((("timestamping blocks")))Jing's 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 1, 1970, midnight UTC/GMT. The time +1388185914+ is equal to Friday, 27 Dec 2013, 23:11:54 UTC/GMT.
((("difficulty target","constructing block headers and")))Jing's 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 1-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>>.
((("proof-of-work target","constructing block headers and")))Jing's node then fills in the target, which defines the required proof-of-work to make this a valid block. The target is stored in the block as a "Target Bits" metric, which is a mantissa-exponent encoding of the target. The encoding has a 1-byte exponent, followed by a 3-byte mantissa (coefficient). In block 277,316, for example, the target bits value is +0x1903a30c+. The first part +0x19+ is a hexadecimal exponent, while the next part, +0x03a30c+, is the coefficient. The concept of a target is explained in <<target>> and the "target bits" representation is explained in <<target_bits>>.
((("nonce,","initializing in block header")))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.
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 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
@ -488,11 +488,11 @@ Each phrase produces a completely different hash result. They seem completely ra
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 SHA256 fingerprint of the phrase.
((("difficulty target","defined")))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 difficult! <<sha256_example_generator_output>> shows 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.
((("proof-of-work target","defined")))To make a challenge out of this algorithm, let's set target: find a phrase that produces a hexadecimal hash that starts with a zero. Fortunately, this isn't difficult! <<sha256_example_generator_output>> shows 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 exceed the target 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.
From the perspective of an observer who knows that the target of the dice game is 2, if someone has succeeded in casting a winning throw it can be assumed that they attempted, on average, 36 throws. In other words, one can estimate the amount of work it takes to succeed from the difficulty imposed by the target. When the algorithm is a based on a deterministic function such as SHA256, the input itself constitutes _proof_ that a certain amount of _work_ was done to produce a result below the difficulty target. Hence, _Proof of Work_.
From the perspective of an observer who knows that the target of the dice game is 2, if someone has succeeded in casting a winning throw it can be assumed that they attempted, on average, 36 throws. In other words, one can estimate the amount of work it takes to succeed from the difficulty imposed by the target. When the algorithm is a based on a deterministic function such as SHA256, the input itself constitutes _proof_ that a certain amount of _work_ was done to produce a result below the target. Hence, _Proof of Work_.
[TIP]
====
@ -501,6 +501,12 @@ Even though each attempt produces a random outcome, the probability of any possi
In <<sha256_example_generator_output>>, 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, because 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.
[TIP]
====
The proof-of-work must produce a hash that is *less than* the target. A higher target means it is less difficult to find a hash that is below the target. A lower target means it is more difficult to find a hash below the target. The target and difficulty are inversely related.
====
Bitcoin's proof-of-work is very similar to the challenge shown in <<sha256_example_generator_output>>. The miner constructs a candidate block filled with transactions. Next, the miner calculates the hash of this block's header and sees 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 in <<pow_example1>>.((("proof of work")))
@ -582,18 +588,12 @@ Hashing Power: 127141 hashes per second
As you can see, increasing the difficulty by 1 bit causes a doubling 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 <<pow_example_outputs>>, 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 120,000 hashes per second, it still requires 10 minutes on a laptop to find this solution.
At the time of writing, the network is attempting to find a block whose header hash is less than +0000000000000000029AB9000000000000000000000000000000000000000000+. As you can see, there are a lot of zeros at the beginning of that target, meaning that the acceptable range of hashes is much smaller, hence it's more difficult to find a valid hash. It will take on average more than 1.8 septa-hashes (thousand billion billion hashes) per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 3 exa-hashes per second (EH/sec) of processing power to bear, which will be able to find a block in about 10 minutes on average.(((range="endofrange", startref="ix_ch10-asciidoc16")))(((range="endofrange", startref="ix_ch10-asciidoc15")))
////
Revise estimates below
////
At the time of writing, the network is attempting to find a block whose header hash is less than +000000000000004c296e6376db3a241271f43fd3f5de7ba18986e517a243baa7+. As you can see, there are a lot of zeros at the beginning of that hash, meaning that the acceptable range of hashes is much smaller, hence it's 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 petahashes per second (PH/sec) of processing power to bear, which will be able to find a block in about 10 minutes on average.(((range="endofrange", startref="ix_ch10-asciidoc16")))(((range="endofrange", startref="ix_ch10-asciidoc15")))
[[difficulty_bits]]
==== Difficulty Representation
[[target_bits]]
==== Target Representation
((("difficulty target")))((("mining","difficulty bits")))((("mining","difficulty targets")))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+.
