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Analysis of Mining Performance Based on Mathmatical Approach of PoW AUTHORS ABSTRACT Blockchain technology has been developed for cryptocurrency systems. Bitcoin, the most famous cryptocurrency type, guarantees a safe consensus using the Proof of Work (PoW) process. The PoW scheme is currently operating as a basic consensus algorithm for blockchain systems that are used widely in various industries. However, the PoW algorithm lacks in support of mathematical analysis, which hinders discoveries of pote
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
300
Analysis of Mining Performance Based on Mathmatical Approach of PoW AUTHORS ABSTRACT Blockchain technology has been developed for cryptocurrency systems. Bitcoin, the most famous cryptocurrency type, guarantees a safe consensus using the Proof of Work (PoW) process. The PoW scheme is currently operating as a basic consensus algorithm for blockchain systems that are used widely in various industries. However, the PoW algorithm lacks in support of mathematical analysis, which hinders discoveries of pote
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
301
ntial weaknesses and flaws in the blockchain system. Therefore, in this paper, the correlation between the key parameters (i.e., TPS, difficulty, miners) in a blockchain system are analyzed based on mathematical analysis. KEYWORDS Blockchain, PoW, Bitcoin, Ehereum SECTION: INTRODUCTION Bitcoin was proposed by Satoshi Nakamoto as a method to support intermediary-less currency systems [1]. Bitcoin is a typical cryptocurrency that uses block chains and is considered to be the first currency system to mai
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
302
ntial weaknesses and flaws in the blockchain system. Therefore, in this paper, the correlation between the key parameters (i.e., TPS, difficulty, miners) in a blockchain system are analyzed based on mathematical analysis. KEYWORDS Blockchain, PoW, Bitcoin, Ehereum SECTION: INTRODUCTION Bitcoin was proposed by Satoshi Nakamoto as a method to support intermediary-less currency systems [1]. Bitcoin is a typical cryptocurrency that uses block chains and is considered to be the first currency system to mai
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
303
ntain decentralization and security simultaneously. This is possible due to the Proof of Work (PoW) process, which is the consensus algorithm used in most blockchains. In the PoW process, miners calculate a cryptographic puzzle for a reward, which is the right to make a valid transaction crypto block that will be added to the blockchain. The cryptographic puzzle is based on the SHA-256 hash function, in which miners spend a certain amount of time to solve them. The PoW algorithm in the block chain forces
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
304
miners to solve the difficult hash puzzles and maintain the blockchain system by paying a reward. However, the PoW algorithm also has disadvantages that it consumes a large amount of energy. Therefore, there are various consensus algorithms that can be used in blockchains, such as, the Proof of Stake (PoS) or Practical Byzantine Fault Tolerance (PBFT). Nevertheless, the reason that PoW is widely used for blockchains is due to the high security level supported by the PoW process. Decentralization, securi
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
305
ty, and scalability are the three features known as the blockchain trilemma, which seem impossible to have a complete solution implemented currently. Bitcoin and Ethereum, which use the PoW process, have low transactions per second (TPS) performances, resulting in long delays, in order to mainta
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Analysis of Mining Performance Based on Mathmatical Approach of PoW
306
Ethereum White Paper A NEXT GENERATION SMART CONTRACT & DECENTRALIZED APPLICATION PLATFORM By Vitalik Buterin When Satoshi Nakamoto first set the Bitcoin blockchain into motion in January 2009, he was simultaneously introducing two radical and untested concepts. The first is the "bitcoin", a decentralized peer-to-peer online currency that maintains a value without any backing, intrinsic value or central issuer. So far, the "bitcoin" as a currency
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Ethereum white paper a next generation smart contr
307
Ethereum White Paper A NEXT GENERATION SMART CONTRACT & DECENTRALIZED APPLICATION PLATFORM By Vitalik Buterin When Satoshi Nakamoto first set the Bitcoin blockchain into motion in January 2009, he was simultaneously introducing two radical and untested concepts. The first is the "bitcoin", a decentralized peer-to-peer online currency that maintains a value without any backing, intrinsic value or central issuer. So far, the "bitcoin" as a currency
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Ethereum white paper a next generation smart contr
308
unit has taken up the bulk of the public attention, both in terms of the political aspects of a currency without a central bank and its extreme upward and downward volatility in price. However, there is also another, equally important, part to Satoshi's grand experiment: the concept of a proof of work-based blockchain to allow for public agreement on the order of transactions. Bitcoin as an application can be described as a firs
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Ethereum white paper a next generation smart contr
309
unit has taken up the bulk of the public attention, both in terms of the political aspects of a currency without a central bank and its extreme upward and downward volatility in price. However, there is also another, equally important, part to Satoshi's grand experiment: the concept of a proof of work-based blockchain to allow for public agreement on the order of transactions. Bitcoin as an application can be described as a firs
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Ethereum white paper a next generation smart contr
310
t-to-file system: if one entity has 50 BTC, and simultaneously sends the same 50 BTC to A and to B, only the transaction that gets confirmed first will process. There is no intrinsic way of determining from two transactions which came earlier, and for decades this stymied the development of decentralized digital currency. Satoshi's blockchain was the first credible decentralized solution. And now, attention is rapidly starting to shi
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Ethereum white paper a next generation smart contr
311
t-to-file system: if one entity has 50 BTC, and simultaneously sends the same 50 BTC to A and to B, only the transaction that gets confirmed first will process. There is no intrinsic way of determining from two transactions which came earlier, and for decades this stymied the development of decentralized digital currency. Satoshi's blockchain was the first credible decentralized solution. And now, attention is rapidly starting to shi
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Ethereum white paper a next generation smart contr
312
