Federal Reserve System and other central banks , because it prompts these institutions to operate sound policies. The legal status of bitcoin varies substantially from one jurisdiction to another. Because of its decentralized nature and its global presence, regulating bitcoin

8722-426: The process's own input value). In the first round of each phase each process broadcasts its own preferred value to all other processes. It then receives the values from all processes and determines which value is the majority value and its count. In the second round of the phase, the process whose id matches the current phase number is designated the king of the phase. The king broadcasts the majority value it observed in

8820-399: The replicated log; i.e., read/write to the files. Many peer-to-peer online real-time strategy games use a modified lockstep protocol as a consensus protocol in order to manage game state between players in a game. Each game action results in a game state delta broadcast to all other players in the game along with a hash of the total game state. Each player validates the change by applying

8918-555: The report is: to provide an overview of key cryptocurrency trends, challenges, and opportunities, while also highlighting the most important developments over the last year . A follow-up report in Q2 2014 highlighted that venture capital investment in bitcoin companies was up 28 percent compared to the previous quarter, and that VC investment was pouring into European Bitcoin startups. Bitcoin Bitcoin (abbreviation: BTC ; sign : ₿ )

9016-504: The same round. In a fully asynchronous message-passing distributed system, in which at least one process may have a crash failure , it has been proven in the famous 1985 FLP impossibility result by Fischer, Lynch and Paterson that a deterministic algorithm for achieving consensus is impossible. This impossibility result derives from worst-case scheduling scenarios, which are unlikely to occur in practice except in adversarial situations such as an intelligent denial-of-service attacker in

9114-407: The transaction's size and the amount of data stored, measured in satoshis per byte. The proof of work system and the chaining of blocks make blockchain modifications very difficult, as altering one block requires changing all subsequent blocks. As more blocks are added, modifying older blocks becomes increasingly challenging. In case of disagreement, nodes trust the longest chain, which required

9212-708: The use of Bitcoin in El Salvador remains low: 80% of businesses refused to accept it despite being legally required to. In April 2022, the Central African Republic (CAR) adopted bitcoin as legal tender alongside the CFA franc , but repealed the reform one year later. Bitcoin is also used by some governments. For instance, the Iranian government initially opposed cryptocurrencies, but later saw them as an opportunity to circumvent sanctions . Since 2020, Iran has required local bitcoin miners to sell bitcoin to

9310-613: Was less volatile than oil , silver , US Treasuries , and 190 stocks in the S&;P 500 during and after the 2020 stock market crash . The term hodl was created in December 2013 for holding bitcoin rather than selling it during periods of volatility. Economists, investors, and the central bank of Estonia have described bitcoin as a potential Ponzi scheme . Legal scholar Eric Posner disagrees, however, as "a real Ponzi scheme takes fraud; bitcoin, by contrast, seems more like

9408-553: Was not used initially, due to withdrawal concerns for US customers, in November 2013, Mt. Gox was added to the BPI due to "a reduction in the risk premium and the option of additional deposit/withdrawal methods". The Mt. Gox bitcoin exchange was eventually removed from the index in February 2014 after its "persistent failure to meet the index's standards for inclusion". The index was restored to an average of three exchanges in March 2014 with

9506-557: Was registered on 18 August 2008. On 31 October 2008, a link to a white paper authored by Satoshi Nakamoto titled Bitcoin: A Peer-to-Peer Electronic Cash System was posted to a cryptography mailing list. Nakamoto implemented the bitcoin software as open-source code and released it in January 2009. Nakamoto's identity remains unknown. According to computer scientist Arvind Narayanan , all individual components of bitcoin originated in earlier academic literature. Nakamoto's innovation

9604-406: Was their complex interplay resulting in the first decentralized, Sybil resistant, Byzantine fault tolerant digital cash system, that would eventually be referred to as the first blockchain. Nakamoto's paper was not peer reviewed and was initially ignored by academics, who argued that it could not work. On 3 January 2009, the bitcoin network was created when Nakamoto mined the starting block of

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