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786 lines
88 KiB
Plaintext
[[ch8]]
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== Mining and Consensus
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[[mining]]
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=== Introduction - Mining and Consensus
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Mining is the process by which new bitcoin is added to the money supply. Mining also serves to secure the bitcoin system against fraudulent transactions or transactions spending the same amount of bitcoin more than once, known as a double-spend. Miners act as a decentralized clearinghouse, validating new transactions and recording them on the global ledger. A new block, containing transactions that occurred since the last block, is "mined" every 10 minutes, thereby adding those transactions to the blockchain. Transactions that become part of a block and added to the blockchain are considered "confirmed", which allows the new owners of bitcoin to spend the bitcoin they received in those transactions. Miners receive two types of reward for mining: new coins created with each new block and transaction fees from all the transactions included in the block. To earn this reward, the miners compete to solve a difficult mathematical problem based on a cryptographic hash algorithm. The solution to the problem, called the Proof-of-Work, is included in the new block and acts as proof that the miner expended significant computing effort. The competition to solve the Proof-of-Work algorithm to earn reward and the right to record transactions on the blockchain is the basis for bitcoin's security model.
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The process of new coin generation is called mining, because the reward is designed to simulate diminishing returns, just like mining for precious metals. Bitcoin's money supply is created through mining, similar to how a central bank issues new money by printing bank notes. The amount of newly created bitcoin a miner can add to a block decreases approximately every four years (or precisely every 210,000 blocks). It started at 50 bitcoin per block in January of 2009 and halved to 25 bitcoin per block in November of 2012. It will halve again to 12.5 bitcoin per block sometime in 2016. Based on this formula, bitcoin mining rewards decrease exponentially until approximately the year 2140 when all bitcoin (20.99999998 million) will have been issued. After 2140, no new bitcoins are issued.
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Bitcoin miners also earn fees from transactions. Every transaction may include a transaction fee, in the form of a surplus of bitcoin between the transaction's inputs and outputs. The winning bitcoin miner gets to "keep the change" on the transactions included in the winning block. Today the fees represent 0.5% or less of a bitcoin miner's income, the vast majority coming from the newly minted bitcoins. However, as the reward decreases over time and the number of transactions per block increases, a greater proportion of bitcoin mining earnings will come from fees. After 2140 all bitcoin miner earnings will be in the form of transaction fees.
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The word "mining" is somewhat misleading. By evoking the extraction of precious metals, it focuses our attention on the reward for mining, the new bitcoins in each block. While mining is incentivized by this reward, the primary purpose of mining is not the reward or the generation of new coins. If you view mining only as the process by which coins are created you are mistaking the means (incentives) as a goal of the process. Mining is the main process of the de-centralized clearinghouse, by which transactions are validated and cleared. Mining secures the bitcoin system and enables the emergence of network-wide consensus without a central authority. Mining is the invention that makes bitcoin special, a de-centralized security mechanism that is the basis for peer-to-peer digital cash. The reward of newly minted coins and transaction fees is an incentive scheme that aligns the actions of miners with the security of the network, while simultaneously implementing the monetary supply.
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In this chapter, we will first examine mining as a monetary supply mechanism and then look at the most important function of mining, the de-centralized emergent consensus mechanism that underpins bitcoin's security.
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==== Bitcoin Economics and Currency Creation
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Bitcoins are "minted" during the creation of each block at a fixed and diminishing rate. Each block, generated on average every 10 minutes, contains entirely new bitcoins, created ex nihilo (from nothing). Every 210,000 blocks or approximately every four years the currency issuance rate is decreased by 50%. For the first four years of operation of the network, each block contained 50 new bitcoin. In November of 2012, the new bitcoin issuance rate was decreased to 25 bitcoin per block and it will decrease again to 12.5 bitcoin at block 420,000, which will be mined sometime in 2016. The rate of new coins decreases like this exponentially over 64 "halvings", until block 13,230,000 (mined approximately in year 2137) when it reaches the minimum currency unit of 1 satoshi. Finally, after 13.44 million blocks, in approximately 2140, all 2,099,999,997,690,000 satoshis, or almost 21 million bitcoin will be issued. Thereafter, blocks will contain no new bitcoin, and miners will be rewarded solely through the transaction fees.
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[[bitcoin_money_supply]]
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.Supply of bitcoin currency over time based on a geometrically decreasing issuance rate
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image::images/BitcoinMoneySupply.png["BitcoinMoneySupply"]
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The finite and diminishing issuance creates a fixed monetary supply that resists inflation. Unlike a fiat currency, which can be printed in infinite numbers by a central bank, bitcoin can never be inflated by printing.
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===== Deflationary Money
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The most important and debated consequence of a fixed and diminishing monetary issuance is that the currency will tend to be inherently _deflationary_. Deflation is the phenomenon of appreciation of value due to a mismatch in supply and demand that drives up the value (and exchange rate) of a currency. The opposite of inflation, price deflation means that the money has more purchasing power over time.
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Many economists argue that a deflationary economy is a disaster that should be avoided at all costs. That is because in a period of rapid deflation people will tend to hoard money instead of spending it, hoping that prices will fall. Such a phenomenon unfolded during Japan's "Lost Decade", when a complete collapse of demand pushed the currency into a deflationary spiral.
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Bitcoin experts argue that deflation is not bad *per se*. Rather, deflation is associated with a collapse in demand because that is the only example of deflation we have to study. In a fiat currency with the possibility of unlimited printing, it is very difficult to enter a deflationary spiral unless there is a complete collapse in demand and an unwillingness to print money. Deflation in bitcoin is not caused by a collapse in demand, but by a predictably constrained supply.
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In practice, it has become evident that the hoarding instinct caused by a deflationary currency can be overcome by discounting from vendors, until the discount overcomes the hoarding instinct of the buyer. Since the seller is also motivated to hoard, the discount becomes the equilibrium price at which the two hoarding instincts are matched. With discounts of 30% on the bitcoin price, most bitcoin retailers are not experiencing difficulty overcoming the hoarding instinct and generating revenue. It remains to be seen whether the deflationary aspect of the currency is really a problem when it is not driven by rapid economic retraction.
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=== De-centralized Consensus
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In the previous chapter we looked at the blockchain, the global public ledger (list) of all transactions, which everyone in the bitcoin network accepts as the authoritative record of ownership.
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But how can everyone in the network agree on a single universal "truth" about who owns what, without having to trust anyone? All traditional payment systems depend on a trust model that has a central authority providing a clearinghouse service, basically verifying and clearing all transactions. Bitcoin has no central authority, yet somehow every node has a complete copy of a public ledger that it can trust as the authoritative record. The blockchain is not created by a central authority, but is assembled independently by every node in the network. Somehow, every node in the network, acting on information transmitted across insecure network connections can arrive at the same conclusion and assemble a copy of the same public ledger as everyone else. This chapter examines the process by which the bitcoin network achieves global consensus without central authority.
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Satoshi Nakamoto's main invention is the decentralized mechanism for _emergent consensus_. Emergent, because consensus is not achieved explicitly -- there is no election or fixed moment when consensus occurs. Instead, consensus is an emergent artifact of the asynchronous interaction of thousands of independent nodes, all following simple rules. All the properties of bitcoin, including currency, transactions, payments, and the security model that does not depend on central authority or trust, derive from this invention.
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Bitcoin's de-centralized consensus emerges from the interplay of four processes that occur independently on nodes across the network:
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* Independent verification of each transaction, by every full node, based on a comprehensive list of criteria
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* Independent aggregation of those transactions into new blocks by mining nodes, coupled with demonstrated computation through a Proof-of-Work algorithm
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* Independent verification of the new blocks by every node and assembly into a chain
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* Independent selection, by every node, of the chain with the most cumulative computation demonstrated through Proof-of-Work
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In the next few sections we will examine these processes and how they interact to create the emergent property of network-wide consensus that allows any bitcoin node to assemble its own copy of the authoritative, trusted, public, global ledger.
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[[tx_verification]]
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=== Independent Verification of Transactions
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In a previous chapter we saw how wallet software creates transactions by collecting UTXO, providing the appropriate unlocking scripts, and then constructing new outputs assigned to a new owner. The resulting transaction is then sent to the neighboring nodes in the bitcoin network so that it may be propagated across the entire bitcoin network.
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However, before forwarding transactions to its neighbors, every bitcoin node that receives a transaction will first verify the transaction. This ensures that only valid transactions are propagated across the network, while invalid transactions are discarded at the first node that encounters them.
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Each node verifies every transaction against a long checklist of criteria:
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* The transaction's syntax and data structure must be correct
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* Neither lists of inputs or outputs are empty
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* The transaction size in bytes is less than MAX_BLOCK_SIZE
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* Each output value, as well as the total, must be within the allowed range of values (less than 21m coins, more than 0)
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* None of the inputs have hash=0, N=-1 (coinbase transactions should not be relayed)
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* nLockTime is less than or equal to INT_MAX
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* The transaction size in bytes is greater than or equal to 100
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* The number of signature operations contained in the transaction is less than the signature operation limit
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* Unlocking script (scriptSig) only push numbers on the stack, and the locking script (scriptPubkey) must match isStandard forms (this rejects "nonstandard" transactions)
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* A matching transaction in the pool, or in a block in the main branch, must exist
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* For each input, if the referenced output exists in any other transaction in the pool, reject this transaction
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* For each input, look in the main branch and the transaction pool to find the referenced output transaction. If the output transaction is missing for any input, this will be an orphan transaction. Add to the orphan transactions, if a matching transaction is not already in the pool
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* For each input, if the referenced output transaction is a coinbase output, it must have at least COINBASE_MATURITY (100) confirmations
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* For each input, the referenced output must exist and cannot already be spent
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* Using the referenced output transactions to get input values, check that each input value, as well as the sum, are in the allowed range of values (less than 21m coins, more than 0)
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* Reject if the sum of input values < sum of output values
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* Reject if transaction fee would be too low to get into an empty block
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* The unlocking scripts for each input must validate against the corresponding output locking scripts
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These conditions can be seen in detail in the functions +AcceptToMemoryPool+, +CheckTransaction+, and +CheckInputs+ in the bitcoin reference client. Note that the conditions change over time, to address new types of Denial-of-Service attacks or sometimes to relax the rules so as to include more types of transactions.