ft toward this second part of Bitcoin's technology, and how the blockchain concept can be used for more than just money. Commonly cited applications include using on-blockchain digital assets to represent custom currencies and financial instruments ("colored coins"), the ownership of an underlying physical device ("smart property"), non-fungible assets such as domain names ("Namecoin") as well as more advanced applications such as decentrali
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Ethereum white paper a next generation smart contr
313
ft toward this second part of Bitcoin's technology, and how the blockchain concept can be used for more than just money. Commonly cited applications include using on-blockchain digital assets to represent custom currencies and financial instruments ("colored coins"), the ownership of an underlying physical device ("smart property"), non-fungible assets such as domain names ("Namecoin") as well as more advanced applications such as decentrali
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Ethereum white paper a next generation smart contr
314
zed exchange, financial derivatives, peer-to-peer gambling and on-blockchain identity and reputation systems. Another important area of inquiry is "smart contracts" - systems which automatically move digital assets according to arbitrary pre-specified rules. For example, one might have a treasury contract of the form "A can withdraw up to X currency units per day, B can withdraw up to Y per day, A and B together can withdraw anything, an
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Ethereum white paper a next generation smart contr
315
d A can shut off B's ability to withdraw". The logical extension of this is decentralized autonomous organizations (DAOs) - long-term smart contracts that contain the assets and encode the bylaws of an entire organization. What Ethereum intends to provide is a blockchain with a built-in fully fledged Turing-complete programming language that can be used to create "contracts" that can be used to encode arbitrary state transition functions
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[ "AP", "##PL", "##Y", "(", "{", "Alice", ":", "$", "50", ",", "Bob", ":", "$", "50", "}", ",", "\"", "send", "$", "70", "from", "Alice", "to", "Bob", "\"", ")", "=", "ER", "##RO", "##R", "The", "\"", "state", "\"", "in", "Bit", "##co", "##in", "is", "the", "collection", "of", "all", "coins", "(", "technically", ",", "\"", "un", "##sp", "##ent", "transaction", "output", "##s", "\"", "or", "U", "##T", "##X", "##O", ")", "that", "have", "been", "mint", "##ed", "and", "not", "yet", "spent", ",", "with", "each", "U", "##T", "##X", "##O", "having", "a", "denomination", "and", "an", "owner", "(", "defined", "by", "a", "20", "-", "by", "##te", "address", "which", "is", "essentially", "a", "cry", "##pt", "##ographic", "public", "key", "[", "1", "]", ")", ".", "A", "transaction", "contains", "one", "or", "more", "inputs", ",", "with", "each", "input", "containing", "a", "reference", "to", "an", "existing", "U", "##T", "##X", "##O", "and", "a", "cry", "##pt", "##ographic", "signature", "produced", "by", "the", "private", "key", "associated", "with", "the", "owner", "'", "s", "address", ",", "and", "one", "or", "more", "output", "##s", ",", "with", "each", "output", "containing", "a", "new", "U", "##T", "##X", "##O", "to", "be", "added", "to", "the", "state", ".", "Page", "5", "et", "##here", "##um", ".", "org", "The", "state", "transition", "function", "AP", "##PL", "##Y", "(", "S", ",", "TX", ")", ">", "S", "'", "can", "be", "defined", "roughly", "as", "follows", ":", "1", ".", "For", "each", "input", "in", "TX", ":", "i", ".", "If", "the", "referenced", "U", "##T", "##X", "##O", "is", "not", "in", "S", ",", "return", "an", "error", ".", "ii", ".", "If", "the", "provided", "signature", "does", "not", "match", "the", "owner", "of", "the", "U", "##T", "##X", "##O", ",", "return", "an", "error", ".", "2", ".", "If", "the", "sum", "of", "the", "denominations", "of", "all", "input", "U", "##T", "##X", "##O", "is", "less", "than", "the", "sum", "of", "the", "denominations", "of", "all", "output", "U", "##T", "##X", "##O", ",", "return", "an", "error", ".", "3", ".", "Return", "S", "with", "all", "input", "U", "##T", "##X", "##O", "removed", "and", "all", "output", "U", "##T", "##X", "##O", "added", ".", "The", "first", "half", "of", "the", "first", "step", "prevents", "transaction", "send", "##ers", "from", "spending", "coins", "that", "do", "not", "exist", ",", "the", "second", "half", "of", "the", "first", "step", "prevents", "transaction", "send", "##ers", "from", "spending", "other", "people", "'", "s", "coins", ",", "and", "the", "second", "step", "enforce", "##s", "conservation", "of", "value", ".", "In", "order", "to", "use", "this", "for", "payment", ",", "the", "protocol", "is", "as", "follows", ".", "Su", "##pp", "##ose", "Alice", "wants", "to", "send", "11", ".", "7", "BT", "##C", "to", "Bob", ".", "First", ",", "Alice", "will", "look", "for", "a", "set", "of", "available", "U", "##T", "##X", "##O", "that", "she", "owns", "that", "totals", "up", "to", "at", "least", "11", ".", "7", "BT", "##C", ".", "Real", "##istic", "##ally", ",", "Alice", "will", "not", "be", "able", "to", "get", "exactly", "11", ".", "7", "BT", "##C", ";", "say", "that", "the", "smallest", "she", "can", "get", "is", "6", "+", "4", "+", "2", "=", "12", ".", "She", "then", "creates", "a", "transaction", "with", "those", "three", "inputs", "and", "two", "output", "##s", ".", "The", "first", "output", "will", "be", "11", ".", "7", "BT", "##C", "with", "Bob", "'", "s", "address", "as", "its", "owner", ",", "and", "the", "second", "output", "will", "be", "the", "remaining", "0", ".", "3", "BT", "##C", "\"", "change", "\"", ",", "with", "the", "owner", "being", "Alice", "herself", ".", "Mining", "If", "we", "had", "access", "to", "a", "trust", "##worthy", "centralized" ]
Ethereum white paper a next generation smart contr
316
, allowing users to create any of the systems described above, as well as many others that we have not yet imagined, simply by writing up the logic in a few lines of code. Page 1 ethereum.org http://www.google.com/url?q=http%3A%2F%2Fbitcoinmagazine.com%2F8640%2Fan-exploration-of-intrinsic-value-what-it-is-why-bitcoin-doesnt-have-it-and-why-bitcoin-does-have-it%2F&sa=D&sntz=1&usg=AFQjCNHIhJ5joZ_huTAMKn106C0c2k7t7w https://docs.google.com/a/buterin.com/document/d/1AnkP_cVZTCMLIz
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Ethereum white paper a next generation smart contr
317
, allowing users to create any of the systems described above, as well as many others that we have not yet imagined, simply by writing up the logic in a few lines of code. Page 1 ethereum.org http://www.google.com/url?q=http%3A%2F%2Fbitcoinmagazine.com%2F8640%2Fan-exploration-of-intrinsic-value-what-it-is-why-bitcoin-doesnt-have-it-and-why-bitcoin-does-have-it%2F&sa=D&sntz=1&usg=AFQjCNHIhJ5joZ_huTAMKn106C0c2k7t7w https://docs.google.com/a/buterin.com/document/d/1AnkP_cVZTCMLIz
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Ethereum white paper a next generation smart contr
318
w4DvsW6M8Q2JC0lIzrTLuoWu2z1BE/edit http://www.google.com/url?q=http%3A%2F%2Fbitcoinmagazine.com%2F7050%2Fbootstrapping-a-decentralized-autonomous-corporation-part-i%2F&sa=D&sntz=1&usg=AFQjCNF8xImt3YrVAid-X0DOflDgk1JSjg Table of contents ● History ○ Bitcoin As A State Transition System ○ Mining ○ Merkle Trees ○ Alternative Blockchain Applications ○ Scripting ● Ethereum ○ Ethereum Accounts ○ Messages and Transactions ○ Ethereum State Transition Function ○ Code Execution ○ Blo
