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# Cryptocurrency mining algorithms 4th

In regular computer science, the kind I learned at MIT, all data is represented as numbers which consist of a series of bits. Each bit is either a zero or a one — either on or off. By collecting bits we can represent any number in binary b for example is four bits and represents the number If you have x bits, you can represent up to 2 raised the power of x.

In most computers, 32 bits or 64 bits are the standard for how numbers are stored The thing that makes QCs different form regular computers is that in addition to regular bits, they are able to use qubits. Qubits are quantum bits which like a quantum particle, can have two different states. This means that while a regular bit must be a zero or a one, a qubit can be either a zero or a one.

If you have a certain number of bits, you can try out all the possible combinations by running through all the values of 0 and 1. For example, to try out all the numbers between 0 and , you need 9 bits. If you have 9 qubits, you can try out all the values from 1 to simultaneously. If you had 64 bits, you could try out the hash algorithm for all possible values of x to figure out which ones when input into function f x lead to a result of y, or in the case of bitcoin mining, less than some target value y.

The bitcoin algorithm, relies on an input shown in Figure 1 source: bitcoinmining. The header of a block consists of several components, including a nonce which is a random 32 bit number. See Table 2 for a list of the possible values.

The result of the hash is a bit integer. Figure 2: Table of Inputs for Bitcoin Hash Closer inspection will reveal that of all the bytes that are used as input, only 4 bytes, the nonce, or 32 bits are actually random. The other bytes are actually coming from a block of transactions and timestamp, etc.

The output is a bit number which has to be less than a target. A qubyte is 8 qubits. So basically, what I needed was to program my QC to use 4 qubytes, or 32 qubits, which represented all of the possible values of the random number, nonce, and append this value to a set of 76 regular bytes, and then run them through the hashing algorithm.

Then I could take the output, which is a bits, and choose one of the output values which is less than the target. Today, with my quantum computer, I had to come up with an actual circuit to accomplish this. The beginnings of languages like this are out there — QASM, QCL, but each of these have different models and results in quantum circuits, at least for the moment. Figure 3 shows the basic circuit architecture for how I programmed my quantum computer, but simplified to 6 bits. In this case the 2 qubits represent the nonce, and the 4 regular bits represent the rest of the header block.

The implementation of the actual Hash Algorithm used by bitcoin SHA is left as an exercise to the reader. The idea in the bitcoin mining that the output of the hash has to be less than M, the hashing difficulty, which is adjusted in the bitcoin network every so often. When you observe the output bits, the quantum probability wave collapses and you see only one set of possible values. While quantum computers are able to have all of the possible values of the qubits simultaneously, we are still at the point of needing to loop through all of the possible output values to find the one that we want at random.

The real problem is how do you measure all of the possible values to get the one you want? Using f2 as simple addition, if the values of x1… xn were all 0 for example, then you would observe the result as 0. By doing this shaking a certain number of times, the input values of the nonce which resulted in outputs of less than target t, are isolated.

We just take those 4 bytes, append them to the other 76 regular bytes that we put as input, and then submit the transaction to the blockchain. The square root of this is , a significant difference. A variety of issues associated with it have been raised, such as network security, cryptoasset management and sustainability impacts.

Investigating Bitcoin mining from a spatial perspective will provide new angles and empirical evidence with respect to extant literature. Here we explore the spatial distribution of Bitcoin mining through bottom-up tracking and geospatial statistics. We find that mining activity has been detected at more than geographical units across countries and regions, which is in line with the distributed design of Bitcoin network.

However, in terms of computing power, it has demonstrated a strong tendency of spatial concentration and association with energy production locations. We also discover that the spatial distribution of Bitcoin mining is dynamic, which fluctuates with diverse patterns, according to economic and regulatory changes. Introduction The validation of Bitcoin transactions is enabled by its proof-of-work PoW consensus mechanism 1.

Bitcoin miners perform scanning for hash value to compete for obtaining the right of recording the block of transactions, and the successful creator of each block is rewarded by a certain amount of bitcoins. At the very beginning, mining activity was only supported by a few participants equipped with regular computers 4. The surge of Bitcoin price and mining profitability incentivized increasing computing power to participate in the game.

