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How Miners Solve a Block

Bitcoin mining requires a great deal of computational power, but what do miners calculate? They repeatedly calculate the double SHA256 hash6 of slight variations of certain information, called the block header, in their new block. When a block of transactions is created, the block header contains a summary of information about the block, including the time it was created, a hash of the transactions within the block, and other data, which we'll delve into shortly. Importantly, in the block header is a field for an arbitrary number called a nonce, which the miner chooses. In fact, it is the only part of the block that is under the full control of the miner. So how does a miner choose a value for this nonce?

A solved block (i.e., a block that will be accepted by others as part of the blockchain and the one the miner is paid for) occurs when the double SHA256 hash of the block header results in a number that is less than some predetermined threshold, known as the difficulty target. If the result is greater than the target, the block remains unsolved. When this happens, the miner must try a different nonce, which is contained in the header and hence affects the hash. Because cryptographic hash functions produce completely new outputs when the input is changed by even the tiniest amount, changing the nonce value results in a totally new hash for the entire block header. By repeatedly changing the nonce value, eventually a hash output will be found that is less than the target. Typically, a miner simply increments the nonce by 1 in this search until a successful nonce value is found. When a working nonce is found, the block is solved.

Anatomy of a Block

Let's take a closer look at a block's structure so you can see how the miners' actions fit into the big picture. At the top level, a Bitcoin block essentially has four parts:

Anatomy of a Block

Anatomy of a Block

Blocksize is a number at the top of the block that indicates the size of the entire block O. This is followed by the block header ©, which we'll discuss in detail shortly. The rest of a block stores a count of the number of transactions © followed by a list of all the transactions 0. One of these transactions is the block reward, which the miner adds to assign himself some new bitcoins. These bitcoins are created from nothing. All bitcoins in existence at one point originated as such a block reward.

Including the nonce @, the block header consists of six pieces of data:

Block header structure

At the top is a version number O. It exists to facilitate the ability to distinguish blocks in the old and new format if ever a major change in the blockchain structure occurs in the future, as Bitcoin is refined. Next, the block header holds a hash of the previous block's header ©. It is a very important field because this value links blocks together in a chain: When miners mine a block, not only are they securing the transactions in their own block, but they are also securing the transactions in all previous blocks that make up this version of the chain. By creating this block, a miner is essentially casting a vote stating, "I believe this is the true history of all Bitcoin transactions, and my block builds upon the work of other miners, as indicated by this hash of the previous miner's block."

Next, the header contains a hash of all transactions in the current block ©. When a node on the Bitcoin network receives a block from other nodes on the network, this hash allows them to verify that the transactions in the block haven't been tampered with; the hash of the transactions must exactly match the value in this field.

Subsequently, a timestamp 0 indicates when the block was created. For the most part, Bitcoin disregards real-world time. In fact, mining blocks in the blockchain can be thought of as a primitive sequential clock, and the ticking of this clock in the form of newly mined blocks is the only concept of time Bitcoin takes into account.

However, setting the block difficulty is one specific instance in which Bitcoin needs to recognize real-world time. Block difficulty © is periodically calculated using the timestamp of previous blocks and is also a field in the block header. Because Bitcoin is designed to solve new blocks roughly every 10 minutes, it needs a way to measure how far apart blocks have been spaced in the recent past, which is the reason the timestamp field exists. If Bitcoin difficulty wasn't periodically adjusted based on real-world time, its block rate would be determined by the currency's popularity. As a result, the Bitcoin network could become unstable if it became too popular or not popular enough. In both of those instances, the block rate would become unreasonable, and the Bitcoin network would no longer function.

So how is the difficulty target value decided? When Bitcoin was created, the target was set to this certain easy number:

26959535291011309493156476344723991336010898738574164086137773096960

* 2.7 x 1067 or 2224

To put this value in 2p56erspective, th77e SHA256 hash function outputs values between 0 and 22 6 (~1.16 x 10 ), and this target requires the output to be less than 2224 (about one-billionth of the maximum output). This is similar to requiring that a random number generator that generates values between 0 and 1 must output a number less than 0.000000001 to solve a block. This target value is the easiest Bitcoin has ever used. Most ordinary personal computers (in 2009) could calculate new hashes at a rate of about 1 million hashes per second, or 1 megahash/s (MH/s). Because the odds of a hash being less than this target value are 1 in a billion, a computer hashing at 1 MH/s would need about 1,000 seconds (~17 minutes) to have a good chance9 at solving a block.

If a faster computer were to start mining at 2 MH/s, the target would automatically decrease to reduce the odds of finding a block (thereby taking longer). The difficulty stored in the blockchain header is expressed as a ratio between the initial target used by Bitcoin (when it started) and the current target. Initially, the difficulty was equal to 1 (because the initial target was the current target), and it has been mostly increasing ever since. If the hash rate decreases (e.g., due to computers withdrawing from the network) so that blocks are found more slowly than ten minutes on average, the difficulty will decrease (which in Bitcoin's first five years has happened very rarely).