((("proof-of-work target")))((("mining","target bits")))((("mining","target")))In <<block277316>>, we saw that the block contains the target, in a notation called "target bits" or just "bits," which in block 277,316 has the value of +0x1903a30c+. This notation expresses the proof-of-work 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:
@ -627,25 +627,25 @@ switching back to hexadecimal:
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 must have more than 60 leading bits set to zero. With this level of difficulty, a single miner processing 1 trillion hashes per second (1 terahash 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]]
==== Difficulty Target and Retargeting
[[target]]
==== Retargeting to Adjust Difficulty
((("difficulty target","retargeting", id="ix_ch10-asciidoc17", range="startofrange")))As we saw, 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?
((("target","retargeting", id="ix_ch10-asciidoc17", range="startofrange")))As we saw, 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?
((("difficulty retargeting")))((("difficulty target","block generation rate and")))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 is periodically adjusted to meet a 10-minute block target. In simple terms, the difficulty target is set so that the current mining power will result in a 10-minute block interval.
((("retargeting")))((("target","block generation rate and")))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, the proof-of-work target is a dynamic parameter that is periodically adjusted to meet a 10-minute block interval goal. In simple terms, the target is set so that the current mining power will result in a 10-minute block interval.
How, then, is such an adjustment made in a completely decentralized network? Difficulty re-targeting occurs automatically and on every node independently. Every 2,016 blocks, all nodes retarget the proof-of-work difficulty. The equation for retargeting difficulty measures the time it took to find the last 2,016 blocks and compares that to the expected time of 20,160 minutes (2,016 blocks times the desired 10-minute block interval). The ratio between the actual timespan and desired timespan is calculated and a proportionate 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.
How, then, is such an adjustment made in a completely decentralized network? Retargeting occurs automatically and on every node independently. Every 2,016 blocks, all nodes retarget the proof-of-work. The equation for retargeting measures the time it took to find the last 2,016 blocks and compares that to the expected time of 20,160 minutes (2,016 blocks times the desired 10-minute block interval). The ratio between the actual timespan and desired timespan is calculated and a proportionate adjustment (up or down) is made to the target. In simple terms: If the network is finding blocks faster than every 10 minutes, the difficulty increases (target decreases). If block discovery is slower than expected, the difficulty decreases (target increases).
The equation can be summarized as:
----
New Difficulty = Old Difficulty * (Actual Time of Last 2016 Blocks / 20160 minutes)
New Target = Old Target * (Actual Time of Last 2016 Blocks / 20160 minutes)
----
<<retarget_difficulty_code>> shows the code used in the Bitcoin Core client.
<<retarget_code>> shows the code used in the Bitcoin Core client.
[[retarget_difficulty_code]]
.Retargeting the proof-of-work difficulty — CalculateNextWorkRequired() in pow.cpp
[[retarget_code]]
.Retargeting the proof-of-work — CalculateNextWorkRequired() in pow.cpp
====
[source,cpp]
----
@ -675,22 +675,22 @@ New Difficulty = Old Difficulty * (Actual Time of Last 2016 Blocks / 20160 minut
[NOTE]
====
While the difficulty calibration happens every 2,016 blocks, because of an off-by-one error in the original Bitcoin Core client it is based on the total time of the previous 2,015 blocks (not 2,016 as it should be), resulting in a retargeting bias towards higher difficulty by 0.05%.
While the target calibration happens every 2,016 blocks, because of an off-by-one error in the original Bitcoin Core client it is based on the total time of the previous 2,015 blocks (not 2,016 as it should be), resulting in a retargeting bias towards higher difficulty by 0.05%.
====
The parameters Interval (2,016 blocks) and TargetTimespan (two weeks as 1,209,600 seconds) are defined in _chainparams.cpp_.
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 because the imbalance will persist through the next 2,016 blocks. Therefore, large discrepancies between hashing power and difficulty might take several 2,016 block cycles to balance out.
To avoid extreme volatility in the difficulty, the retargeting adjustment must be less than a factor of four (4) per cycle. If the required target adjustment is greater than a factor of four, it will be adjusted by a factor of 4 and not more. Any further adjustment will be accomplished in the next retargeting period because the imbalance will persist through the next 2,016 blocks. Therefore, large discrepancies between hashing power and difficulty might take several 2,016 block cycles to balance out.
[TIP]
====
The difficulty of mining a bitcoin block is approximately '10 minutes of processing' for the entire network, based on the time it took to mine the previous 2,016 blocks, adjusted every 2,016 blocks.