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By independently verifying each transaction as it is received and before propagating it, every node builds a pool of valid new transactions (the transaction pool), roughly in the same order.
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=== Mining Nodes
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Some of the nodes on the bitcoin network are specialized nodes called _miners_. In Chapter 1 we introduced Jing, a computer engineering student in Shanghai, China, who is a bitcoin miner. Jing earns bitcoin by running a "mining rig", which is a specialized computer-hardware system designed to mine bitcoins. Jing's specialized mining hardware is connected to a server running a full bitcoin node. Unlike Jing, some miners mine without a full node as we will see in <<mining pools>>. Like every other full node, Jing's node receives and propagates unconfirmed transactions on the bitcoin network. Jing's node, however, also aggregates these transactions into new blocks.
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Jing's node is listening for new blocks, propagated on the bitcoin network, as do all nodes. However, the arrival of a new block has special significance for a mining node. The competition among miners effectively ends with the propagation of a new block which acts as an announcement of a winner. To a miner, receiving a new block means someone else won the competition and they lost. However, the end of one round of a competition is also the beginning of the next round. The new block is not just a checkered flag, marking the end of the race, it is also the starting pistol starting the race for the next block.
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=== Aggregating Transactions into Blocks
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After validating transactions, a bitcoin node will add them to the _memory pool_, or _transaction pool_, where transactions await until they can be included (mined) into a block. Jing's node collects, validates and relays new transactions just like any other node. Unlike other nodes, however, Jing's node will then aggregate these transactions into a _candidate block_.
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Let's follow the blocks that were created during the time Alice bought a cup of coffee from Bob's Cafe (see <<cup_of_coffee>>). Alice's transaction was included in block 277,316. For the purpose of demonstrating the concepts in this chapter let's assume that block was mined by Jing's mining system and follow Alice's transaction as it becomes part of this new block.
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Jing's mining node maintains a local copy of the blockchain, the list of all blocks created since the beginning of the bitcoin system in 2009. By the time Alice buys the cup of coffee, Jing's node has assembled a chain of 277,314 blocks. Jing's node is listening for transactions, trying to mine a new block and also listening for blocks discovered by other nodes. As Jing's node is mining, it receives block 277,315 through the bitcoin network. The arrival of this block signifies the end of the competition for block 277,315 and the beginning of the competition to create block 277,316.
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During the previous 10 minutes, while Jing's node was searching for a solution to block 277,315, it was also collecting transactions in preparation for the next block. By now it has collected a few hundred transactions in the memory pool. Upon receiving block 277,315 and validating it, Jing's node will also check all the transactions in the memory pool and remove any that were included in block 277,315. Whatever transaction remain in the memory pool are unconfirmed and are waiting to be recorded in a new block.
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Jing's node immediately constructs a new empty block, a candidate for block 277,316. This block is called a candidate block because it is not yet a valid block, as it does not contain a valid proof-of-work. The block becomes valid only if the miner succeeds in finding a solution to the Proof-of-Work algorithm.
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==== Transaction Age, Fees, and Priority
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To construct the candidate block Jing's bitcoin node selects transactions from the memory pool, by applying a priority metric to each transaction and adding the highest priority transactions first. Transactions are prioritized based on the "age" of the UTXO that is being spent in their inputs, allowing for old and high-value inputs to be prioritized over newer and smaller inputs. Prioritized transactions can be sent without any fees, if there is enough space in the block.
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The priority of a transaction is calculated as the sum of the value and age of the inputs divided by the total size of the transaction:
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----
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Priority = Sum (Value of input * Input Age) / Transaction Size
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----
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In the equation above, the value of an input is measured in the base unit, satoshis (1/100m of a bitcoin). The age of a UTXO is the number of blocks that have elapsed since the UTXO was recorded on the blockchain, measuring how many blocks "deep" into the blockchain it is. The size of the transaction is measured in bytes.
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For a transaction to be considered "high priority" its priority must be greater than 57,600,000, which corresponds to one bitcoin (100m satoshis), aged one day (144 blocks) in a transaction of 250 bytes total size.
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----
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High Priority > 100,000,000 satoshis * 144 blocks / 250 bytes = 57,600,000
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----
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The first 50 kilobytes of transaction space in a block are set aside for high priority transactions. Jing's node will fill the first 50 kilobytes, prioritizing the highest priority transactions first, regardless of fee. This allows high-priority transactions to be processed even if they carry zero fees.
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Jing's mining node then fills the rest of the block up to the maximum block size (MAX_BLOCK_SIZE in the code), with transactions that carry at least the minimum fee, prioritizing those with the highest fee per kilobyte of transaction.
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If there is any space remaining in the block, Jing's mining node may choose to fill it with no-fee transactions. Some miners choose to mine transactions without fees on a best-effort basis. Other miners may choose to ignore transactions without fees.
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Any transactions left in the memory pool, after the block is filled, will remain in the pool for inclusion in the next block. As transactions remain in the memory pool, their inputs "age", as the UTXO they spend get deeper into the blockchain with new blocks added on top. Since a transaction's priority depends on the age of its inputs, transactions remaining in the pool will age and therefore increase in priority. Eventually a transaction without fees may reach a high enough priority to be included in the block for free.
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Bitcoin transactions do not have an expiration time-out. A transaction that is valid now will be valid in perpetuity. However, if a transaction is only propagated across the network once it will persist only as long as it is held in a mining node memory pool. When a mining node is restarted, its memory pool is wiped clear, as it is a transient non-persistent form of storage. While a valid transaction may have been propagated across the network, if it is not executed it may eventually not reside in the memory pool of any miner. Wallet software are expected to retransmit such transactions or reconstruct them with higher fees if they are not successfully executed within a reasonable amount of time.
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When Jing's node aggregates all the transactions from the memory pool, the new candidate block has 418 transactions with total transaction fees of 0.09094928 bitcoin. You can see this block in the blockchain using the Bitcoin Core client command line interface:
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====
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[source,bash]
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----
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$ bitcoin-cli getblockhash 277316
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0000000000000001b6b9a13b095e96db41c4a928b97ef2d944a9b31b2cc7bdc4
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$ bitcoin-cli getblock 0000000000000001b6b9a13b095e96db41c4a928b97ef2d944a9b31b2cc7bdc4
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----
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====
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[[block277316]]
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.Block 277,316
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====
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[source,json]
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----
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{
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"hash" : "0000000000000001b6b9a13b095e96db41c4a928b97ef2d944a9b31b2cc7bdc4",
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"confirmations" : 35561,
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"size" : 218629,
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"height" : 277316,
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"version" : 2,
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"merkleroot" : "c91c008c26e50763e9f548bb8b2fc323735f73577effbc55502c51eb4cc7cf2e",
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"tx" : [
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"d5ada064c6417ca25c4308bd158c34b77e1c0eca2a73cda16c737e7424afba2f",
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"b268b45c59b39d759614757718b9918caf0ba9d97c56f3b91956ff877c503fbe",
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... 417 more transactions ...
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],
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"time" : 1388185914,
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"nonce" : 924591752,
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"bits" : "1903a30c",
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"difficulty" : 1180923195.25802612,
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"chainwork" : "000000000000000000000000000000000000000000000934695e92aaf53afa1a",
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"previousblockhash" : "0000000000000002a7bbd25a417c0374cc55261021e8a9ca74442b01284f0569",
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"nextblockhash" : "000000000000000010236c269dd6ed714dd5db39d36b33959079d78dfd431ba7"
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}
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----
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====
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==== The Generation Transaction
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The first transaction added to the block is a special transaction, called a _generation transaction_ or _coinbase transaction_. This transaction is constructed by Jing's node and is his reward for the mining effort. Jing's node creates the generation transaction as a payment to his own wallet: "Pay Jing's address 25.09094928 bitcoin". The total amount of reward that Jing collects for mining a block is the sum of the coinbase reward (25 new bitcoins) and the transaction fees (0.09094928) from all the transactions included in the block.
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====
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[source, bash]
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----
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$ bitcoin-cli getrawtransaction d5ada064c6417ca25c4308bd158c34b77e1c0eca2a73cda16c737e7424afba2f 1
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----
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====
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[[generation_tx_example]]
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.Generation Transaction
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====
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[source,json]
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----
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{
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"hex" : "01000000010000000000000000000000000000000000000000000000000000000000000000ffffffff0f03443b0403858402062f503253482fffffffff0110c08d9500000000232102aa970c592640d19de03ff6f329d6fd2eecb023263b9ba5d1b81c29b523da8b21ac00000000",
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"txid" : "d5ada064c6417ca25c4308bd158c34b77e1c0eca2a73cda16c737e7424afba2f",
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"version" : 1,
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"locktime" : 0,
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"vin" : [
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{
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"coinbase" : "03443b0403858402062f503253482f",
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"sequence" : 4294967295
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}
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],
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"vout" : [
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{
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"value" : 25.09094928,
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"n" : 0,
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"scriptPubKey" : {
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"asm" : "02aa970c592640d19de03ff6f329d6fd2eecb023263b9ba5d1b81c29b523da8b21 OP_CHECKSIG",
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"hex" : "2102aa970c592640d19de03ff6f329d6fd2eecb023263b9ba5d1b81c29b523da8b21ac",
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"reqSigs" : 1,
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"type" : "pubkey",
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"addresses" : [
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"1MxTkeEP2PmHSMze5tUZ1hAV3YTKu2Gh1N"
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]
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}
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}
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],
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"blockhash" : "0000000000000001b6b9a13b095e96db41c4a928b97ef2d944a9b31b2cc7bdc4",
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"confirmations" : 35566,
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"time" : 1388185914,
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"blocktime" : 1388185914
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}
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----
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====
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Unlike regular transactions, the generation transaction does not consume (spend) UTXO as inputs. Instead, it has only one input, called the _coinbase_, which creates bitcoin from nothing. The generation transaction has one output, payable to the miner's own bitcoin address. The output of the generation transaction sends the value of 25.09094928 bitcoins to the miner's bitcoin address, in this case +1MxTkeEP2PmHSMze5tUZ1hAV3YTKu2Gh1N+.