Moreover, specific mining rigs were quickly designed, manufactured and upgraded 5. Mining sites were purposefully selected and developed. Huge amounts of energy and resources were put into mining industry 6 , 7 , 8. Bitcoin and its mining activity have aroused attention in a variety of fields, including but not limited to blockchain technology 2 , 3 , financial econometrics 9 , 10 , and sustainability issues 7 , 8 , 11 , 12 , 13 , Exploring the spatial distribution of Bitcoin mining will provide new angles and evidence with respect to a large portion of extant literature.

In particular, the investigation from a spatial perspective will help to verify the decentralized design of blockchain technology, to identify certain kinds of price effects on cryptocurrencies and to make accurate estimations on energy consumption and carbon emissions from mining activity. Some sustainability studies have brought valuable tracking ideas and provided interesting mapping outputs into spatial aspect of mining activity 15 , 16 , 17 , Nevertheless, the spatial analyses as by-products from these studies are still limited in terms of data granularity and analytic methods.

On the other hand, geographers and economists have a long tradition to describe geographical locations, patterns and dynamics of human production and trading activities 19 , 20 , 21 , Bitcoin mining behaves quite differently in space when compared to conventional industrial activities. However, there is barely any novel idea published with regard to this nascent activity. Therefore, in this paper we aim to fill this gap by investigating the spatial patterns, characteristics and shaping forces of mining activity, as well as to understand, from a spatial perspective, the implications to the aforementioned topics from adjacent fields.

We carried out the research by extracting the hash rate data from million-level mining records and then desensitizing, geocoding and aggregating the data by hash rate, month and location with unique longitude and latitude coordinates. We then explored the statistical analysis of spatial measures over the processed data sets. We disclosed four kinds of spatial phenomena of mining activity: diffusion, concentration, association and fluctuation.

Furthermore, we put the results in the context of the drivers and stages of Bitcoin mining to better understand the causes for such spatial formations. Basics of mining activity Prior to diving into spatial analysis, we explain some basics of mining activity up front. Although there are a number of studies on the economics of Bitcoin mining 24 , 25 , 26 , we simplify the economic concepts of mining to better understand its relation with spatial choices as follows.

In Eq. FCij is the fixed cost for period i at location j, which consists of the amortization cost of hardware and initial settlement. VCAij is the variable cost Type A for period i at location j, which changes along with hash rate, mainly including the electricity cost. VCBij is the variable cost Type B for period i at location j, which also varies, but not strictly with hash rate, e. Three key takeaways are worth noting here: i any economic decision made by miners is based on the dynamics at a specific period and location but not on the static assumptions regardless of spatiotemporal factors; ii revenue factors are almost the same worldwide, while cost factors are highly localized.

This means that miners obtain the same economic incentive regardless of where they are located. However, the cost breakdown of mining activity differs from location to location; iii it is difficult to achieve a real break-even point because of the high volatility of the Bitcoin price and the constant change in mining competition.

Mining hardware has quickly upgraded from central processing units CPUs , graphic processing units GPUs and field programmable gate arrays FPGAs to application-specific integrated circuits ASICs , with an exponential increase in computational performance and energy efficiency 5. This has apparently influenced the aforementioned economic equations on both the revenue and cost sides. Meanwhile, a set of modern technologies including communication, engineering, logistics, etc. Regulatory attitudes towards Bitcoin mining vary significantly jurisdiction by jurisdiction Some regulators take it favourable as data centre, cloud computing or fintech, while others treat it as a traditional energy-intensive industry or speculative bubble.

Even within the same country, different sub-regions may hold totally different views. For example, mining activity was temporally banned in Plattsburgh, New York 28 , while it became more favourable in Austin, Texas, due to cheap electricity and a relaxed regulatory environment The lack of a clear global-level regulatory framework on how to define and regulate mining activity leaves room for Bitcoin miners to maneuver around the world. Theoretically, mining activity is therefore free to move wherever it wants to exist.

This is different from most industrial activities today, which are tightly constrained in space by two or more factors e. In addition, Bitcoin mining, to some extent, can be viewed as a prototype of the autonomous economy 30 Supplementary Note 2. That is to say, the algorithm, the economic formula and the built-in technology determine the suitable locations for mining and drive human activity to move accordingly.