The difficulty of mining a bitcoin block is approximately '10 minutes of processing' for the entire network, based on the time it took to mine the previous 2,016 blocks, adjusted every 2,016 blocks. This is achieved by lowering or raising the target.
====
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.
Note that the target 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.
((("difficulty target","electricity cost and")))((("electricity cost and target difficulty")))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 of electricity in bitcoin, because that determines the profitability of mining and therefore the incentives to enter or exit the mining market.(((range="endofrange", startref="ix_ch10-asciidoc17")))(((range="endofrange", startref="ix_ch10-asciidoc14")))(((range="endofrange", startref="ix_ch10-asciidoc13")))
((("proof-of-work target","electricity cost and")))((("electricity cost and difficulty")))The difficulty of mining 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 of electricity in bitcoin, because that determines the profitability of mining and therefore the incentives to enter or exit the mining market.(((range="endofrange", startref="ix_ch10-asciidoc17")))(((range="endofrange", startref="ix_ch10-asciidoc14")))(((range="endofrange", startref="ix_ch10-asciidoc13")))
=== Successfully Mining the Block
@ -719,7 +719,7 @@ In the next section, we'll look at the process each node uses to validate a bloc
When a node receives a new block, it will validate the block by checking it against a long list of criteria that must all be met; otherwise, the block is rejected. These criteria can be seen in the Bitcoin Core client in the functions((("CheckBlock function (Bitcoin Core client)")))((("CheckBlockHeader function (Bitcoin Core client)"))) +CheckBlock+ and +CheckBlockHeader+ and include:
* The block data structure is syntactically valid
* The block header hash is less than the target difficulty (enforces the proof of work)
* The block header hash is less than the target (enforces the proof of work)
* The block timestamp is less than two hours in the future (allowing for time errors)
* The block size is within acceptable limits
* The first transaction (and only the first) is a coinbase coinbase transaction
@ -733,22 +733,22 @@ The independent validation of each new block by every node on the network ensure
((("nodes","sets of blocks maintained by")))Nodes maintain three sets of blocks: those connected to the main blockchain, those that form branches off the main blockchain((("secondary chains"))) (secondary chains), and finally, blocks that do not have a known parent in the known chains((("orphan blocks"))) (orphans). Invalid blocks are rejected as soon as any one of the validation criteria fails and are therefore not included in any chain.
((("blockchains","main")))((("main blockchain")))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. ((("sibling chains (to main chain)")))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.
((("blockchains","main")))((("main blockchain")))The "main chain" at any time is whichever chain of blocks has the most cumulative proof-of-work 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. ((("sibling chains (to main chain)")))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 work. 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.
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 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.
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.
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 work of the secondary chain to the main chain. If the secondary chain has more cumulative work 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.
If a valid block is received and no parent is found in the existing chains, 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).
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.
By selecting the greatest-cumulative-work chain, all nodes eventually achieve network-wide consensus. Temporary discrepancies between chains are resolved eventually as more 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.
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.
In the next section we will look at how discrepancies between competing chains (forks) are resolved by the independent selection of the greatest-cumulative-work chain.
[[forks]]
==== Blockchain Forks
((("blockchains","forks", id="ix_ch10-asciidoc22", range="startofrange")))Because the blockchain is a decentralized data structure, different copies of it are not always consistent. Blocks might 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 reconvergence as more blocks are added to one of the forks.
((("blockchains","forks", id="ix_ch10-asciidoc22", range="startofrange")))Because the blockchain is a decentralized data structure, different copies of it are not always consistent. Blocks might 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 work chain. By summing the work recorded in each block in a chain, a node can calculate the total amount of work that has been expended to create that chain. As long as all nodes select the greatest-cumulative-work 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 reconvergence as more blocks are added to one of the forks.
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 might 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 on their physical location. For illustration purposes, different blocks are shown as different colors, spreading across the network and coloring the connections they traverse.
@ -774,7 +774,7 @@ As the two blocks propagate, some nodes receive block "red" first and some recei
.Visualization of a blockchain fork event: two blocks propagate, splitting the network
image::images/msbt_0804.png["globalfork3"]
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 proof of work for these candidate blocks. The miners that accepted "green" instead will start building on top of "green" and extending that chain.
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-work 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 proof of work for these candidate blocks. The miners that accepted "green" instead will start building on top of "green" and extending that chain.
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 as shown in <<fork4>>.