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==== Coinbase Reward and Fees
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To construct the generation transaction, Jing's node first calculates the total amount of transaction fees by adding all the inputs and outputs of the 418 transactions that were added to the block. The fees are calculated as:
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----
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Total Fees = Sum(Inputs) - Sum(Outputs)
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----
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In block 277,316 the total transaction fees are 0.09094928 bitcoin.
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Next, Jing's node calculates the correct reward for the new block. The reward is calculated based on the block height, starting at 50 bitcoin per block and reduced by half every 210,000 blocks. Since this block is at height 277,316, the correct reward is 25 bitcoin.
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The calculation can be seen in function +GetBlockValue+ in the Bitcoin Core client:
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[[getblockvalue_source]]
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.Calculating the block reward - Function GetBlockValue, Bitcoin Core Client, main.cpp, line 1305
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====
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[source, cpp]
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----
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int64_t GetBlockValue(int nHeight, int64_t nFees)
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{
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int64_t nSubsidy = 50 * COIN;
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int halvings = nHeight / Params().SubsidyHalvingInterval();
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// Force block reward to zero when right shift is undefined.
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if (halvings >= 64)
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return nFees;
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// Subsidy is cut in half every 210,000 blocks which will occur approximately every 4 years.
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nSubsidy >>= halvings;
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return nSubsidy + nFees;
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}
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----
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====
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The initial subsidy is calculated in satoshis by multiplying 50 with the +COIN+ constant (100,000,000 satoshis). This sets the initial reward (+nSubsidy+) at 5 billion satoshis.
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Next, the function calculates the number of +halvings+ that have occurred by dividing the current block height by the halving interval (+SubsidyHalvingInterval+). In the case of block 277,316, with a halving interval every 210,000 blocks, the result is 1 halving.
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The maximum number of halvings allowed is 64, so the code imposes a zero reward (return only the fees) if the 64 halvings is exceeded.
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Next, the function uses the binary-right-shift operator to divide the reward (+nSubsidy+) by 2 for each round of halving. In the case of block 277,316 this would binary-right-shift the reward of 5 billion satoshis once (one halving) and result in 2.5 billion satoshis, or 25 bitcoin. The binary-right-shift operator is used because it is more efficient for division by 2 than integer or floating point division.
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Finally, the coinbase reward (+nSubsidy+) is added to the transaction fees (+nFees+), and the sum is returned.
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==== Structure of the Generation Transaction
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With these calculations, Jing's node then constructs the generation transaction to pay himself 25.09094928 bitcoin. The generation transaction is the first transaction in the block, so we can see it in more detail using the Bitcoin Core command-line interface:
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As you can see in <<generation_tx_example>>, the generation transaction has a special format. Instead of a transaction input specifying a previous UTXO to spend, it has a "coinbase" input. We examined transaction inputs in <<tx_in_structure>>. Let's compare a regular transaction input with a generation transaction input. A regular transaction looks like this:
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.The structure of a "normal" transaction input
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[options="header"]
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|=======
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|Size| Field | Description
|
|
| 32 bytes | Transaction Hash | Pointer to the transaction containing the UTXO to be spent
|
|
| 4 bytes | Output Index | The index number of the UTXO to be spent, first one is 0
|
|
| 1-9 bytes (VarInt) | Unlocking-Script Size | Unlocking-Script length in bytes, to follow
|
|
| Variable | Unlocking-Script | A script that fulfills the conditions of the UTXO locking-script.
|
|
| 4 bytes | Sequence Number | Currently-disabled Tx-replacement feature, set to 0xFFFFFFFF
|
|
|=======
|
|
|
|
|
|
The generation transaction input, however, looks like this:
|
|
|
|
.The structure of a generation transaction input
|
|
[options="header"]
|
|
|=======
|
|
|Size| Field | Description
|
|
| 32 bytes | Transaction Hash | All bits are zero: Not a transaction hash reference
|
|
| 4 bytes | Output Index | All bits are ones: 0xFFFFFFFF
|
|
| 1-9 bytes (VarInt) | Coinbase Data Size | Length of the Coinbase Data, from 2 to 100 bytes
|
|
| Variable | Coinbase Data | Arbitrary Data used for extra nonce and mining tags
|
|
In v2 blocks, must begin with block height
|
|
| 4 bytes | Sequence Number | Set to 0xFFFFFFFF
|
|
|=======
|
|
|
|
In a generation transaction, the first two fields are set to values that do not represent a UTXO reference. Instead of a "Transaction Hash", the first field is filled with 32 bytes all set to zero. The "Output Index" is filled with 4 bytes all set to 0xFF (255 decimal). The "Unlocking Script" is replaced by coinbase data, an arbitrary data field used by the miners.
|
|
|
|
==== Coinbase Data
|
|
|
|
Generation transactions do not have an unlocking script (a.k.a. scriptSig) field. Instead, this field is replaced by coinbase data, which must be between 2 and 100 bytes. Except for the first few bytes (see below) the rest of the coinbase data can be used by miners in any way they want; it is arbitrary data.
|
|
|
|
In the genesis block, for example, Satoshi Nakamoto added the text "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks" in the coinbase data, using it as a proof of the date and to convey a message. Currently, miners use the coinbase data to include extra nonce values (see <<mining>>) and strings identifying the mining pool, as we will see in the following sections.
|
|
|
|
The first few bytes of the coinbase used to be arbitrary, but that is no longer the case. As per Bitcoin Improvement Proposal 34 (BIP0034), version-2 blocks (blocks with the version field set to 2) must contain the block height index as a script "push" operation in the beginning of the coinbase field.
|
|
|
|
In block 277,316 we see that the coinbase (see <<generation_tx_example>>), which is in the "Unlocking Script" or scriptSig field of the transaction input, contains the hexadecimal value +03443b0403858402062f503253482f+. Let's decode this value.
|
|
|
|
The first byte, +03+ instructs the script execution engine to push the next 3 bytes onto the script stack (see <<tx_script_ops_table_pushdata>>). The next 3 bytes, +0x443b04+, are the block height encoded in little-endian format (backwards, least significant byte first). Reverse the order of the bytes and the result is +0x043b44+ which is 277,316 in decimal.
|
|
|
|
The next few hexadecimal digits (+03858402062+) are used to encode an extra _nonce_, or random value, used to find a suitable Proof-of-Work solution. This is discussed in more detail in the next section on <<mining>>
|
|
|
|
The final part of the coinbase data (+2f503253482f+) is the ASCII-encoded string "/P2SH/", which indicates that the mining node that mined this block supports the Pay-to-Script-Hash (P2SH) improvement defined in BIP0016. The introduction of the P2SH capability required a "vote" by miners to endorse either BIP0016 or BIP0017. Those endorsing the BIP0016 implementation were to include "/P2SH/" in their coinbase data. Those endorsing the BIP0017 implementation of P2SH were to include the string "p2sh/CHV" in their coinbase data. The BIP0016 was elected as the winner, and many miners continued including the string "/P2SH/" in their coinbase to indicate support for this feature.
|
|
|
|
=== Constructing the Block Header
|
|
|
|
To construct the block header, the mining node needs to fill in six fields:
|
|
|
|
[[block_header_structure]]
|
|
.The structure of the block header
|
|
[options="header"]
|
|
|=======
|
|
|Size| Field | Description
|
|
| 4 bytes | Version | A version number to track software/protocol upgrades
|
|
| 32 bytes | Previous Block Hash | A reference to the hash of the previous (parent) block in the chain
|
|
| 32 bytes | Merkle Root | A hash of the root of the Merkle-Tree of this block's transactions
|
|
| 4 bytes | Timestamp | The approximate creation time of this block (seconds from Unix Epoch)
|
|
| 4 bytes | Difficulty Target | The Proof-of-Work algorithm difficulty target for this block
|
|
| 4 bytes | Nonce | A counter used for the Proof-of-Work algorithm
|
|
|=======
|
|
|
|
At the time block 277,316 was mined, the version number describing the block structure is version "2", which is encoded in little-endian format in 4 bytes as +0x02000000+.
|
|
|
|
Next, the mining node needs to add the "Previous Block Hash". That is the hash of the block header of block 277,315, the previous block received from the network, which Jing's node has accepted and selected as the parent of the candidate block 277,316. The block header hash for block 277,315 is +0000000000000002a7bbd25a417c0374cc55261021e8a9ca74442b01284f0569+.
|
|
|
|
The next step is to summarize all the transactions with a Merkle Tree, in order to add the Merkle Root to the block header. The generation transaction is listed as the first transaction in the block. Then, 418 more transactions are added after it, for a total of 419 transactions in the block. As we saw in the <<merkle_trees>>, there must be an even number of "leaf" nodes in the tree, so the last transaction is duplicated, creating 420 nodes, each containing the hash of one transaction. The transaction hashes are then combined, in pairs, creating each level of the tree, until all the transactions are summarized into one node at the "root" of the tree. The root of the merkle tree summarizes all the transactions into a single 32 byte value +c91c008c26e50763e9f548bb8b2fc323735f73577effbc55502c51eb4cc7cf2e+ which you can see listed as "merkle root" in <<block277316>>
|
|
|
|
The mining node will then add a 4-byte timestamp, encoded as a Unix "Epoch" timestamp, which is based on the number of seconds elapsed from January 1st, 1970, midnight UTC/GMT. The time +1388185914+ is equal to Friday, 27 Dec 2013, 23:11:54 UTC/GMT.