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Ethereum white paper a next generation smart contr
319
w4DvsW6M8Q2JC0lIzrTLuoWu2z1BE/edit http://www.google.com/url?q=http%3A%2F%2Fbitcoinmagazine.com%2F7050%2Fbootstrapping-a-decentralized-autonomous-corporation-part-i%2F&sa=D&sntz=1&usg=AFQjCNF8xImt3YrVAid-X0DOflDgk1JSjg Table of contents ● History ○ Bitcoin As A State Transition System ○ Mining ○ Merkle Trees ○ Alternative Blockchain Applications ○ Scripting ● Ethereum ○ Ethereum Accounts ○ Messages and Transactions ○ Ethereum State Transition Function ○ Code Execution ○ Blo
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Ethereum white paper a next generation smart contr
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ckchain and Mining ● Applications ○ Token Systems ○ Financial derivatives ○ Identity and Reputation Systems ○ Decentralized File Storage ○ Decentralized Autonomous Organizations ○ Further Applications ● Miscellanea And Concerns ○ Modified GHOST Implementation ○ Fees ○ Computation And Turing-Completeness ○ Currency And Issuance ○ Mining Centralization ○ Scalability ● Putting It All Together: Decentralized Applications ● Conclusion ● References and Further Reading Pa
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Ethereum white paper a next generation smart contr
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ckchain and Mining ● Applications ○ Token Systems ○ Financial derivatives ○ Identity and Reputation Systems ○ Decentralized File Storage ○ Decentralized Autonomous Organizations ○ Further Applications ● Miscellanea And Concerns ○ Modified GHOST Implementation ○ Fees ○ Computation And Turing-Completeness ○ Currency And Issuance ○ Mining Centralization ○ Scalability ● Putting It All Together: Decentralized Applications ● Conclusion ● References and Further Reading Pa
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Ethereum white paper a next generation smart contr
322
ge 2 ethereum.org https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fethereum%2Fwiki%2Fwiki%2F%255BEnglish%255D-White-Paper%23mining&sa=D&sntz=1&usg=AFQjCNHXheZ8d-JmIOGWH50cFYBAeHO3rg https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fethereum%2Fwiki%2Fwiki%2F%255BEnglish%255D-White-Paper%23merkle-trees&sa=D&sntz=1&usg=AFQjCNH-5TTaR5zzahKRFajdXdRQSm29XQ https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fethereum%2Fwiki%2Fwiki%2F%255BEnglish%255D-White-Paper%23alternative-blockchain-appl
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Ethereum white paper a next generation smart contr
323
ications&sa=D&sntz=1&usg=AFQjCNG35ozH-fsZ_Ga6f0-lMLPTAJUV-g https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fethereum%2Fwiki%2Fwiki%2F%255BEnglish%255D-White-Paper%23scripting&sa=D&sntz=1&usg=AFQjCNHNIVNIiHeNkEoRRqs6_gnqRzKpEw Page 3 ethereum.org History The concept of decentralized digital currency, as well as alternative applications like property registries, has been around for decades. The anonymous e-cash protocols of the 1980s and the 1990s, mostly
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Ethereum white paper a next generation smart contr
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ications&sa=D&sntz=1&usg=AFQjCNG35ozH-fsZ_Ga6f0-lMLPTAJUV-g https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fethereum%2Fwiki%2Fwiki%2F%255BEnglish%255D-White-Paper%23scripting&sa=D&sntz=1&usg=AFQjCNHNIVNIiHeNkEoRRqs6_gnqRzKpEw Page 3 ethereum.org History The concept of decentralized digital currency, as well as alternative applications like property registries, has been around for decades. The anonymous e-cash protocols of the 1980s and the 1990s, mostly
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Ethereum white paper a next generation smart contr
325
reliant on a cryptographic primitive known as Chaumian blinding, provided a currency with a high degree of privacy, but the protocols largely failed to gain traction because of their reliance on a centralized intermediary. In 1998, Wei Dai's b-money became the first proposal to introduce the idea of creating money through solving computational puzzles as well as decentralized consensus, but the proposal was scant on details as to how d
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Ethereum white paper a next generation smart contr
326
ecentralized consensus could actually be implemented. In 2005, Hal Finney introduced a concept of "reusable proofs of work", a system which uses ideas from b-money together with Adam Back's computationally difficult Hashcash puzzles to create a concept for a cryptocurrency, but once again fell short of the ideal by relying on trusted computing as a backend. Because currency is a first-to-file application, where the order of transactions is often of critic
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Ethereum white paper a next generation smart contr
327
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Ethereum white paper a next generation smart contr
328
al importance, decentralized currencies require a solution to decentralized consensus. The main roadblock that all pre-Bitcoin currency protocols faced is the fact that, while there had been plenty of research on creating secure Byzantine-fault-tolerant multiparty consensus systems for many years, all of the protocols described were solving only half of the problem. The protocols assumed that all participants in the system were
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Ethereum white paper a next generation smart contr
329
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Ethereum white paper a next generation smart contr
330
known, and produced security margins of the form "if N parties participate, then the system can tolerate up to N/4 malicious actors". The problem is, however, that in an anonymous setting such security margins are vulnerable to sybil attacks, where a single attacker creates thousands of simulated nodes on a server or botnet and uses these nodes to unilaterally secure a majority share. The innovation provided by Satoshi is the idea of combining a very s
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Ethereum white paper a next generation smart contr
331
known, and produced security margins of the form "if N parties participate, then the system can tolerate up to N/4 malicious actors". The problem is, however, that in an anonymous setting such security margins are vulnerable to sybil attacks, where a single attacker creates thousands of simulated nodes on a server or botnet and uses these nodes to unilaterally secure a majority share. The innovation provided by Satoshi is the idea of combining a very s
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Ethereum white paper a next generation smart contr
332
imple decentralized consensus protocol, based on nodes combining transactions into a "block" every ten minutes creating an ever-growing blockchain, with proof of work as a mechanism through which nodes gain the right to participate in the system. While nodes with a large amount of computational power do have proportionately greater influence, coming up with more computational power than the entire network combined is much harder