@ -782,7 +782,7 @@ Forks are almost always resolved within one block. As part of the network's hash
.Visualization of a blockchain fork event: a new block extends one fork
image::images/msbt_0805.png["globalfork4"]
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, as shown in <<fork5>>. This is a chain reconvergence, because 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, because 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.
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 work) 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, as shown in <<fork5>>. This is a chain reconvergence, because 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, because 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.
[[fork5]]
.Visualization of a blockchain fork event: the network reconverges on a new longest chain
@ -815,7 +815,7 @@ In the chart in <<network_hashing_power>>, we see the bitcoin network's hashing
.Total hashing power, gigahashes per second, over two years
image::images/msbt_0807.png["NetworkHashingRate"]
((("difficulty target","hashing power and")))As the amount of hashing power applied to mining bitcoin has exploded, the difficulty has risen to match it. The difficulty metric in the chart shown in <<bitcoin_difficulty>> is measured as a ratio of current difficulty over minimum difficulty (the difficulty of the first block).
((("proof-of-work target","hashing power and")))As the amount of hashing power applied to mining bitcoin has exploded, the difficulty has risen to match it. The difficulty metric in the chart shown in <<bitcoin_difficulty>> is measured as a ratio of current difficulty over minimum difficulty (the difficulty of the first block).
[[bitcoin_difficulty]]
.Bitcoin's mining difficulty metric, over two years
@ -826,7 +826,7 @@ In the last two years, the ASIC mining chips have become increasingly denser, ap
[[extra_nonce]]
==== The Extra Nonce Solution
((("block headers","computing power and")))((("difficulty target","computing power and")))((("difficulty target","extra nonce solution and")))((("nonce","extra")))((("extra nonce solution to increasing difficulty targets")))((("hashing race","extra nonce solutions")))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. Because 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 because 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. Because 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 zeros) possibilities _per second_ without having to modify the timestamp. If, in the future, miners 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.
((("block headers","computing power and")))((("proof-of-work target","computing power and")))((("proof-of-work target","extra nonce solution and")))((("nonce","extra")))((("extra nonce solution to increasing hashing power")))((("hashing race","extra nonce solutions")))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. Because 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 because 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. Because 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 zeros) possibilities _per second_ without having to modify the timestamp. If, in the future, miners 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.
[[mining_pools]]
==== Mining Pools
@ -843,27 +843,27 @@ Mining pools coordinate many hundreds or thousands of miners, over specialized p
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.
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.
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 higher target (lower difficulty) for earning a share, typically more than 1,000 times easier than the bitcoin network's target. 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.
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, and 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, she proves she has 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.
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, and 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 target, she proves she has 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.
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 pool players throw 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 it occasionally produces a less-than-four throw.
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.(((range="endofrange", startref="ix_ch10-asciidoc27")))(((range="endofrange", startref="ix_ch10-asciidoc26")))
Similarly, a mining pool will set a (higher and easier) pool target that will ensure that an individual pool miner can find block header hashes that are less than the pool target 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.(((range="endofrange", startref="ix_ch10-asciidoc27")))(((range="endofrange", startref="ix_ch10-asciidoc26")))
===== Managed pools
((("managed pools")))((("mining pools","managed pools")))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 of mining pools"))) _pool operator_, and he charges pool miners a percentage fee of the earnings.
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, because a full node requires a dedicated computer with at least 15 to 20 GB of persistent storage (disk) and at least 2 GB 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 hurt 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.
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, because a full node requires a dedicated computer with at least 100 to 150 GB of persistent storage (disk) and at least 2 to 4 GB 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 hurt 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.
Pool miners connect to the pool server using a mining protocol such as((("Stratum (STM) mining protocol"))) Stratum (STM) or((("GetBlockTemplate (GBT) mining protocol"))) GetBlockTemplate (GBT). An older standard called((("GetWork (GWK) mining protocol"))) GetWork (GWK) has been mostly obsolete since late 2012, because it does not easily support mining at hash rates above 4 GH/s. Both the STM and GBT protocols create((("block templates"))) 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.
Pool miners connect to the pool server using a mining protocol such as((("Stratum (STM) mining protocol"))) Stratum (STM) or((("GetBlockTemplate (GBT) mining protocol"))) GetBlockTemplate (GBT). An older standard called((("GetWork (GWK) mining protocol"))) GetWork (GWK) has been mostly obsolete since late 2012, because it does not easily support mining at hash rates above 4 GH/s. Both the STM and GBT protocols create((("block templates"))) 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 higher (easier) target than the bitcoin network target, and sends any successful results back to the pool server to earn shares.