|
|
|
|
The node then fills in the difficulty target, which defines the required Proof-of-Work difficulty to make this a valid block. The difficulty is stored in the block as a "difficulty bits" metric, which is a mantissa-exponent encoding of the target. The encoding has a one-byte exponent, followed by a 3 byte mantissa (coefficient). In block 277,316, for example, the difficulty bits value is +0x1903a30c+. The first part +0x19+ is a hexadecimal exponent, while the next part +0x03a30c+ is the coefficient. The concept of a difficulty target is explained in <<difficulty_target>> and the "difficulty bits" representation is explained in <<difficulty_bits>>.
|
|
|
|
The final field is the nonce, which is initialized to zero.
|
|
|
|
With all the other fields filled, the block header is now complete and the process of mining can begin. The goal is now to find a value for the nonce that results in a block header hash that is less than the difficulty target. The mining node will need to test billions or trillions of nonce values before a nonce is found that satisfies the requirement.
|
|
|
|
=== Mining the Block
|
|
|
|
Now that a candidate block has been constructed by Jing's node, it is time for Jing's hardware mining rig to "mine" the block, to find a solution to the Proof-of-Work algorithm that makes the block valid. Throughout this book we have studied cryptographic hash functions as used in various aspects of the bitcoin system. The hash function SHA-256 is the function used in bitcoin's mining process.
|
|
|
|
In the simplest terms, mining is the process of hashing the block header repeatedly, changing one parameter, until the resulting hash matches a specific target. The hash function's result cannot be determined in advance, nor can a pattern be created that will produce a specific hash value. This feature of hash functions means that the only way to produce a hash result matching a specific target, is to try again and again, randomly modifying the input until the desired hash result appears by chance.
|
|
|
|
==== Proof-of-Work Algorithm
|
|
|
|
A hash algorithm takes an arbitrary-length data input and produces a fixed-length deterministic result, a digital fingerprint of the input. For any specific input, the resulting hash will always be the same and can be easily calculated and verified by anyone implementing the same hash algorithm. The key characteristic of a cryptographic hash algorithm is that it is impossible to find two different inputs that produce the same fingerprint. As a corollary, it is also impossible to select an input in such a way as to produce a desired fingerprint, other than trying random inputs.
|
|
|
|
With SHA-256, the output is always 256 bits long, regardless of the size of the input. In the example below, we will use the Python interpreter to calculate the SHA256 hash of the phrase "I am Satoshi Nakamoto".
|
|
|
|
[[sha256_example1]]
|
|
.SHA256 Example
|
|
====
|
|
[source,bash]
|
|
----
|
|
$ python
|
|
----
|
|
[source,pycon]
|
|
----
|
|
Python 2.7.1
|
|
>>> import hashlib
|
|
>>> print hashlib.sha256("I am Satoshi Nakamoto").hexdigest()
|
|
5d7c7ba21cbbcd75d14800b100252d5b428e5b1213d27c385bc141ca6b47989e
|
|
----
|
|
====
|
|
|
|
The example shows that if we calculate the hash of the phrase +"I am Satoshi Nakamoto"+, it will produce +5d7c7ba21cbbcd75d14800b100252d5b428e5b1213d27c385bc141ca6b47989e+. This 256-bit number is the _hash_ or _digest_ of the phrase and depends on every part of the phrase. Adding a single letter, punctuation mark or any character will produce a different hash.
|
|
|
|
Now, if we change the phrase, we will expect to see completely different hashes. Let's try that by adding a number to the end of our phrase, using this simple Python script
|
|
|
|
[[sha256_example_generator]]
|
|
.SHA256 A script for generating many hashes by iterating on a nonce
|
|
====
|
|
[source, python]
|
|
----
|
|
include::code/hash_example.py[]
|
|
----
|
|
====
|
|
|
|
Running this will produce the hashes of several phrases, made different by adding a number at the end of the text. By incrementing the number, we can get different hashes.
|
|
|
|
((("nonce")))
|
|
[[sha256_example_generator_output]]
|
|
.SHA256 Output of a script for generating many hashes by iterating on a nonce
|
|
====
|
|
[source,bash]
|
|
----
|
|
$ python hash_example.py
|
|
----
|
|
|
|
----
|
|
I am Satoshi Nakamoto0 => a80a81401765c8eddee25df36728d732...
|
|
I am Satoshi Nakamoto1 => f7bc9a6304a4647bb41241a677b5345f...
|
|
I am Satoshi Nakamoto2 => ea758a8134b115298a1583ffb80ae629...
|
|
I am Satoshi Nakamoto3 => bfa9779618ff072c903d773de30c99bd...
|
|
I am Satoshi Nakamoto4 => bce8564de9a83c18c31944a66bde992f...
|
|
I am Satoshi Nakamoto5 => eb362c3cf3479be0a97a20163589038e...
|
|
I am Satoshi Nakamoto6 => 4a2fd48e3be420d0d28e202360cfbaba...
|
|
I am Satoshi Nakamoto7 => 790b5a1349a5f2b909bf74d0d166b17a...
|
|
I am Satoshi Nakamoto8 => 702c45e5b15aa54b625d68dd947f1597...
|
|
I am Satoshi Nakamoto9 => 7007cf7dd40f5e933cd89fff5b791ff0...
|
|
I am Satoshi Nakamoto10 => c2f38c81992f4614206a21537bd634a...
|
|
I am Satoshi Nakamoto11 => 7045da6ed8a914690f087690e1e8d66...
|
|
I am Satoshi Nakamoto12 => 60f01db30c1a0d4cbce2b4b22e88b9b...
|
|
I am Satoshi Nakamoto13 => 0ebc56d59a34f5082aaef3d66b37a66...
|
|
I am Satoshi Nakamoto14 => 27ead1ca85da66981fd9da01a8c6816...
|
|
I am Satoshi Nakamoto15 => 394809fb809c5f83ce97ab554a2812c...
|
|
I am Satoshi Nakamoto16 => 8fa4992219df33f50834465d3047429...
|
|
I am Satoshi Nakamoto17 => dca9b8b4f8d8e1521fa4eaa46f4f0cd...
|
|
I am Satoshi Nakamoto18 => 9989a401b2a3a318b01e9ca9a22b0f3...
|
|
I am Satoshi Nakamoto19 => cda56022ecb5b67b2bc93a2d764e75f...
|
|
----
|
|
====
|
|
|
|
Each phrase produces a completely different hash result. They seem completely random, but you can re-produce the exact results in this example on any computer with Python and see the same exact hashes.
|
|
|
|
The number used as a variable in such a scenario is called a _nonce_. The nonce is used to vary the output of a cryptographic function, in this case to vary the SHA-256 fingerprint of the phrase.
|
|
|
|
To make a challenge out of this algorithm, let's set an arbitrary target: find a phrase that produces a hexadecimal hash that starts with a zero. Fortunately, this isn't so difficult! If you notice above, we can see that the phrase "I am Satoshi Nakamoto13" produces the hash 0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5, which fits our criteria. It took 13 attempts to find it. In terms of probabilities, if the output of the hash function is evenly distributed we would expect to find a result with a 0 as the hexadecimal prefix once every 16 hashes (one out of 16 hexadecimal digits 0 through F). In numerical terms, that means finding a hash value that is less than +0x1000000000000000000000000000000000000000000000000000000000000000+. We call this threshold the _target_ and the goal is to find a hash that is numerically _less than the target_. If we decrease the target, the task of finding a hash that is less than the target becomes more and more difficult.
|
|
|
|
To give a simple analogy, imagine a game where players throw a pair of dice repeatedly, trying to throw less than a specified target. In the first round, the target is 12. Unless you throw double-six, you win. In the next round the target is 11. Players must throw 10 or less to win, again an easy task. Let's say a few rounds later the target is down to 5. Now, more than half the dice throws will add up to more than 5 and therefore be invalid. It takes exponentially more dice throws to win, the lower the target gets. Eventually, when the target is 2 (the minimum possible), only one throw out of every 36, or 2% of them will produce a winning result.
|
|
|
|
In the example above, the winning "nonce" is 13 and this result can be confirmed by anyone independently. Anyone can add the number 13 as a suffix to the phrase "I am Satoshi Nakamoto" and compute the hash, verifying that it is less than the target. The successful result is also proof-of-work, as it proves we did the work to find that nonce. While it only takes one hash computation to verify, it took us 13 hash computations to find a nonce that worked. If we had a lower target (higher difficulty) it would take many more hash computations to find a suitable nonce, but only one hash computation for anyone to verify. Furthermore, by knowing the target, anyone can estimate the difficulty using statistics and therefore know how much work was needed to find such a nonce.
|
|
|
|
Bitcoin's Proof-of-Work is very similar to the problem above. The miner constructs a candidate block filled with transactions. Next, the miner calculates the hash of this block's header and see if it is smaller than the current _target_. If the hash is not less than the target, the miner will modify the nonce (usually just incrementing it by one) and try again. At the current difficulty in the bitcoin network, miners have to try quadrillions of times before finding a nonce that results in a low enough block header hash.
|
|
|
|
A very simplified Proof-of-Work algorithm is implemented in Python here:
|
|
((("proof of work")))
|
|
[[pow_example1]]
|
|
.Simplified Proof-Of-Work Implementation
|
|
====
|
|
[source, python]
|
|
----
|
|
include::code/proof-of-work-example.py[]
|
|
----
|
|
====
|
|
|
|
Running the code above, you can set the desired difficulty (in bits, how many of the leading bits must be zero) and see how long it takes for your computer to find a solution. In the following examples, you can see how it works on an average laptop:
|
|
|
|
[[pow_example_outputs]]
|
|
.Running the Proof-of-Work example for various difficulties
|
|
====
|
|
[source, bash]
|
|
----
|
|
$ python proof-of-work-example.py*
|
|
----
|
|
|
|
----
|
|
Difficulty: 1 (0 bits)
|
|
|
|
[...]