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Ethereum white paper a next generation smart contr
333
imple decentralized consensus protocol, based on nodes combining transactions into a "block" every ten minutes creating an ever-growing blockchain, with proof of work as a mechanism through which nodes gain the right to participate in the system. While nodes with a large amount of computational power do have proportionately greater influence, coming up with more computational power than the entire network combined is much harder
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Ethereum white paper a next generation smart contr
334
than simulating a million nodes. Despite the Bitcoin blockchain model's crudeness and simplicity, it has proven to be good enough, and would over the next five years become the bedrock of over two hundred currencies and protocols around the world. Page 4 ethereum.org http://www.google.com/url?q=http%3A%2F%2Fwww.weidai.com%2Fbmoney.txt&sa=D&sntz=1&usg=AFQjCNEythBdNq0vi1G--o4hwyuOSCbiqA http://www.google.com/url?q=http%3A%2F%2Fwww.finney.org%2F%257Ehal%2Frpow%2F
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Ethereum white paper a next generation smart contr
335
than simulating a million nodes. Despite the Bitcoin blockchain model's crudeness and simplicity, it has proven to be good enough, and would over the next five years become the bedrock of over two hundred currencies and protocols around the world. Page 4 ethereum.org http://www.google.com/url?q=http%3A%2F%2Fwww.weidai.com%2Fbmoney.txt&sa=D&sntz=1&usg=AFQjCNEythBdNq0vi1G--o4hwyuOSCbiqA http://www.google.com/url?q=http%3A%2F%2Fwww.finney.org%2F%257Ehal%2Frpow%2F
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Ethereum white paper a next generation smart contr
336
&sa=D&sntz=1&usg=AFQjCNFzG0g7MWXcLfkI1yqvMfqEeiPE2A Bitcoin As A State Transition System From a technical standpoint, the Bitcoin ledger can be thought of as a state transition system, where there is a "state" consisting of the ownership status of all existing bitcoins and a "state transition function" that takes a state and a transaction and outputs a new state which is the result. In a standard banking system, for example, the state is a
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Ethereum white paper a next generation smart contr
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balance sheet, a transaction is a request to move $X from A to B, and the state transition function reduces the value in A's account by $X and increases the value in B's account by $X. If A's account has less than $X in the first place, the state transition function returns an error. Hence, one can formally define: APPLY(S,TX) ­> S' or ERROR In the banking system defined above: APPLY({Alice:$50,Bob:$50},"send$20fromAlicetoBob")={Ali
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Ethereum white paper a next generation smart contr
338
balance sheet, a transaction is a request to move $X from A to B, and the state transition function reduces the value in A's account by $X and increases the value in B's account by $X. If A's account has less than $X in the first place, the state transition function returns an error. Hence, one can formally define: APPLY(S,TX) ­> S' or ERROR In the banking system defined above: APPLY({Alice:$50,Bob:$50},"send$20fromAlicetoBob")={Ali
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Ethereum white paper a next generation smart contr
339
ce:$30,                            Bob: $70 } But: APPLY({ Alice: $50, Bob: $50 },"send $70 from Alice to Bob") = ERROR    The "state" in Bitcoin is the collection of all coins (technically, "unspent transaction outputs" or UTXO) that have been minted and not yet spent, with each UTXO having a denomination and an owner (defined by a 20-byte address which is essentially a cryptographic public key[1]). A transaction contains one or more inputs, w
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Ethereum white paper a next generation smart contr
340
ce:$30,                            Bob: $70 } But: APPLY({ Alice: $50, Bob: $50 },"send $70 from Alice to Bob") = ERROR    The "state" in Bitcoin is the collection of all coins (technically, "unspent transaction outputs" or UTXO) that have been minted and not yet spent, with each UTXO having a denomination and an owner (defined by a 20-byte address which is essentially a cryptographic public key[1]). A transaction contains one or more inputs, w
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Ethereum white paper a next generation smart contr
341
ith each input containing a reference to an existing UTXO and a cryptographic signature produced by the private key associated with the owner's address, and one or more outputs, with each output containing a new UTXO to be added to the state. Page 5 ethereum.org The state transition function APPLY(S,TX) ­> S' can be defined roughly as follows: 1. For each input in TX: i. If the referenced UTXO is not in S, return an error. ii. If the provided sign
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Ethereum white paper a next generation smart contr
342
ith each input containing a reference to an existing UTXO and a cryptographic signature produced by the private key associated with the owner's address, and one or more outputs, with each output containing a new UTXO to be added to the state. Page 5 ethereum.org The state transition function APPLY(S,TX) ­> S' can be defined roughly as follows: 1. For each input in TX: i. If the referenced UTXO is not in S, return an error. ii. If the provided sign
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Ethereum white paper a next generation smart contr
343
ature does not match the owner of the UTXO, return an error. 2. If the sum of the denominations of all input UTXO is less than the sum of the denominations of all output UTXO, return an error. 3. Return S with all input UTXO removed and all output UTXO added. The first half of the first step prevents transaction senders from spending coins that do not exist, the second half of the first step prevents transaction senders from spending other people's coins, and
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Ethereum white paper a next generation smart contr
344
ature does not match the owner of the UTXO, return an error. 2. If the sum of the denominations of all input UTXO is less than the sum of the denominations of all output UTXO, return an error. 3. Return S with all input UTXO removed and all output UTXO added. The first half of the first step prevents transaction senders from spending coins that do not exist, the second half of the first step prevents transaction senders from spending other people's coins, and
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Ethereum white paper a next generation smart contr
345
the second step enforces conservation of value. In order to use this for payment, the protocol is as follows. Suppose Alice wants to send 11.7 BTC to Bob. First, Alice will look for a set of available UTXO that she owns that totals up to at least 11.7 BTC. Realistically, Alice will not be able to get exactly 11.7 BTC; say that the smallest she can get is 6+4+2=12. She then creates a transaction with those three inputs a
