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The Bitcoin network is burning a large amount of energy for mining. In this paper, we estimate the lower bound for the global mining energy cost for a period of 10 years from to , taking into account changes in energy costs, improvements in hashing technologies and hashing activity. We estimate energy cost for Bitcoin mining using two methods: Brent Crude oil prices as a global standard and regional industrial electricity prices weighted by the share of hashing activity.

Despite a billion-fold increase in hashing activity and a million-fold increase in total energy consumption, we find the cost relative to the volume of transactions has not increased nor decreased since This is consistent with the perspective that, in order to keep the Blockchain system secure from double spending attacks, the proof or work must cost a sizable fraction of the value that can be transferred through the network.

Bitcoin is a digital currency launched in by an anonymous inventor or group of inventors under the alias of Satoshi Nakamoto Nakamoto, It is the largest cryptocurrency in market capitalization with over billion dollars Chan et al.

As a decentralized currency, Bitcoin differs from government regulated fiat currencies in that there exists no central authority within the network to verify transactions and prevent frauds and attacks Sin and Wang, Instead, Bitcoin relies on a highly replicated public ledger, secured by means of a hash chain and validated through community consensus Akcora et al.

All users can announce a new transaction but such a transaction will be considered valid and included in the ledger only once it is verified by a majority of the network nodes. Transactions are written into blocks that are interlocked into a chain by hashes. Hashing is a one-way function that maps an input of arbitrary length into a string of a fixed number of digits. The hash function must guarantee that the output string is quasi- uniquely related to the given input deterministic and that small changes in the input should cause arbitrarily large changes in the output so that reconstructing the input based on the output is infeasible.

In the case of Bitcoin, the transactions in the new proposed block and the header of the most recent block is inputted into the SHA hash algorithm, making therefore a chain with unique direction. Such a chain is at the heart of the Bitcoin security because it makes it difficult to alter the content of a block once subsequent blocks are added to the chain.

In Bitcoin, this cryptographic sealing process through a hash chain is intentionally designed to be computationally intensive by accepting hashes only if the randomly generated hash number is smaller than a given target. This is called proof of work PoW and serves the purpose to determine majority consensus. Indeed, in an anonymous distributed system, participants can arbitrarily generate new identities so consensus cannot be accounted in terms of individuals.

Rather, it must be accounted in terms of some participation cost demonstrating the commitment of computational power. The network incentivizes users to participate in the block validation process by assigning newly mined Bitcoins to the first user who randomly finds a hash with a value smaller than the threshold.

Presently, after the latest Bitcoin halving, this remuneration is 6. Sometimes forks occur in the blockchain when two blocks containing different transactions are attached to the same block. Eventually other blocks are mined and attached to them, forming two branching chains after the fork. In this case, the longer chain, the one with more cumulative proof of work or hash computations, would be considered as the main chain upon which future blocks are built on.

The Bitcoin proof of work is very costly economically Thum, and environmentally Stoll et al. Technological improvements over the years have made hashing a very efficient operation, consuming at little as 0. See Table 2. This has reduced energy cost per hash by about thirty thousand times during the last 10 years. However, the miners in the Bitcoin network are presently May computing nearly 10 25 hashes per day, up over 10 orders of magnitude from the levels. We estimate in this paper that this hashing activity currently corresponds to an energy cost of around 1 million USD per day and around a billion USD over the past year.

In turn, this corresponds a per transaction costs as high as 13 USD in January This cost is not borne by either the sender nor the receiver in a transaction but rather by the miners.

While a billion a year burned in hashing is definitely a large amount of money that could be seen as a waste of resources, the Bitcoin proof of work is a necessary process for such an anonymous permission-less network to function.

It is indeed required to validate transactions and obtain community consensus to secure the system from attacks. Table 2. Mining hardware with optimal energy efficiency and their dates of release.

One question arises: is this cost fair or could it be lowered? In Aste made the argument that, at equilibrium, the cost of Bitcoin proof of work should be such to make a double spending attack too expensive to be profitably carried out. From this principle, it is relatively straightforward to estimate the fair cost of the proof of work under an ideal equilibrium assumption.