|
|
|
|
Difficulty: 8 (3 bits)
|
|
Starting search...
|
|
Success with nonce 9
|
|
Hash is 1c1c105e65b47142f028a8f93ddf3dabb9260491bc64474738133ce5256cb3c1
|
|
Elapsed Time: 0.0004 seconds
|
|
Hashing Power: 25065 hashes per second
|
|
Difficulty: 16 (4 bits)
|
|
Starting search...
|
|
Success with nonce 25
|
|
Hash is 0f7becfd3bcd1a82e06663c97176add89e7cae0268de46f94e7e11bc3863e148
|
|
Elapsed Time: 0.0005 seconds
|
|
Hashing Power: 52507 hashes per second
|
|
Difficulty: 32 (5 bits)
|
|
Starting search...
|
|
Success with nonce 36
|
|
Hash is 029ae6e5004302a120630adcbb808452346ab1cf0b94c5189ba8bac1d47e7903
|
|
Elapsed Time: 0.0006 seconds
|
|
Hashing Power: 58164 hashes per second
|
|
|
|
[...]
|
|
|
|
Difficulty: 4194304 (22 bits)
|
|
Starting search...
|
|
Success with nonce 1759164
|
|
Hash is 0000008bb8f0e731f0496b8e530da984e85fb3cd2bd81882fe8ba3610b6cefc3
|
|
Elapsed Time: 13.3201 seconds
|
|
Hashing Power: 132068 hashes per second
|
|
Difficulty: 8388608 (23 bits)
|
|
Starting search...
|
|
Success with nonce 14214729
|
|
Hash is 000001408cf12dbd20fcba6372a223e098d58786c6ff93488a9f74f5df4df0a3
|
|
Elapsed Time: 110.1507 seconds
|
|
Hashing Power: 129048 hashes per second
|
|
Difficulty: 16777216 (24 bits)
|
|
Starting search...
|
|
Success with nonce 24586379
|
|
Hash is 0000002c3d6b370fccd699708d1b7cb4a94388595171366b944d68b2acce8b95
|
|
Elapsed Time: 195.2991 seconds
|
|
Hashing Power: 125890 hashes per second
|
|
|
|
[...]
|
|
|
|
Difficulty: 67108864 (26 bits)
|
|
Starting search...
|
|
Success with nonce 84561291
|
|
Hash is 0000001f0ea21e676b6dde5ad429b9d131a9f2b000802ab2f169cbca22b1e21a
|
|
Elapsed Time: 665.0949 seconds
|
|
Hashing Power: 127141 hashes per second
|
|
----
|
|
====
|
|
|
|
As you can see, increasing the difficulty by 1 bit causes an exponential increase in the time it takes to find a solution. If you think of the entire 256-bit number space, each time you constrain one more bit to zero, you decrease the search space by half. In the example above, it takes 84 million hash attempts to find a nonce that produces a hash with 26 leading bits as zero. Even at a speed of more than 120 thousand hashes per second, it still requires ten minutes on a consumer laptop to find this solution.
|
|
|
|
At the time of writing this, the network is attempting to find a block whose header hash is less than +000000000000004c296e6376db3a241271f43fd3f5de7ba18986e517a243baa7+. As you can see, there are a lot of zeroes at the beginning of that hash, meaning that the acceptable range of hashes is much smaller, hence more difficult to find a valid hash. It will take on average more than 150 quadrillion hash calculations per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 100 Peta Hashes per second of processing power to bear, which will be able to find a block in about 10 minutes on average.
|
|
|
|
==== Difficulty Representation
|
|
|
|
In <<block277316>> we saw that the block contains the difficulty target, in a notation called "difficulty bits" or just "bits", which in block 277,316 has the value of +0x1903a30c+. This notation expresses the difficulty target as a coefficient/exponent format, with the first two hexadecimal digits for the exponent and the next six hex digits as the coefficient. In this block, therefore, the exponent is +0x19+ and the coefficient is +0x03a30c+.
|
|
|
|
The formula to calculate the difficulty target from this representation is:
|
|
|
|
target = coefficient * 2^(8 * (exponent - 3))
|
|
|
|
Using that formula, and the difficulty bits value 0x1903a30c, we get:
|
|
|
|
target = 0x03a30c * 2^(0x08 * (0x19 - 0x03))^
|
|
|
|
=> target = 0x03a30c * 2^(0x08 * 0x16)^
|
|
|
|
=> target = 0x03a30c * 2^0xB0^
|
|
|
|
which in decimal is:
|
|
|
|
=> target = 238,348 * 2^176^
|
|
|
|
=> target = 22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328
|
|
|
|
switching back to hexadecimal:
|
|
|
|
=> target = 0x0000000000000003A30C00000000000000000000000000000000000000000000
|
|
|
|
This means that a valid block for height 277,316 is one that has a block header hash that is less than the target. In binary that number would have more than the first 60 bits set to zero. With this level of difficulty, a single miner processing 1 trillion hashes per second (1 tera-hash per second or 1 TH/sec) would only find a solution once every 8,496 blocks or once every 59 days, on average.
|
|
|
|
==== Difficulty Target and Re-Targeting
|
|
|
|
As we saw above the target determines the difficulty and therefore affects how long it takes to find a solution to the Proof-of-Work algorithm. This leads to the obvious questions: Why is the difficulty adjustable, who adjusts it and how?
|
|
|
|
Bitcoin's blocks are generated every 10 minutes, on average. This is bitcoin's heartbeat and underpins the frequency of currency issuance and the speed of transaction settlement. It has to remain constant not just over the short term, but over a period of many decades. Over this time, it is expected that computer power will continue to increase at a rapid pace. Furthermore, the number of participants in mining and the computers they use will also constantly change. To keep the block generation time at 10 minutes, the difficulty of mining must be adjusted to account for these changes. In fact, difficulty is a dynamic parameter that will be periodically adjusted to meet a 10-minute block target. In simple terms, the difficulty target is set to whatever mining power will result in a 10-minute block interval.
|
|
|
|
How then is such an adjustment made in a completely de-centralized network? Difficulty re-targeting occurs automatically and on every full node independently. Every 2016 blocks, all nodes re-target the Proof-of-Work difficulty. The equation for retargeting difficulty measures the time it took to find the last 2016 blocks and compares that to the expected time of 20160 minutes (two weeks based upon a desired 10 minute block time). The ratio between the actual timespan and desired timespan is calculated and a corresponding adjustment (up or down) is made to the difficulty. In simple terms: If the network is finding blocks faster than every 10 minutes, the difficulty increases. If block discovery is slower than expected, the difficulty decreases.
|
|
|
|
The equation can be summarized as:
|
|
|
|
New Difficulty = Old Difficulty * (Actual Time of Last 2016 Blocks / 20160 minutes)
|
|
|
|
Here's the code used in the Bitcoin Core client
|
|
|
|
[[retarget_difficulty_code]]
|
|
.Re-targeting the Proof-of-Work difficulty - +GetNextWorkRequired()+ in +pow.cpp+, line 43
|
|
====
|
|
[source,cpp]
|
|
----
|
|
|
|
// Go back by what we want to be 14 days worth of blocks
|
|
const CBlockIndex* pindexFirst = pindexLast;
|
|
for (int i = 0; pindexFirst && i < Params().Interval()-1; i++)
|
|
pindexFirst = pindexFirst->pprev;
|
|
assert(pindexFirst);
|
|
|
|
// Limit adjustment step
|
|
int64_t nActualTimespan = pindexLast->GetBlockTime() - pindexFirst->GetBlockTime();
|
|
LogPrintf(" nActualTimespan = %d before bounds\n", nActualTimespan);
|
|
if (nActualTimespan < Params().TargetTimespan()/4)
|
|
nActualTimespan = Params().TargetTimespan()/4;
|
|
if (nActualTimespan > Params().TargetTimespan()*4)
|
|
nActualTimespan = Params().TargetTimespan()*4;
|
|
|
|
// Retarget
|
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uint256 bnNew;
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uint256 bnOld;
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bnNew.SetCompact(pindexLast->nBits);
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bnOld = bnNew;
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bnNew *= nActualTimespan;
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bnNew /= Params().TargetTimespan();
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if (bnNew > Params().ProofOfWorkLimit())
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bnNew = Params().ProofOfWorkLimit();
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----
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====
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The parameters Interval (2016 blocks) and TargetTimespan (two weeks as 1,209,600 seconds) are defined in +chainparams.cpp+
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To avoid extreme volatility in the difficulty, the retargeting adjustment must be less than a factor of four (4) per cycle. If the required difficulty adjustment is greater than a factor of four, it will be adjusted by the maximum and not more. Any further adjustment will be accomplished in the next retargeting period as the imbalance will persist through the next 2016 blocks. Therefore, large discrepancies between hashing power and difficulty may take several 2016 block cycles to balance out.
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[TIP]
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====
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The difficulty of finding a bitcoin block is approximately '10 minutes of processing' for the entire network, based on the time it took to find the previous 2016 blocks, adjusted every 2016 blocks.
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====
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Note that the target difficulty is independent of the number of transactions or the value of transactions. This means that the amount of hashing power and therefore electricity expended to secure bitcoin is also entirely independent of the number of transactions. Bitcoin can scale up, achieve broader adoption and remain secure without any increase in hashing power from today's level. The increase in hashing power represents market forces as new miners enter the market to compete for the reward. As long as enough hashing power is under the control of miners acting honestly in pursuit of the reward, it is enough to prevent "takeover" attacks and therefore it is enough to secure bitcoin.