Spatial diffusion and concentration It is natural to think that mining activity should be diffused all over the world due to its technical enablers and economic incentives. However, it is still astonishing to see how widely mining activity is distributed. Except for well-known locations e. Owing to the arm race of computing efficiency, nonspecific machines were squeezed out, such as desktops, laptops, consoles and smartphones.

Otherwise, it will be overwhelming in terms of spatial presence if all the spare capacities of those devices are put into mining activity. Figure 1 Global presence of Bitcoin mining activity. Details of each location are provided in Supplementary Table S2.

The results are based on the monthly data from June to May The map is created by Geoda 1. Full size image Figure 2 Share of computing power in terms of hash rate by grid. The share of computing power in each grid is represented as a percentage of total hash rates. Full size image Although a small portion of miners are hobbyists or believers, the majority of miners nowadays are mining for economic purposes. Undoubtedly, they should tend to concentrate in locations with a competitive advantage for mining.

Our results demonstrate this tendency by aggregating and counting all hash rates of individual locations within each grid Fig. In fact, miners not only concentrate in a few grids but also cluster with each other in adjacent grids. In other words, mining activity demonstrated a strong tendency of concentration, in terms of computing power. Our data extended from June to May In addition, mining activity is virtually concentrated in the format of mining pools.

An increasing number of miners are now joining pools to optimize the scanning of hash values and share returns based on their computing power contribution 3 , In this analysis, we focus on the spatial phenomena in the physical world, so we will not pursue that in detail here. Figure 3 Hot and cold spots of Bitcoin mining activity with the corresponding significance map. The maps are created by Geoda 1. Spatial association As illustrated in Eqs. In this way, most miners should be inclined to locations that can provide cheap and constant sources of power.

The results indicate a high significance of the spatial association between hash rate and all three energy variables Fig. The scatter plot is depicted with the spatially lagged energy capacity on the y-axis and the original hash rate on the x-axis. The reference distribution demonstrates the result by randomly permuting the observed values over the locations, which is depicted as a distribution curve in the left. The results associated with this map are shown in Supplementary Table S4.

It is worth noting that it is an adaptive process that mining activity demonstrates a strong spatial association with renewable energy. Renewable energy is not always the cheapest power source and sometimes might be expensive when transmission costs are also included. However, most types of renewable energy e.

Renewable energy providers are willing to offer miners with heavy discounts during peak seasons Miners did not realize this at the early stage, while they learned and reacted through continuous testing and iteration. This will be further addressed in the next section. Spatial fluctuation When we drilled down to monthly data, we found that mining activity fluctuated in space based on the rolling twelve-month hash rate from June to May We further categorized twelve clusters into four groups with reference to the real operational environment: ascending, descending, relatively stable and seasonal fluctuation Fig.

Figure 6 Classification of the grids with differentiated fluctuation patterns. The twelve-month fluctuation indices of medoids are plotted in the radar chart as representatives of each cluster. Details of the results are provided in Supplementary Tables S5 , S6 and the repository. Full size image Every fluctuating grid fluctuated in its own way, which might follow a combination of multiple patterns and can only be explicitly explained case by case.

However, four primary patterns are studied and summarized here. Large mining farms choose to migrate to locations with more cost advantages or update their mining machines, while most individual or small miners are reluctant to take immediate actions and wait for the suitable time to reopen their mining rigs. All these factors lead to a change in computing power in grids but to different degrees. It also happens when these miners move back to their original locations during the off-season.

Favourable measures e. Miners in particular large ones continue to learn and search for better mining locations. The process is iterative for optimal solutions, and the radius of search is expanded to adjacent grids and then gradually to the global scale.

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First of all, the cryptocurrency network collects all the transactions done in a period. And it creates a block out of these transactions. For Bitcoin, this block generation window is 10 minutes. But for newer altcoins like Monero , this is 1 minute. For Verge cryptocurrency, it is only 30 seconds! Bitcoin also can handle blocks up to 1MB in size. But newer cryptocurrencies support block size as high as 8MB. When the network creates a new block, it announces the block to all the mining nodes.

Now the real competition begins! Using the raw data from the block transaction details as well as the data from the previous block the miners generate hashes. By using the data from the previous block the new block can be linked to it to continue the blockchain. These hashes are generated by using a cryptographic algorithm. The miners also use another piece of data when creating the hashes.