Let us consider an attacker that owns some amount of Bitcoin and wants to artificially multiply it by spending the same Bitcoin with several different users. This is known as a double spend attack. Indeed, a transaction involving a substantially larger sum than the usual will capture unwanted attention from the network.

Of course, the duplication can be repeated several times both in parallel or serially but, as we shall see shortly, this does not affect the outcomes of the present argument.

To be successful the attacker must make sure that both the duplicated transactions are validated and this requires the generation of a fork with two blocks containing the double spent transaction attached to the previous block.

If the attacker has sufficient computing power, she can generate two valid hashes to seal the two blocks giving the false impression that both transactions have been verified and validated. However, for a final settlement of the transaction, it is presently considered that one should wait six new blocks to be attached to the chain to make the transaction statistically unlikely to be reverted. The attacker should therefore use her computing power to generate six valid hashes before the double spent transaction might be considered settled.

Note that only one of the two forks the shortest must be artificially validated by the attacker since the other will be considered valid by the system and can be let to propagate by the other miners. Of course, it is quite unrealistic to assume that nobody notices the propagating fork for such a long time, but let's keep this as a working hypothesis.

The artificial propagation of the fork has a cost that is the cost of the proof of work per block times six. The attacker will make profits if this cost is inferior to the gain made from duplicated spending. In the previous unpublished note by Aste the following formula is reported:. We can re-write this formula to formally express the cost of proof of work per day, C t , as. The value of p must be considerably smaller than one because an attacker will be spotted immediately by the community if she tries to fork with a large double-spent value with operations that involve a significant portion of the entire network activity.

We must note that this formula is an upper bound for the cost of the proof of work. It greatly underestimates the costs of an attack and largely overestimates the attacker's gains. It indeed considers a system that has no other protections or security system than the proof of work. Further, it does not consider that after a successful attack, the Bitcoin value is likely to plunge making it therefore unlikely for the attacker to spend her gain at current market value.

This requires either huge investments in mining equipment not taken into account in the formula or other methods to control the mining farms, such as through a cyber or a conventional physical attack, which will also cost considerable amount of money.

Independently on the estimate of a realistic value for the parameter p , the principle that the cost of the proof of work must be a sizable fraction of the value transferred by the network to avoid double spending attacks should rest valid Aste, ; Aste et al.

Specifically, according to this principle, we expect that, for a given system, the ratio between the cost of the proof of work and the value transferred by the network should oscillate around some constant value which reflects the fair balance between the possible gains in an attack and the cost to perform it.

In this paper, we test if this is indeed the case for the Bitcoin proof of work. For this purpose we are looking across the entire period of existence of Bitcoin, estimating the mining costs and comparing them with the value transferred through the network.

This is an amazing period during which the value transferred through the Bitcoin network has increased several million times and the hashing activity has increased by 10 orders of magnitude.

Let us note that ten orders of magnitude is an immense change. To put it into perspective this is the ratio between the diameter of the sun and the diameter of a one-cent coin. These are formidable changes to a scale never observed in financial systems or in human activity in general. We show in this paper that, despite these underlying formidable changes in the Bitcoin mining and trading activities, the ratio between the estimated mining cost and the transaction volume rests oscillating within a relatively narrow band supporting therefore the argument about the fair cost of the proof of work by Aste The energy cost of mining.

The overheads for the maintenance of the mining farm, such as infrastructure costs and cooling facilities. The cost of purchasing and renewing the mining hardware. For the purpose of this study, we focus only on the first element, the energy cost of running the Bitcoin mining hardware which is likely to be the key driver and is the only cost that can be estimated with some precision.

The maintenance costs for running a Bitcoin mining farm varies widely depending on the location, design and scale of the facility and since such information are usually not disclosed to the public, it is infeasible to estimate it accurately. The sales price of mining hardware is publicly available but incorporating it into cost calculations is arduous because of the rapid rate of evolution in the industry and the information opacity regarding the market share of each hardware and the rate at which obsolete mining hardware are replaced.