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The target difficulty is closely related to the cost of electricity and the exchange rate of bitcoin vis-a-vis the currency used to pay for electricity. High performance mining systems are about as efficient as possible with the current generation of silicon fabrication, converting electricity into hashing computation at the highest rate possible. The primary influence on the mining market is the price of one kilowatt-hour in bitcoin, as that determines the profitability of mining and therefore the incentives to enter or exit the mining market.
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=== Successfully Mining the Block
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As we saw earlier, Jing's node has constructed a candidate block and prepared it for mining. Jing has several hardware mining rigs with Application Specific Integrated Circuits, where hundreds of thousands of integrated circuits run the SHA-256 algorithm in parallel at incredible speeds. These specialized machines are connected to his mining node over USB. Next, the mining node running on Jing's desktop transmits the block header to his mining hardware, which start testing trillions of nonces per second.
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Almost eleven minutes after starting to mine block 277,316, one of the hardware mining machines finds a solution and sends it back to the mining node. The nonce 4,215,469,401 when inserted into the block header produces a block hash of +0000000000000002a7bbd25a417c0374cc55261021e8a9ca74442b01284f0569+, which is less than the target of +0000000000000003A30C00000000000000000000000000000000000000000000+.
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Immediately, Jing's mining node transmits the block to all its peers. They receive, validate and then propagate the new block. As the block ripples out across the network, each node adds it to its own copy of the blockchain, extending it to a new height of 277,316 blocks. As mining nodes receive and validate the block, they abandon their efforts to find a block at the same height and immediately start computing the next block in the chain.
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In the next section we'll look at the process each node uses to validate a block and select the longest chain, creating the consensus that forms the de-centralized blockchain.
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=== Validating a New Block
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The third step in bitcoin's consensus mechanism is independent validation of each new block by every node on the network. As the newly solved block moves across the network, each node performs a series of tests to validate it before propagating it to its peers. This ensures that only valid blocks are propagated on the network. The independent validation also ensures that miners who act honestly get their blocks incorporated in the blockchain, thus earning the reward. Those miners who act dishonestly have their blocks rejected and not only lose the reward but also waste the effort expended to find a Proof-of-Work solution, thus incurring the cost of electricity without compensation.
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When a node receives a new block, it will validate the block by checking it against a long list of criteria. These criteria can be seen in the Bitcoin Core client in the functions +CheckBlock+ and +CheckBlockHeader+. These criteria include:
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* Check the syntactic validity of the block data structure
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* Check the Proof-of-Work, by checking the block header hash is less than the target difficulty
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* Check the block timestamp is less than two hours in the future (allowing for time errors)
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* Check the block size is within acceptable limits
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* Check the first transaction (and only the first) is a coinbase generation transaction
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* Validate all transactions within the block, using the transaction checklist discussed in <<tx_verification>>
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The independent validation of each new block by every node on the network ensures that the miners can't cheat. In previous sections we saw how the miners get to write a transaction that awards them the new bitcoins created within the block and claim the transaction fees. Why doesn't the miner write themselves a transaction for a thousand bitcoin instead of the correct reward? Because every node validates blocks according to the same rules. An invalid coinbase transaction would make the entire block invalid, which would result in the block being rejected and therefore that transaction would never become part of the ledger. The miner has to construct a perfect block, based on the shared rules that all nodes follow and mine it with a correct solution to the Proof-of-Work. To do so they expend a lot of electricity in mining and if they cheat all the electricity and effort is wasted. This is why independent validation is a key component of decentralized consensus.
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=== Assembling and Selecting Chains of Blocks
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The final step in bitcoin's de-centralized consensus mechanism is the assembly of blocks into chains and the selection of the chain with the most Proof-of-Work. Once a node has validated a new block, it will then attempt to assemble a chain, by connecting the block to the existing blockchain.
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Nodes maintain three sets of blocks: those connected to the main blockchain, those that form branches off the main blockchain (secondary chains) and finally blocks that do not have a known parent in the known chains (orphans). Invalid blocks are rejected as soon as any one of the validation criteria fails and are therefore not included in any chain.
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The "main chain" at any time is whichever chain of blocks has the most cumulative difficulty associated with it. Under most circumstances this is also the chain with the most blocks in it, unless there are two equal length chains and one has more proof-of-work. The main chain will also have branches with blocks that are "siblings" to the blocks on the main chain. These blocks are valid but not part of the main chain. They are kept for future reference, in case one of those chains is extended to exceed the main chain in difficulty. In the next section (<<forks>>), we will see how secondary chains occur as a result of an almost simultaneous mining of blocks at the same height.
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When a new block is received, a node will try to slot it into the existing blockchain. The node will look at the block's "previous block hash" field, which is the reference to the new block's parent. Then, the node will attempt to find that parent in the existing blockchain. Most of the time, the parent will be the "tip" of the main chain, meaning this new block extends the main chain. For example, the new block 277,316 has a reference to the hash of its parent block 277,315. Most nodes that receive 277,316 will already have block 277,315 as the tip of their main chain and will therefore link the new block and extend that chain.
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Sometimes, as we will see in <<forks>>, the new block extends a chain that is not the main chain. In that case, the node will attach the new block to the secondary chain it extends and then compare the difficulty of the secondary chain to the main chain. If the secondary chain has more cumulative difficulty than the main chain, the node will _reconverge_ on the secondary chain, meaning it will select the secondary chain as its new main chain, making the old main chain a secondary chain. If the node is a miner, it will now construct a block extending this new, longer, chain.
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If a valid block is received and no parent is found in the existing chains, then that block is considered an "orphan". Orphan blocks are saved in the orphan block pool where they will stay until their parent is received. Once the parent is received and linked into the existing chains, the orphan can be pulled out of the orphan pool and linked to the parent, making it part of a chain. Orphan blocks usually occur when two blocks that were mined within a short time of each other are received in reverse order (child before parent).
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By selecting the greatest-difficulty chain, all nodes eventually achieve network-wide consensus. Temporary discrepancies between chains are resolved eventually as more Proof-of-Work is added, extending one of the possible chains. Mining nodes "vote" with their mining power by choosing which chain to extend by mining the next block. When they mine a new block and extend the chain, the new block itself represents their vote.
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In the next section we will look at how discrepancies between competing chains (forks) are resolved by the independent selection of the longest difficulty chain.
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[[forks]]
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==== Blockchain Forks
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Because the blockchain is a decentralized data structure, different copies of it are not always consistent. Blocks may arrive at different nodes at different times, causing the nodes to have different perspectives of the blockchain. To resolve this, each node always selects and attempts to extend the chain of blocks that represents the most Proof-of-Work, also known as the longest chain or greatest cumulative difficulty chain. By summing the difficulty recorded in each block in a chain, a node can calculate the total amount of Proof-of-Work that has been expended to create that chain. As long as all nodes select the longest cumulative difficulty chain, the global bitcoin network eventually converges to a consistent state. Forks occur as temporary inconsistencies between versions of the blockchain, which are resolved by eventual re-convergence as more blocks are added to one of the forks.
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In the next few diagrams, we follow the progress of a "fork" event across the network. The diagram is a simplified representation of bitcoin as a global network. In reality, the bitcoin network's topology is not organized geographically. Rather, it forms a mesh network of interconnected nodes, which may be located very far from each other geographically. The representation of a geographic topology is a simplification used for the purposes of illustrating a fork. In the real bitcoin network, the "distance" between nodes is measured in "hops" from node to node, not in terms of their physical location. For illustration purposes, different blocks are shown as different colors, spreading across the network and coloring the connections they traverse.
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In the first diagram below, the network has a unified perspective of the blockchain, with the blue block as the tip of the main chain.
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[[fork1]]
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.Visualization of a blockchain fork event - Before the Fork
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image::images/GlobalFork1.png["globalfork1"]
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A "fork" occurs whenever there are two candidate blocks competing to form the longest blockchain. This occurs under normal conditions whenever two miners solve the Proof-of-Work algorithm within a short period of time from each other. As both miners discover a solution for their respective candidate blocks, they immediately broadcast their own "winning" block to their immediate neighbors who begin propagating the block across the network. Each node that receives a valid block will incorporate it into their blockchain, extending the blockchain by one block. If that node later sees another candidate block extending the same parent, they connect the second candidate on a secondary chain. As a result, some nodes will "see" one candidate block first, while other nodes will see the other candidate block and two competing versions of the blockchain will emerge.
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In the diagram below, we see two miners who mine two different blocks almost simultaneously. Both of these blocks are children of the blue block, meant to extend the chain by building on top of the blue block. To help us track it, one is visualized as a red block originating from Canada, and the other is marked as a green block originating from Australia.
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[[fork2]]
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.Visualization of a blockchain fork event - Two blocks found simultaneously
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image::images/GlobalFork2.png["globalfork2"]
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Let's assume for example that a miner in Canada finds a Proof-of-Work solution for a block "red" that extends the blockchain, building on top of the parent block "blue". Almost simultaneously, an Australian miner who was also extending block "blue", finds a solution for block "green", their candidate block. Now, there are two possible blocks, one we call "red", originating in Canada and one we call "green", originating in Australia. Both blocks are valid, both blocks contain a valid solution to the proof of work, both blocks extend the same parent. Both blocks likely contain most of the same transactions, with only perhaps a few differences in the order of transactions.
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As the two blocks propagate, some nodes receive block "red" first and some receive block "green" first. The network splits into two different perspectives of the blockchain, one side topped with a red block, the other with a green block.
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[[fork2]]
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.Visualization of a blockchain fork event - Two blocks propagate, splitting the network
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image::images/GlobalFork3.png["globalfork3"]
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From that moment, the bitcoin network nodes closest (topologically, not geographically) to the Canadian node will hear about block "red" first and will create a new greatest-cumulative-difficulty blockchain with "red" as the last block in the chain (e.g. blue-red), ignoring the candidate block "green" that arrives a bit later. Meanwhile, nodes closer to the Australian node will take that block as the winner and extend the blockchain with "green" as the last block (e.g. blue-green), ignoring "red" when it arrives a few seconds later. Any miners that saw "red" first will immediately build candidate blocks that reference "red" as the parent and start trying to solve the PoW for these candidate blocks. The miners that accepted "green" instead, will start building on top of "green" and extending that chain.