As you can see, target numbers are large and unwieldy. Therefore, it is more convenient, when discussing bitcoin mining, to calculate a difficulty, which is simply the ratio of the current target number to the target number on Satoshi's very first block, the genesis block:

The difficulty is not adjusted immediately in response to increases or decreases in the hash rate. Instead, the difficulty is adjusted every time the blockchain grows by 2,016 blocks, which happens approximately every two weeks (2,016 x 10 minutes = 14 days). If it takes less than two weeks to mine 2,016 blocks, the difficulty is increased, but if it takes longer than two weeks, the difficulty is decreased.

During the first five years, the mining difficulty in Bitcoin increased from 1 to over 50 billion. At this difficulty, an ordinary personal computer (tablet, laptop, etc.) would be lucky to solve one block every 3.5 million years! This difficulty corresponds to a network hash rate that is ~360,000,000,000 MH/s, or 360 petahash/s (PH/s). All of the world's conventional supercomputers combined would hash at a rate less than 1 PH/s.

The incredible rise in computational power used for Bitcoin mining derives from a combination of wider adoption and the use of increasingly specialized hardware. In the first year, most miners used the CPUs on their laptops to mine bitcoins. Then people realized they could repurpose graphics cards designed originally for demanding computer games to mine bitcoins. The graphics cards, specifically the graphics-processing units (GPUs) on them, were thousands of times faster and more energy efficient than CPUs. Not long thereafter, hardware developers discovered they could use field programmable gate arrays (FPGAs), which are specialized devices used for computer chip prototype development, to mine bitcoins even faster than GPUs. Until this point, nobody had manufactured hardware specifically to mine bitcoins. GPUs and FPGAs were off-the-shelf hardware that was just repurposed for Bitcoin mining. However, when the Bitcoin economy became extensive, it became worthwhile for computer chip developers to create application specific integrated circuits (ASICs), like the one in Figure 8-3.

An early ASIC Bitcoin-mining machine from the Avalon Corporation. The small chips arranged in a grid are each custom ASIC chips designed to perform Bitcoin hash operations.

Figure 8-3: An early ASIC Bitcoin-mining machine from the Avalon Corporation. The small chips arranged in a grid are each custom ASIC chips designed to perform Bitcoin hash operations.

These single-purpose computer chips were manufactured specifically to mine bitcoins in the fastest, most energy-efficient way possible. Bitcoin ASICs are optimized to calculate SHA256 hashes. Today, practically all Bitcoin mining is done with ASIC-based hardware. Further increases in speed and efficiency are being achieved continually by designing the chips with smaller and smaller features (from 130 nm to 65 nm to 28 nm features, and so on). Consequently, more calculations can be made per unit of area. Each new breakthrough in hardware performance leads to a network hash rate that increases by many orders of magnitude (see Figure 8-4), especially if the price of bitcoins rises at the same time (further justifying capital investment in mining hardware).

The amount of computation performed over time on the Bitcoin network (in terrahashes, or trillions of hashes per second). The left graph uses a traditional linear scale for the y-axis, in which the enormous comput¬ing power of ASIC miners in 2013 dwarfs all previous methods of mining. In the right graph, we use a logarith¬mic scale for showing the hash rate of the network, making it possible to see the progress in computing power on the network more clearly, progressing from CPU, to GPU, to FPGA, and finally ASIC mining.

Figure 8-4: The amount of computation performed over time on the Bitcoin network (in terrahashes, or trillions of hashes per second). The left graph uses a traditional linear scale for the y-axis, in which the enormous computing power of ASIC miners in 2013 dwarfs all previous methods of mining. In the right graph, we use a logarithmic scale for showing the hash rate of the network, making it possible to see the progress in computing power on the network more clearly, progressing from CPU, to GPU, to FPGA, and finally ASIC mining.

At a difficulty of 50 billion, a Bitcoin-mining device capable of 10 TH/s could find a block about once every 8 months, which is an average time, and the variance can be significant. For Bitcoin miners who want to receive a more steady income, it is best to join forces with other miners in what is known as pooled mining.

Pooled Mining

Although the network solves blocks about every 10 minutes, individual miners might only solve a block once every few months. With such an unpredictable revenue stream, it can be difficult to plan and operate a Bitcoin-mining operation. To help make the reward more regular and predictable, most miners who don't control enormous computational power (i.e., greater than 1 percent of the network hash rate)join a mining pool.

A mining pool is a collection of miners who combine computational resources and then split the block reward. From the network's perspective, a mining pool is a single mining node, but hundreds or perhaps thousands of individual miners are calculating hashes within that node. A mining pool solves blocks more often than an individual miner; therefore, the miners' income is more frequent. When the block reward is divided among the miners, it is usually allocated proportionally based on the number of hashes a miner contributed. Because it is difficult to know exactly how many hashes an individual contributed, the typical measurement of contribution is in the form of calculated shares. Although the exact details vary between mining pools, a miner earns a share when she calculates a hash output that is less than a much easier-to-reach target than the real target. As a result, it might take an individual miner years before he would find a hash less than the real target but only a few minutes to find a hash less than the pool's share target. The number of shares accumulated by a miner represents how much of the pool's hashing power that miner contributed.

Using a pool, a casual Bitcoin user can try her hand at mining and collect tiny fractions of bitcoins using a moderately powerful computing device (e.g., a cheap Bitcoin-mining ASIC that can be plugged into a USB slot). Although it may not be profitable, considering the costs of electricity, it can be fun to accumulate a few microbitcoins by contributing computational power to the network.

 
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