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Ethereum white paper a next generation smart contr
346
the second step enforces conservation of value. In order to use this for payment, the protocol is as follows. Suppose Alice wants to send 11.7 BTC to Bob. First, Alice will look for a set of available UTXO that she owns that totals up to at least 11.7 BTC. Realistically, Alice will not be able to get exactly 11.7 BTC; say that the smallest she can get is 6+4+2=12. She then creates a transaction with those three inputs a
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Ethereum white paper a next generation smart contr
347
nd two outputs. The first output will be 11.7 BTC with Bob's address as its owner, and the second output will be the remaining 0.3 BTC "change", with the owner being Alice herself. Mining If we had access to a trustworthy centralized service, this system would be trivial to implement; it could simply be coded exactly as described. However, with Bitcoin we are trying to build a decentralized currency system, so we will need to
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Ethereum white paper a next generation smart contr
348
nd two outputs. The first output will be 11.7 BTC with Bob's address as its owner, and the second output will be the remaining 0.3 BTC "change", with the owner being Alice herself. Mining If we had access to a trustworthy centralized service, this system would be trivial to implement; it could simply be coded exactly as described. However, with Bitcoin we are trying to build a decentralized currency system, so we will need to
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Ethereum white paper a next generation smart contr
349
combine the state transition system with a consensus system in order to ensure that everyone agrees on the order of transactions. Bitcoin's decentralized consensus process requires nodes in the network to continuously attempt to produce packages of transactions called "blocks". The network is intended to produce roughly one block every ten minutes, with each block containing a timestamp, a nonce, a reference to (ie. hash of) the
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Ethereum white paper a next generation smart contr
350
combine the state transition system with a consensus system in order to ensure that everyone agrees on the order of transactions. Bitcoin's decentralized consensus process requires nodes in the network to continuously attempt to produce packages of transactions called "blocks". The network is intended to produce roughly one block every ten minutes, with each block containing a timestamp, a nonce, a reference to (ie. hash of) the
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Ethereum white paper a next generation smart contr
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Page 6 ethereum.org previous block and a list of all of the transactions that have taken place since the previous block. Over time, this creates a persistent, ever-growing, "blockchain" that constantly updates to represent the latest state of the Bitcoin ledger. The algorithm for checking if a block is valid, expressed in this paradigm, is as follows: 1. Check if the previous block referenced by the block exists and is valid 2. Check that the timestamp of th
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Ethereum white paper a next generation smart contr
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Page 6 ethereum.org previous block and a list of all of the transactions that have taken place since the previous block. Over time, this creates a persistent, ever-growing, "blockchain" that constantly updates to represent the latest state of the Bitcoin ledger. The algorithm for checking if a block is valid, expressed in this paradigm, is as follows: 1. Check if the previous block referenced by the block exists and is valid 2. Check that the timestamp of th
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Ethereum white paper a next generation smart contr
353
e block is greater than that of the previous block[2] and less than 2 hours into the future. 3. Check that the proof of work on the block is valid. 4. Let S[0] be the state at the end of the previous block. 5. Suppose TX is the block's transaction list with n transactions. For all i in 0...n-1, setS[i+1] = APPLY(S[i],TX[i]) If any application returns an error, exit and return false. 6. Return true, and register S[n] as the state at the end of this block E
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Ethereum white paper a next generation smart contr
354
e block is greater than that of the previous block[2] and less than 2 hours into the future. 3. Check that the proof of work on the block is valid. 4. Let S[0] be the state at the end of the previous block. 5. Suppose TX is the block's transaction list with n transactions. For all i in 0...n-1, setS[i+1] = APPLY(S[i],TX[i]) If any application returns an error, exit and return false. 6. Return true, and register S[n] as the state at the end of this block E
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Ethereum white paper a next generation smart contr
355
ssentially, each transaction in the block must provide a state transition that is valid. Note that the state is not encoded in the block in any way; it is purely an abstraction to be remembered by the validating node and can only be (securely) computed for any block by starting from the genesis state and sequentially applying every transaction in every block. Additionally, note that the order in which the miner includes transactions into
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Ethereum white paper a next generation smart contr
356
ssentially, each transaction in the block must provide a state transition that is valid. Note that the state is not encoded in the block in any way; it is purely an abstraction to be remembered by the validating node and can only be (securely) computed for any block by starting from the genesis state and sequentially applying every transaction in every block. Additionally, note that the order in which the miner includes transactions into
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Ethereum white paper a next generation smart contr
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the block matters; if there are two transactions A and B in a block such that B spends a UTXO created by A, then the block will be valid if A comes before B but not otherwise. The interesting part of the block validation algorithm is the concept of "proof of work": the condition is that the SHA256 hash of every block, treated as a 256-bit number, must be less than a dynamically adjusted target, which as of the time of this writing
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Ethereum white paper a next generation smart contr
358
the block matters; if there are two transactions A and B in a block such that B spends a UTXO created by A, then the block will be valid if A comes before B but not otherwise. The interesting part of the block validation algorithm is the concept of "proof of work": the condition is that the SHA256 hash of every block, treated as a 256-bit number, must be less than a dynamically adjusted target, which as of the time of this writing
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Ethereum white paper a next generation smart contr