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[[fork4]]
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.Visualization of a blockchain fork event - A new block extends one fork
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|
image::images/GlobalFork4.png["globalfork4"]
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|
Forks are almost always resolved within one block. As part of the network's hashing power is dedicated to building on top of "red" as the parent, another part of the hashing power is focused on building on top of "green". Even if the hashing power is almost evenly split, it is likely that one set of miners will find a solution and propagate it before the other set of miners have found any solutions. Let's say for example that the miners building on top of "green" find a new block "pink" that extends the chain (e.g. blue-green-pink). They immediately propagate this new block and the entire network sees it as a valid solution.
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[[fork5]]
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|
.Visualization of a blockchain fork event - The network re-converges on a new longest chain
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|
image::images/GlobalFork5.png["globalfork5"]
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|
All nodes that had chosen "green" as the winner in the previous round will simply extend the chain one more block. The nodes that chose "red" as the winner, however, will now see two chains: blue-green-pink and blue-red. The chain blue-green-pink is now longer (more cumulative difficulty) than the chain blue-red. As a result, those nodes will set the chain blue-green-pink as main chain and change the blue-red chain to being a secondary chain. This is a chain re-convergence, as those nodes are forced to revise their view of the blockchain to incorporate the new evidence of a longer chain. Any miners working on extending the chain blue-red will now stop that work because their candidate block is an "orphan", as its parent "red" is no longer on the longest chain. The transactions within "red" are queued up again for processing in the next block, as that block is no longer in the main chain. The entire network re-converges on a single blockchain blue-green-pink, with "pink" as the last block in the chain. All miners immediately start working on candidate blocks that reference "pink" as their parent to extend the blue-green-pink chain.
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|
It is theoretically possible for a fork to extend to two blocks, if two blocks are found almost simultaneously by miners on opposite "sides" of a previous fork. However, the chance of that happening is very low. Whereas a one-block fork may occur every week, a two-block fork is exceedingly rare.
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Bitcoin's block interval of 10 minutes is a design compromise between fast confirmation times (settlement of transactions) and the probability of a fork. A faster block time would make transactions clear faster but lead to more frequent blockchain forks, whereas a slower block time would decrease the number of forks but make settlement slower.
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|
=== Mining and the Hashing Race
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|
Bitcoin mining is an extremely competitive industry. The hashing power has increased exponentially, every year of bitcoin's existence. Some years the growth has reflected a complete change of technology, such as in 2010 and 2011 when many miners switched from using CPU mining to Graphical Processing Unit (GPU) mining and Field Programmable Gate Array (FPGA) mining. In 2013 the introduction of Application Specific Integrated Circuit (ASIC) mining lead to another giant leap in mining power, by placing the SHA-256 function directly on silicon chips specialized for the purpose of mining. The first such chips could deliver more mining power in a single box than the entire bitcoin network in 2010.
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|
* 2009 - 0.5 MH/sec to 8 MH/sec (x 16 growth)
|
|
* 2010 - 8 MH/sec to 116 GH/sec (x 14,500 growth)
|
|
* 2011 - 16 GH/sec - 9 TH/sec (x 562 growth)
|
|
* 2012 - 9 TH/sec - 23 TH/sec (x 2.5 growth)
|
|
* 2013 - 23 TH/sec - 10 PH/sec (x 450 growth)
|
|
* 2014 - 10 PH/sec - 150 PH/sec in August (x 15 growth)
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|
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|
In the chart below, we see the bitcoin network's hashing power increase over the past two years. As you can see, the competition between miners and the growth of bitcoin has resulted in an exponential increase in the hashing power (total hashes per second across the network):
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|
|
|
[[network_hashing_power]]
|
|
.Total hashing power, giga-hashes per second, over two years
|
|
image::images/NetworkHashingRate.png["NetworkHashingRate"]
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|
As the amount of hashing power applied to mining bitcoin has exploded, the difficulty has risen to match it. The difficulty metric in the following chart is measured as a ratio of current difficulty over minimum difficulty (the difficulty of the first block):
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|
[[bitcoin_difficulty]]
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|
.Bitcoin's mining difficulty metric, over two years
|
|
image::images/BitcoinDifficulty.png["BitcoinDifficulty"]
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|
In the last two years, the ASIC mining chips have become denser and denser, approaching the cutting edge of silicon fabrication with a feature size (resolution) of 22 nanometers (nm). Currently, ASIC manufacturers are aiming to overtake general purpose CPU chip manufacturers, designing chips with a feature size of 16nm, because the profitability of mining is driving this industry even faster than general computing. There are no more giant leaps left in bitcoin mining, because the industry has reached the forefront of "Moore's Law". Still, the mining power of the network continues to advance at an exponential pace as the race for higher density chips is matched with a race for higher density data centers where thousands of these chips can be deployed. It's no longer about how much mining can be done with one chip but how many chips can be squeezed into a building, while still dissipating the heat and providing adequate power.
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|
|
==== The Extra Nonce Solution
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|
Since 2012 bitcoin mining has evolved to resolve a fundamental limitation in the structure of the block header. In the early days of bitcoin, a miner could find a block by iterating through the nonce until the resulting hash was below the target. As difficulty increased, miners often cycled through all 4 billion values of the nonce without finding a block. However, this was easily resolved by updating the block timestamp to account for the elapsed time. Since the timestamp is part of the header, the change would allow miners to iterate through the values of the nonce again with different results. Once mining hardware exceeded 4 GH/sec however, this approach became increasingly difficult as the nonce values were exhausted in less than a second. As ASIC mining equipment started pushing and then exceeding the TH/sec hash rate, the mining software needed more space for nonce values in order to find valid blocks. The timestamp could be stretched a bit, but moving it too far into the future would cause the block to become invalid. A new source of "change" was needed in the block header. The solution was to use the coinbase transaction as a source of extra nonce values. Since the coinbase script can store between 2 and 100 bytes of data, miners started using that space as extra nonce space, allowing them to explore a much larger range of block header values to find valid blocks. The coinbase transaction is included in the merkle tree, which means that any change in the coinbase script causes the merkle root to change. Eight bytes of extra nonce, plus the 4 bytes of "standard" nonce allow miners to explore a total 2^96^ (8 followed by 28 zeroes) possibilities *per second* without having to modify the timestamp. If, in the future, a miner could run through all these possibilities, they could then modify the timestamp. There is also more space in the coinbase script for future expansion of the extra nonce space.
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|
==== Mining Pools
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In this highly competitive environment, individual miners working alone (also known as solo miners) don't stand a chance. The likelihood of them finding a block to offset their electricity and hardware costs is so low that it represents a gamble, like playing the lottery. Even the fastest consumer ASIC mining system cannot keep up with commercial systems that stack tens of thousands of these chips in giant warehouses near hydro-electric power stations. Miners now collaborate to form mining pools, pooling their hashing power and sharing the reward among thousands of participants. By participating in a pool, miners get a smaller share of the overall reward, but typically get rewarded every day, reducing uncertainty.
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Let's look at a specific example. Assume a miner has purchased mining hardware with a combined hashing rate of 6,000 giga-hashes per second (GH/s) or 6 TH/s. In August of 2014 this equipment costs approximately $10,000 USD. The hardware also consumes 3 kilowatts (kW) of electricity when running, 72 kW-hours a day, at a cost of $7 or $8 per day on average. At current bitcoin difficulty, the miner will be able to solo-mine a block approximately once every 155 days, or every 5 months. If the miner does find a single block in that timeframe, the payout of 25 bitcoin, at approximately $600 per bitcoin will result in a single payout of $15,000 which will cover the entire cost of the hardware and the electricity consumed over the time period, leaving a net profit of approximately $3,000. However, the chance of finding a block in a 5-month period depends on the miner's luck. They might find two blocks in 5 months and make a very large profit. Or they might not find a block for 10 months and suffer a financial loss. Even worse, the difficulty of the bitcoin proof-of-work algorithm is likely to go up significantly over that period, at the current rate of growth of hashing power, meaning the miner has at most 6 months to break-even before the hardware is effectively obsolete and must be replaced by more powerful mining hardware. If this miner participates in a mining pool, instead of waiting for a once-in-5-month $15,000 windfall, they will be able to earn approximately $500 to $750 per week. The regular payouts from a mining pool will help them amortize the cost of hardware and electricity over time without taking an enormous risk. The hardware will still be obsolete in 6-9 months and the risk is still high, but the revenue is at least regular and reliable over that period.
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|
Mining pools coordinate many hundreds or thousands of miners, over specialized pool mining protocols. The individual miners configure their mining equipment to connect to a pool server, after creating an account with the pool. Their mining hardware remains connected to the pool server while mining, synchronizing their efforts with the other miners. Thus, the pool miners share the effort to mine a block and then share in the rewards.
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Successful blocks pay the reward to a pool bitcoin address, rather than individual miners. The pool server will periodically make payments to the miners' bitcoin addresses, once their share of the rewards has reached a certain threshold. Typically, the pool server charges a percentage fee of the rewards for providing the pool mining service.
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Miners participating in a pool, split the work of searching for a solution to a candidate block, earning "shares" for their mining contribution. The mining pool sets a lower difficulty target for earning a share, typically more than 1,000 times easier than the bitcoin network's difficulty. When someone in the pool successfully mines a block, the reward is earned by the pool and then shared with all miners in proportion to the number of shares they contributed to the effort.