Newer mining hardware may achieve faster hash rates and higher energy efficiency but the renewing costs makes it unlikely that all Bitcoin miners immediately replace all their existing mining hardware with the latest versions as they are released.

Certainly a combination of both old and new mining hardware should coexist in the Bitcoin network as long as each machine continue to generate a profit. However, the market share of each hardware and its evolution over time is an unknown.

With respect to the purpose of the present estimate of the lower bound of the mining cost, we must stress that the maintenance and the hardware costs must be anyway proportional to the energy consumption costs.

By ignoring them we are under-estimating the total mining cost by some factor but, beside this factor, the estimation of the overall behavior of the mining cost should not be significantly affected. Most prior works have priced energy usage according to global average electricity prices see for instance Vranken, ; Derks et al.

In this paper, we introduce a different approach, by converting the energy consumed during Bitcoin mining into barrels of oil equivalent and priced according to the Brent Crude spot price.

Our rationale is that the Brent Crude oil price is a publicly available daily value standardized around the world whereas electricity prices varies widely across different countries and suppliers. Note that there is a premium that electricity producers and distributors charge on the electricity price with respect to the oil cost and there can be also taxes.

These extra charges depends on countries and situations but they will add a certain percentage to our estimate of the mining cost based on oil prices. As another point of comparison, regional electricity prices were also used as a proxy for the energy cost.

The average global electricity price used for mining was calculated based on the geographic distribution of hash rate on the Bitcoin network and the local industrial electricity price.

An overwhelming proportion of Bitcoins are mined in China so the data there is further stratified based on provinces. They are shown in Table 3. The three nations also publish government statistics regarding industrial electricity prices on a regular basis China: NEA, USA: EIA, Russia: Petroelectrosbyt which allowed for the annual weighted average electricity price for Bitcoin mining, E t , to be calculated as.

Table 3. Geographic distribution of the share of hash rate on the Bitcoin network, — A disproportionately large percentage of mining activity within China was based in provinces with lower than average electricity prices so where provincial data were not available, a 0.

Regional share of hash rate and electricity prices were not available for USA or Russia so similar adjustments weren't possible. Another limitation of electricity prices is that a growing proportion of Bitcoin mining uses low-cost stranded renewables Andoni et al. Due to these other factors and the lack of historic data on electricity prices in several other countries around the world, the majority of this paper will focus on energy pricing using the Brent Crude oil index.

A comparison of ratio between the cost of mining and Bitcoin transaction volume is presented in Figure 6 to show the standardized oil prices as a measure of energy cost yield similar results to using regional electricity prices. For the purpose of estimating a lower bound to the energy costs of Bitcoin mining, we considered at any point in time that the entire network is adopting the most energy efficient machine available at that time. In situations where a mining hardware has different power setting options in which the user may choose to increase or decrease the hashing speed of the machine along with energy consumption, the most efficient power setting is used for calculation.

The lower bound of the energy costs of Bitcoin mining is estimated from total number of hashes times the energy cost of hashing by the most energy efficient Bitcoin mining hardware available on the market at any give time, divided by the conversion factor between energy and barrel of oil and multiplied by the cost of the oil.



Web Usage Mining by Neural Hybrid Prediction with Markov Chain Components

Abstract Data mining is one of the most applicable area of research in computer applications among the various types of data mining. This paper is going to focus on web mining. This is the review paper which shows deep and intense study of various techniques available for web minings. Web mining — i. Above definition of web mining is explored in this paper.

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This important annual publication is based on exclusive in-depth interviews with 37 senior executives from mining companies. The concerns are divided into three categories, Trust, Transformation and Traditional, and finds leaders working hard to deal with the immediate challenges of Covid alongside the longer term need to transform and modernise the sector. It includes detailed analysis and findings from the research and edited transcripts of the interviews with mining luminaries. Key findings Safety remains the highest immediate priority for the C-suite, while responsible sourcing tops the list of future priorities Regulatory compliance has become a higher priority as world events trigger fears of resource nationalisation.


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