359
is approximately 2190. The purpose of this is to make block creation computationally "hard", thereby preventing sybil attackers from remaking the entire blockchain in their favor. Because SHA256 is designed to be a completely unpredictable pseudorandom function, the only way to create a valid block is simply trial and error, repeatedly incrementing the nonce and seeing if the new hash matches. At the current target of 2192, this mea
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Ethereum white paper a next generation smart contr
360
ns an average of 264 tries; in general, the target is recalibrated by the network every 2016 blocks so that on average a new block is produced by some node in the network every ten minutes. In order to compensate miners for this computational work, the miner of every block is entitled to include a transaction giving themselves 25 BTC out of nowhere. Additionally, if any transaction has a higher total denomination in its input
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Ethereum white paper a next generation smart contr
361
ns an average of 264 tries; in general, the target is recalibrated by the network every 2016 blocks so that on average a new block is produced by some node in the network every ten minutes. In order to compensate miners for this computational work, the miner of every block is entitled to include a transaction giving themselves 25 BTC out of nowhere. Additionally, if any transaction has a higher total denomination in its input
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Ethereum white paper a next generation smart contr
362
s than in its outputs, the difference also goes to the miner as a "transaction fee". Incidentally, this is also the only mechanism by which BTC are issued; the genesis state contained no coins at all. Page 7 ethereum.org In order to better understand the purpose of mining, let us examine what happens in the event of a malicious attacker. Since Bitcoin's underlying cryptography is known to be secure, the attacker will target the
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Ethereum white paper a next generation smart contr
363
s than in its outputs, the difference also goes to the miner as a "transaction fee". Incidentally, this is also the only mechanism by which BTC are issued; the genesis state contained no coins at all. Page 7 ethereum.org In order to better understand the purpose of mining, let us examine what happens in the event of a malicious attacker. Since Bitcoin's underlying cryptography is known to be secure, the attacker will target the
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Ethereum white paper a next generation smart contr
364
one part of the Bitcoin system that is not protected by cryptography directly: the order of transactions. The attacker's strategy is simple: 1. Send 100 BTC to a merchant in exchange for some product (preferably a rapid-delivery digital good) 2. Wait for the delivery of the product 3. Produce another transaction sending the same 100 BTC to himself 4. Try to convince the network that his transaction to himself was the one that came first. Once
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Ethereum white paper a next generation smart contr
365
one part of the Bitcoin system that is not protected by cryptography directly: the order of transactions. The attacker's strategy is simple: 1. Send 100 BTC to a merchant in exchange for some product (preferably a rapid-delivery digital good) 2. Wait for the delivery of the product 3. Produce another transaction sending the same 100 BTC to himself 4. Try to convince the network that his transaction to himself was the one that came first. Once
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Ethereum white paper a next generation smart contr
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step (1) has taken place, after a few minutes some miner will include the transaction in a block, say block number 270000. After about one hour, five more blocks will have been added to the chain after that block, with each of those blocks indirectly pointing to the transaction and thus "confirming" it. At this point, the merchant will accept the payment as finalized and deliver the product; since we are assuming this is a digital
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Ethereum white paper a next generation smart contr
367
step (1) has taken place, after a few minutes some miner will include the transaction in a block, say block number 270000. After about one hour, five more blocks will have been added to the chain after that block, with each of those blocks indirectly pointing to the transaction and thus "confirming" it. At this point, the merchant will accept the payment as finalized and deliver the product; since we are assuming this is a digital
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Ethereum white paper a next generation smart contr
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good, delivery is instant. Now, the attacker creates another transaction sending the 100 BTC to himself. If the attacker simply releases it into the wild, the transaction will not be processed; miners will attempt to run APPLY(S,TX) and notice that TX consumes a UTXO which is no longer in the state. So instead, the attacker creates a "fork" of the blockchain, starting by mining another version of block 270000 pointing to the same
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Ethereum white paper a next generation smart contr
369
good, delivery is instant. Now, the attacker creates another transaction sending the 100 BTC to himself. If the attacker simply releases it into the wild, the transaction will not be processed; miners will attempt to run APPLY(S,TX) and notice that TX consumes a UTXO which is no longer in the state. So instead, the attacker creates a "fork" of the blockchain, starting by mining another version of block 270000 pointing to the same
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Ethereum white paper a next generation smart contr
370
block 269999 as a parent but with the new transaction in place of the old one. Because the block data is different, this requires redoing the proof of work. Furthermore, the attacker's new version of block 270000 has a different hash, so the original blocks 270001 to 270005 do not "point" to it; thus, the original chain and the attacker's new chain are completely separate. The rule is that in a fork the longest blockchain (ie. the one
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Ethereum white paper a next generation smart contr
371
block 269999 as a parent but with the new transaction in place of the old one. Because the block data is different, this requires redoing the proof of work. Furthermore, the attacker's new version of block 270000 has a different hash, so the original blocks 270001 to 270005 do not "point" to it; thus, the original chain and the attacker's new chain are completely separate. The rule is that in a fork the longest blockchain (ie. the one
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Ethereum white paper a next generation smart contr