You see the cryptocurrency network has its own requirements regarding how the hash looks. These requirements also change after generation of each new block. The miners can neither manipulate the transaction details nor the data from the previous block. The miner who generates the matching hash before anyone else is awarded the reward. The network then adds the newly generated block to the blockchain. And this is how the mining process works under the hood. SHA is a widely used and extremely popular hashing algorithm.

Other than cryptocurrencies SHA is also used in various other technologies. And the SHA standard generates a bit hash. This not only encrypts the data but it also standardizes the size. Actually, this is a case for all of the hashing algorithms. Popularly known as bitcoin mining algorithm. Because only a handful of people used Bitcoin and even lesser mined it. So back in those days, anyone with a computer could use their CPU to mine. But then some people realized the hash rate is even faster when mining with GPU.

After GPU mining became very competitive experts probed for more efficient hardware. And this is how FPGA miners came into existence. But they were not very efficient either. So they were soon switched by ASIC s. They are built for one task only; in this case, only mining a particular cryptocurrency. You can also try buying cloud mining contracts from trusted companies like Hashflare , Genesis Mining, Hashnet etc.

Because the initial investment is overwhelming. Plus the ASICs generate a lot of heat, so you will be needing proper cooling solutions. They also consume loads of electricity. So only get in this field if you can afford all these. Because it will be a lot less hassle.

It is much more memory intensive than the SHA So it dramatically reduces the protection against custom hardware attacks. But that will not be profitable at all. The most profitable way to mine is by using an ASIC rig. The most popular ones are from Antminer, A2 Mega, Gridseed etc. The algorithm uses two different hashing algorithm — Dagger by Vitalik Buterin and Hashimoto hash, shift, and modulo by Thaddeus Dryja.

The Dagger algorithm is a memory hard hashing algorithm like Scrypt. But it performs better than Scrypt when the hardness is increased to a very high level. But it has some vulnerabilities too. That is why it is used in conjunction with Hashimoto.

In short, we can call it Eth mining. The first block is hardcoded into the blockchain network to form the Genesis Block. New blocks reference the previous block and contain a copy of the ledger. A miner must possess a rig with sufficient computational energy and hash rate to win the race to update the ledger. This will enable them to propose valid blocks according to the rules guiding the blockchain.

The validation of transactions is carried out by devices running mining software that determine if the new block should be added to the block. In the proof of work algorithm, miners combine their computational resources with public-key cryptography to reach a consensus and validate transactions. The process involved in creating a new block is called hashing, which involves guessing a random set of characters and numbers a hash and combining it with the available data in the block.

It is then passed through a hash function computer for Bitcoin, it is SHA to attain a result that agrees with the conditions set by the algorithm. The hash that wins is published on the network for other miners to confirm its accuracy. It is added to the blockchain upon confirmation, and the miner is rewarded with the block reward. The block reward is in the form of new cryptocurrency, which is given to the miner by the blockchain for every valid and accepted block.

A breach in consensus leads to the creation of a fork, as has been seen with Bitcoin Bitcoin Cash and Bitcoin Gold. This consensus has helped create a trustless system. The proof of work algorithm also helps protect the blockchain from cyber-attacks. Proof of Stake The proof of stake algorithm is the second most popular consensus algorithm, having been launched in as an alternative to its proof of work counterpart.

Unlike the proof of work algorithm, it has no need for miners, and instead uses validators. Participants are required to have a sizable stake so that they can partake in validating transactions and creating new blocks. However, they can only create blocks that are proportional to their stake in the blockchain. Most blockchains today, including Cardano, Polkadot, Tezos, and Atmos, use different variants of this algorithm. It requires no computational power and, as such, is entirely virtual.

Validators are chosen based on their stakes. The proof of stake algorithm randomly selects validators with a specific amount of staked cryptocurrency to validate transactions. This serves as cryptographic proof of their ownership and vested interest in the project. These selected nodes are responsible for verifying a valid transaction, signing it, and proposing the block for validation. Unlike proof of work blockchains, new blocks are minted or forged.

This algorithm uses the time of stake and randomization to make node selection unpredictable. As in the proof of work algorithm, proof of stake validators are rewarded for their contribution to the blockchain , and they get block rewards for proposing valid blocks. There are staking services that allow users to stake their coins with exchange platforms for regular payouts.