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Pools are open to any miner, big or small, professional or amateur. A pool will therefore have some participants with a single small mining machine, others with a garage-full of high-end mining hardware. Some will be mining with a few tens of a kilowatt of electricity, others will be running a data center consuming a megawatt of power. How does a mining pool measure the individual contributions, so as to fairly distribute the rewards, without the possibility of cheating? The answer is to use bitcoin's Proof-of-Work algorithm to measure each pool miner's contribution, but set at a lower difficulty so that even the smallest pool miners win a share frequently enough to make it worthwhile to contribute to the pool. By setting a lower difficulty for earning shares, the pool measures the amount of work done by each miner. Each time a pool miner finds a block header hash that is less than the pool difficulty, they prove they have done the hashing work to find that result. More importantly, the work to find shares contributes, in a statistically measurable way, to the overall effort to find a hash lower than the bitcoin network's target. Thousands of miners trying to find low-value hashes will eventually find one low enough to satisfy the bitcoin network target.
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Let's return to the analogy of a dice game. If the dice players are throwing dice with a goal of throwing less than four (the overall network difficulty), a pool would set an easier target, counting how many times the pool players managed to throw less than eight. When a pool player throws less than eight (the pool share target), they earn shares, but they don't win the game because they don't achieve the game target (less than four). The pool players will achieve the easier pool target much more often, earning them shares very regularly, even when they don't achieve the harder target of winning the game. Every now and then, one of the pool players will throw a combined dice throw of less than four and the pool wins. Then, the earnings can be distributed to the pool players based on the shares they earned. Even though the target of eight-or-less wasn't winning, it was a fair way to measure dice throws for the players and occasionally produces a less-than-four throw.
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Similarly, a mining pool will set a pool difficulty that will ensure that an individual pool miner can find block header hashes that are less than the pool difficulty quite often, earning shares. Every now and then, one of these attempts will produce a block header hash that is less than the bitcoin network target, making it a valid block and the whole pool wins.
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===== Managed Pools
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Most mining pools are "managed", meaning that there is a company or individual running a pool server. The owner of the pool server is called the _pool operator_ and they charge pool miners a percentage fee of the earnings.
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The pool server runs specialized software and a pool-mining protocol that coordinates the activities of the pool miners. The pool server is also connected to one or more full bitcoin nodes and has direct access to a full copy of the blockchain database. This allows the pool server to validate blocks and transactions on behalf of the pool miners, relieving them of the burden of running a full node. For pool miners, this is an important consideration, as a full node requires a dedicated computer with at least 15-20 gigabytes of persistent storage (disk) and at least 2 gigabytes of memory (RAM). Furthermore, the bitcoin software running on the full node needs to be monitored, maintained and upgraded frequently. Any downtime caused by a lack of maintenance or lack of resources will impact the miner's profitability. For many miners the ability to mine without running a full node is another big benefit of joining a managed pool.
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Pool miners connect to the pool server using a mining protocol such as Stratum (STM) or GetBlockTemplate (GBT). An older standard called GetWork (GWK) is now mostly obsolete since late 2012, as it does not easily support mining at hash rates above 4 GH/s. Both the STM and GBT protocols create block _templates_ that contain a template of a candidate block header. The pool server constructs a candidate block by aggregating transactions, adding a coinbase transaction (with extra nonce space), calculating the merkle root and linking to the previous block hash. The header of the candidate block is then sent to each of the pool miners as a template. Each pool miner then mines using the block template, at a lower difficulty than the bitcoin network difficulty and sends any successful results back to the pool server to earn shares.
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===== P2Pool
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Managed pools create the possibility of cheating by the pool operator, who might direct the pool effort to double-spend transactions or invalidate blocks (see <<51pct>>). Furthermore, centralized pool servers represent a single-point-of-failure. If the pool server is down or is attacked by Denial-of-Service, the pool miners cannot mine. In 2011, to resolve these issues of centralization, a new pool mining method was proposed and implemented: P2Pool is a peer-to-peer mining pool, without a central operator.
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P2Pool works by de-centralizing the functions of the pool server, implementing a parallel blockchain-like system called a _sharechain_. A sharechain is a blockchain running at a lower difficulty than the bitcoin blockchain. The sharechain allows pool miners to collaborate in a de-centralized pool, by mining shares on the sharechain at a rate of one share block every 30 seconds. Each of the blocks on the sharechain records a proportionate share reward for the pool miners who contribute work, carrying the shares forward from the previous share block. When one of the share blocks also achieves the difficulty target of the bitcoin network it is propagated and included on the bitcoin blockchain, rewarding all the pool miners who contributed to the all the shares that preceded the winning share block. Essentially, instead of a pool server keeping track of pool miner shares and rewards, the sharechain allows all pool miners to keep track of all shares using a de-centralized consensus mechanism like bitcoin's blockchain consensus mechanism.
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P2Pool mining is more complex than pool mining, as it requires that the pool miners run a dedicated computer with enough disk space, memory and internet bandwidth to support a full bitcoin node and the p2pool node software. P2Pool miners connect their mining hardware to their local p2pool node, which simulates the functions of a pool server by sending block templates to the mining hardware. On P2Pool, individual pool miners construct their own candidate blocks, aggregating transactions much like solo-miners but then mine collaboratively on the sharechain. P2Pool is a hybrid approach that has the advantage of much more granular payouts than solo mining, but without giving too much control to a pool operator like managed pools.
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Recently, participation in P2Pool has increased significantly as mining concentration in mining pools has approached levels that create concerns of a 51% attack (see <<51pct>>). Further development of the P2Pool protocol continues with the expectation of removing the need for running a full node and therefore making de-centralized mining even easier to use.
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[[51pct]]
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[[consensus_attacks]]
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=== Consensus Attacks
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Bitcoin's consensus mechanism is, at least theoretically, vulnerable to attack by miners (or pools) that attempt to use their hashing power to dishonest or destructive ends. As we saw, the consensus mechanism depends on having a majority of the miners acting honestly out of self-interest. However, if a miner or group of miners can achieve a significant share of the mining power, they can attack the consensus mechanism so as to disrupt the security and availability of the bitcoin network.
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It is important to note that consensus attacks can only affect future consensus, or at best the most recent past (tens of blocks). Bitcoin's ledger becomes more and more immutable as time passes. Beyond a certain "depth", blocks are absolutely immutable, even under a sustained consensus attack that causes a fork. Consensus attacks also do not affect the security of the private keys and signing algorithm (ECDSA). A consensus attack cannot steal bitcoins, spend bitcoins without signatures, redirect bitcoins or otherwise change past transactions or ownership records. Consensus attacks can only affect the most recent blocks and cause denial-of-service disruptions on the creation of future blocks.
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One attack scenario against the consensus mechanism is called the "51% attack". In this scenario a group of miners, controlling a majority (51%) of the total network's hashing power, collude to attack bitcoin. With the ability to mine the majority of the blocks, the attacking miners can cause deliberate "forks" in the blockchain and double-spend transactions or execute denial-of-service attacks against specific transactions or addresses. A fork/double-spend attack is one where the attacker causes previously confirmed blocks to be invalidated by forking below them and re-converging on an alternate chain. With sufficient power, an attacker can invalidate six or more blocks in a row, causing transactions that were considered immutable (6 confirmations) to be invalidated. Note that a double-spend can only be done on the attacker's own transactions, for which the attacker can produce a valid signature. Double-spending one's own transactions is profitable if by invalidating a transaction the attacker can get a non-reversible exchange payment or product without paying for it.
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In addition to a double-spend attack, the other scenario for a consensus attack is to deny service to specific bitcoin participants (specific bitcoin addresses). An attacker with a majority of the mining power can simply ignore specific transactions. If they are included in a block mined by another miner the attacker can deliberately fork and re-mine that block, again excluding the specific transactions. This type of attack can result in a sustained denial of service against a specific address or set of addresses for as long as the attacker controls the majority of the mining power.
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Despite its name, the 51% attack scenario doesn't actually require 51% of the hashing power. In fact, such an attack can be attempted with a smaller percentage of the hashing power. The 51% threshold is simply the level at which such an attack is almost guaranteed to succeed. A consensus attack is essentially a tug-of-war for the next block and the "stronger" group is more likely to win. With less hashing power, the probability of success is reduced, as other miners control the generation of some blocks with their "honest" mining power. One way to look at it is that the more hashing power an attacker has, the longer the fork they can deliberately create, the more blocks in the recent past they can invalidate, or the more blocks in the future they can control. Security research groups have used statistical modeling to claim that various types of consensus attacks are possible with as little as 30% of the hashing power.
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The massive increase of total hashing power has arguably made bitcoin impervious to attacks by a single miner. There is no possible way for a solo miner to control even 1% of the total mining power. However, the centralization of control caused by mining pools has introduced the risk of for-profit attack by a mining pool operator. The pool operator in a managed pool controls the construction of candidate blocks and also controls which transactions are included. This gives the pool operator the power to exclude transactions or introduce double-spend transactions. If such abuse of power is done in a limited and subtle way, a pool operator could conceivably profit from a consensus attack without being noticed.
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Not all attackers will be motivated by profit, however. One potential attack scenario is where an attacker intends to disrupt the bitcoin network without the possibility of profiting from such disruption. A malicious attack aimed at crippling bitcoin would require enormous investment and covert planning, but could conceivably be launched by a well funded, most likely state-sponsored attacker. Alternatively, a well-funded attacker could attack bitcoin's consensus by simultaneously amassing mining hardware, compromising pool operators and attacking other pools with denial-of-service. All of these scenarios are theoretically possible, but increasingly impractical as the bitcoin network's overall hashing power continues to grow exponentially. Recent advancements in bitcoin, such as P2Pool mining, aim to further de-centralize mining control, making bitcoin consensus even harder to attack.
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Undoubtedly, a serious consensus attack would erode confidence in bitcoin in the short term, possibly causing a significant price decline. However, the bitcoin network and software is constantly evolving, so consensus attacks would be met with immediate counter-measures by the bitcoin community, making bitcoin hardier, stealthier and more robust.
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