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backed by the largest quantity of proof of work) is taken to be the truth, and so legitimate miners will work on the 270005 chain while the attacker alone is working on the 270000 chain. In order for the attacker to make his blockchain the longest, he would need to have more computational power than the rest of the network combined in order to catch up (hence, "51% attack"). Page 8 ethereum.org
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Ethereum white paper a next generation smart contr
373
backed by the largest quantity of proof of work) is taken to be the truth, and so legitimate miners will work on the 270005 chain while the attacker alone is working on the 270000 chain. In order for the attacker to make his blockchain the longest, he would need to have more computational power than the rest of the network combined in order to catch up (hence, "51% attack"). Page 8 ethereum.org
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Ethereum white paper a next generation smart contr
374
Merkle Trees Left: it suffices to present only a small number of nodes in a Merkle tree to give a proof of the validity of a branch. Right: any attempt to change any part of the Merkle tree will eventually lead to an inconsistency somewhere up the chain. An important scalability feature of Bitcoin is that the block is stored in a multi-level data structure. The "hash" of a block is actually only the hash of the block header, a roughly 200-byte piece o
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Ethereum white paper a next generation smart contr
375
Merkle Trees Left: it suffices to present only a small number of nodes in a Merkle tree to give a proof of the validity of a branch. Right: any attempt to change any part of the Merkle tree will eventually lead to an inconsistency somewhere up the chain. An important scalability feature of Bitcoin is that the block is stored in a multi-level data structure. The "hash" of a block is actually only the hash of the block header, a roughly 200-byte piece o
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Ethereum white paper a next generation smart contr
376
f data that contains the timestamp, nonce, previous block hash and the root hash of a data structure called the Merkle tree storing all transactions in the block. A Merkle tree is a type of binary tree, composed of a set of nodes with a large number of leaf nodes at the bottom of the tree containing the underlying data, a set of intermediate nodes where each node is the hash of its two children, and finally a single
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Ethereum white paper a next generation smart contr
377
f data that contains the timestamp, nonce, previous block hash and the root hash of a data structure called the Merkle tree storing all transactions in the block. A Merkle tree is a type of binary tree, composed of a set of nodes with a large number of leaf nodes at the bottom of the tree containing the underlying data, a set of intermediate nodes where each node is the hash of its two children, and finally a single
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Ethereum white paper a next generation smart contr
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root node, also formed from the hash of its two children, representing the "top" of the tree. The purpose of the Merkle tree is to allow the data in a block to be delivered piecemeal: a node can download only the header of a block from one source, the small part of the tree relevant to them from Page 9 ethereum.org another source, and still be assured that all of the data is correct. The reason why this works is that hashes
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Ethereum white paper a next generation smart contr
379
root node, also formed from the hash of its two children, representing the "top" of the tree. The purpose of the Merkle tree is to allow the data in a block to be delivered piecemeal: a node can download only the header of a block from one source, the small part of the tree relevant to them from Page 9 ethereum.org another source, and still be assured that all of the data is correct. The reason why this works is that hashes
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Ethereum white paper a next generation smart contr
380
propagate upward: if a malicious user attempts to swap in a fake transaction into the bottom of a Merkle tree, this change will cause a change in the node above, and then a change in the node above that, finally changing the root of the tree and therefore the hash of the block, causing the protocol to register it as a completely different block (almost certainly with an invalid proof of work). The Merkle tree protocol is ar
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Ethereum white paper a next generation smart contr
381
propagate upward: if a malicious user attempts to swap in a fake transaction into the bottom of a Merkle tree, this change will cause a change in the node above, and then a change in the node above that, finally changing the root of the tree and therefore the hash of the block, causing the protocol to register it as a completely different block (almost certainly with an invalid proof of work). The Merkle tree protocol is ar
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Ethereum white paper a next generation smart contr
382
guably essential to long-term sustainability. A "full node" in the Bitcoin network, one that stores and processes the entirety of every block, takes up about 15 GB of disk space in the Bitcoin network as of April 2014, and is growing by over a gigabyte per month. Currently, this is viable for some desktop computers and not phones, and later on in the future only businesses and hobbyists will be able to participate. A protoco
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Ethereum white paper a next generation smart contr
383
guably essential to long-term sustainability. A "full node" in the Bitcoin network, one that stores and processes the entirety of every block, takes up about 15 GB of disk space in the Bitcoin network as of April 2014, and is growing by over a gigabyte per month. Currently, this is viable for some desktop computers and not phones, and later on in the future only businesses and hobbyists will be able to participate. A protoco
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Ethereum white paper a next generation smart contr
384
l known as "simplified payment verification" (SPV) allows for another class of nodes to exist, called "light nodes", which download the block headers, verify the proof of work on the block headers, and then download only the "branches" associated with transactions that are relevant to them. This allows light nodes to determine with a strong guarantee of security what the status of any Bitcoin transaction, and their current balance, i
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Ethereum white paper a next generation smart contr
385
l known as "simplified payment verification" (SPV) allows for another class of nodes to exist, called "light nodes", which download the block headers, verify the proof of work on the block headers, and then download only the "branches" associated with transactions that are relevant to them. This allows light nodes to determine with a strong guarantee of security what the status of any Bitcoin transaction, and their current balance, i