===== Peer-to-Peer Mining Pool (P2Pool)
((("mining pools","P2Pool")))((("P2Pool")))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 <<consensus_attacks>>). Furthermore, centralized pool servers represent a single-point-of-failure. If the pool server is down or is slowed by a denial-of-service attack, 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.
P2Pool works by decentralizing the functions of the pool server, implementing a parallel blockchain-like system called a((("share chains"))) _share chain_. A share chain is a blockchain running at a lower difficulty than the bitcoin blockchain. The share chain allows pool miners to collaborate in a decentralized pool, by mining shares on the share chain at a rate of one share block every 30 seconds. Each of the blocks on the share chain 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 all the shares that preceded the winning share block. Essentially, instead of a pool server keeping track of pool miner shares and rewards, the share chain allows all pool miners to keep track of all shares using a decentralized consensus mechanism like bitcoin's blockchain consensus mechanism.
P2Pool works by decentralizing the functions of the pool server, implementing a parallel blockchain-like system called a((("share chains"))) _share chain_. A share chain is a blockchain running at a lower difficulty than the bitcoin blockchain. The share chain allows pool miners to collaborate in a decentralized pool, by mining shares on the share chain at a rate of one share block every 30 seconds. Each of the blocks on the share chain 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 bitcoin network target, it is propagated and included on the bitcoin blockchain, rewarding all the pool miners who contributed to all the shares that preceded the winning share block. Essentially, instead of a pool server keeping track of pool miner shares and rewards, the share chain allows all pool miners to keep track of all shares using a decentralized consensus mechanism like bitcoin's blockchain consensus mechanism.
P2Pool mining is more complex than pool mining because 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 share chain. 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.
@ -947,9 +947,9 @@ Once a miner using the new rules mines a block, the mining power and chain will
As miners diverge into mining two different chains, the hashing power is split between the chains. The mining power can be split in any proportion between the two chains. The new rules may only be followed by a minority, or by the vast majority of the mining power.
Let's assume for example an 80%-20% split, with the majority of the mining power using the new consensus rules. Let's also assume that the fork occurs immediately after a difficulty retargetting period.
Let's assume for example an 80%-20% split, with the majority of the mining power using the new consensus rules. Let's also assume that the fork occurs immediately after a retargetting period.
The two chains would each inherit the adjusted difficulty from the retargetting period. The new consensus rules would have 80% of the previously available mining power committed to them. From the perspective of this chain, the mining power has suddenly declined by 20% vis-a-vis the previous period. Blocks will be found on average every 12 minutes, representing the 20% decline in mining power available to extend this chain. This rate of block issuance will continue (barring any changes in hashing power) until 2016 blocks are mined, which will take approximately 24,192 minutes (at 12 minutes per block), or 16.8 days. After 16.8 days, a difficulty recalculation will occur and the difficulty will adjust (reduced by 20%) to produce 10 minute blocks again, based on the reduced amount of hashing power in this chain.
The two chains would each inherit the difficulty from the retargetting period. The new consensus rules would have 80% of the previously available mining power committed to them. From the perspective of this chain, the mining power has suddenly declined by 20% vis-a-vis the previous period. Blocks will be found on average every 12 minutes, representing the 20% decline in mining power available to extend this chain. This rate of block issuance will continue (barring any changes in hashing power) until 2016 blocks are mined, which will take approximately 24,192 minutes (at 12 minutes per block), or 16.8 days. After 16.8 days, a retarget will occur and the difficulty will adjust (reduced by 20%) to produce 10 minute blocks again, based on the reduced amount of hashing power in this chain.
The minority chain, mining under the old rules with only 20% of the hashing power will face a much more difficult task. On this chain, blocks will now be mined every 50 minutes on average. The difficulty will not be adjusted for 2016 blocks, which will take 100,800 minutes, or approximately 10 weeks to mine. Assuming a fixed capacity per block, this will also result in a reduction of transaction capacity by a factor of 5, as there are fewer blocks per hour available to record transactions.
@ -1071,7 +1071,7 @@ Proposals start in the DEFINED state, once their parameters are known (defined)
BIP-9 was first implemented for the activation of CHECKSEQUENCEVERIFY and associated BIPs (68, 112, 113). The proposal named "csv" was activated successfully in July of 2016.
BIP-9 (Version bits with timeout and delay):: https://github.com/bitcoin/bips/blob/master/bip-0009.mediawiki[https://github.com/bitcoin/bips/blob/master/bip-0009.mediawiki]
Andreas M. Antonopoulos
7 years ago