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Ethereum white paper a next generation smart contr
386
s while downloading only a very small portion of the entire blockchain. Alternative Blockchain Applications The idea of taking the underlying blockchain idea and applying it to other concepts also has a long history. In 2005, Nick Szabo came out with the concept of "secure property titles with owner authority", a document describing how "new advances in replicated database technology" will allow for a blockchain-based system for storing a registry
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Ethereum white paper a next generation smart contr
387
of who owns what land, creating an elaborate framework including concepts such as homesteading, adverse possession and Georgian land tax. However, there was unfortunately no effective replicated database system available at the time, and so the protocol was never implemented in practice. After 2009, however, once Bitcoin's decentralized consensus was developed a number of alternative applications rapidly began to emerge: ● Namecoin - created
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Ethereum white paper a next generation smart contr
388
of who owns what land, creating an elaborate framework including concepts such as homesteading, adverse possession and Georgian land tax. However, there was unfortunately no effective replicated database system available at the time, and so the protocol was never implemented in practice. After 2009, however, once Bitcoin's decentralized consensus was developed a number of alternative applications rapidly began to emerge: ● Namecoin - created
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Ethereum white paper a next generation smart contr
389
in 2010, Namecoin is best described as a decentralized name registration database. In decentralized protocols like Tor, Bitcoin and BitMessage, there needs to be some way of identifying accounts so that other people can interact with them, but in all existing solutions the only kind of identifier available is a pseudorandom hash like1LW79wp5ZBqaHW1jL5TCiBCrhQYtHagUWy. Ideally, one would like to be able to have an
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Ethereum white paper a next generation smart contr
390
in 2010, Namecoin is best described as a decentralized name registration database. In decentralized protocols like Tor, Bitcoin and BitMessage, there needs to be some way of identifying accounts so that other people can interact with them, but in all existing solutions the only kind of identifier available is a pseudorandom hash like1LW79wp5ZBqaHW1jL5TCiBCrhQYtHagUWy. Ideally, one would like to be able to have an
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Ethereum white paper a next generation smart contr
391
Adaptation of Proof-of-Stake-based Blockchains for IoT Data Streams Adaptation of Proof-of-Stake-based Blockchains for IoT Data Streams Sina Rafati Niya1, Eryk Schiller1, Ile Cepilov1, Fabio Maddaloni1, Kürsat Aydinli1, Timo Surbeck1, Thomas Bocek2, Burkhard Stiller1 1Communication Systems Group CSG, Department of Informatics IfI, University of Zürich (UZH) Binzmühlestrasse 14, CH-8050 Zürich, Switzerland {rafati,schiller,stiller}@ifi.uzh.ch, {ile.cepilov,fabio.maddaloni,kuersat.adinli,timo.surbeck}@
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
392
Adaptation of Proof-of-Stake-based Blockchains for IoT Data Streams Adaptation of Proof-of-Stake-based Blockchains for IoT Data Streams Sina Rafati Niya1, Eryk Schiller1, Ile Cepilov1, Fabio Maddaloni1, Kürsat Aydinli1, Timo Surbeck1, Thomas Bocek2, Burkhard Stiller1 1Communication Systems Group CSG, Department of Informatics IfI, University of Zürich (UZH) Binzmühlestrasse 14, CH-8050 Zürich, Switzerland {rafati,schiller,stiller}@ifi.uzh.ch, {ile.cepilov,fabio.maddaloni,kuersat.adinli,timo.surbeck}@
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
393
uzh.ch 2HSR University of Applied Sciences Rapperswil, Switzerland [email protected] Abstract—Proof-of-Work (PoW) in Blockchains (BC), which is a widely used consensus algorithm, suffers from high power consumption of miners and low transaction rates. This work demonstrates a Proof-of-Stake (PoS)-based BC called Bazo, which is specially designed and adapted for Internet of Things (IoT) data streams. Bazo displays enhanced performance in terms of energy consumption and transactions processing in compar
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
394
uzh.ch 2HSR University of Applied Sciences Rapperswil, Switzerland [email protected] Abstract—Proof-of-Work (PoW) in Blockchains (BC), which is a widely used consensus algorithm, suffers from high power consumption of miners and low transaction rates. This work demonstrates a Proof-of-Stake (PoS)-based BC called Bazo, which is specially designed and adapted for Internet of Things (IoT) data streams. Bazo displays enhanced performance in terms of energy consumption and transactions processing in compar
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
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ison to PoW-based BC. To further improve performance of Bazo, sharding and transaction aggregation methods are employed. Moreover, IoT-BC adaptation helpers of a modular and layered architecture are provided to allow wireless devices to submit data into the BC. The designed architecture can support multiple hardware and software platforms as well as network technologies. Index Terms—Blockchains, Proof-of-Stake (PoS), Consensus Mechanisms, IoT, Long Range (LoRa) Communication Protocols I. INTRODUCTION M
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
396
iners or validators are the main actors that verify the data to be stored in the Blockchain (BC). Every BC uses consensus mechanisms to agree on a single chain of blocks, however, short-lived forks of the chain may be possible. Different consensus algorithms are used to validate transactions, for ex- ample based on Proof-of-Work (PoW) or Proof-of-Stake (PoS) mechanisms [1]. However, typical PoW-based BC come with severe problems such as long delay of transaction processing, extensive energy consumption, a
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
397
nd low scalability limiting the possible use-cases that typically require high transaction rates and low transaction delay. Among BC use cases, Internet of Things (IoT)-integrated use cases have recently ris
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Adaptation of Proof of Stake based Blockchains for IoT Data Streams
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How to Make a Digital Currency on a Blockchain Stable Kenji Saitoa,∗, Mitsuru Iwamurab aKeio Research Institute at SFC, Keio University, (Murai Lab.) 5322 Endo, Fujisawa, Kanagawa 252-0882 Japan bGraduate School of Business and Finance, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050 Japan Abstract Bitcoin and other similar digital currencies on blockchains are not ideal means for payment, because their prices tend to go up in the long term (thus people are incentivized to hoard
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How to make a digital currency on a blockchain stable
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