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.
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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. Specifically, the lower bound for daily mining cost, C t , is:. H t is the daily number of hashing operations in Th on day t ;.
Table 2 reports a list of the Bitcoin mining hardware which consumed the least energy per hash operations at the time of their release to the market. In a previous work a power-law model was proposed by Kristoufek However, the exponential model is more consistent with what is commonly expected for the rate of technology growth, according to the Moore's Law Moore, Figure 1. Figure 2 displays the total number of hashing operations per day. We note that the number of daily hashes have increased from 10 15 to 10 25 in the period between September to May when this paper was written.
Daily hashes have been growing at exponential rates linear trends in semi-log scale , which is in agreement with previous observations O'Dwyer and Malone, However, we can see from the figure that there are four, very distinct, periods with different grow rates.
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Specifically: i mid to mid ; ii mid to early ; iii early to early ; iv early to early The estimated best-fit doubling times in these periods are respectively: 1 33 days; ii days; iii 38 days; iv days. Figure 2. Daily hashes computed by the Bitcoin network. The lines are best-fits with exponential growth laws in the corresponding sub-periods. Doubling times are respectively i 33 days, during mid to mid ; ii days, during mid to early ; iii 38 days during early to early ; iv days, during early to early Figure 3 shows the variations of the energy price per gigajoule in the period — computed from the Brent Crude spot prices.
One can notice that the cost of one gigajoule of energy has two distinct levels—around 20 USD from to mid and around 10 USD from late to early Oil prices has since collapsed under the coronavirus pandemic, dropping to below 3 USD per gigajoule of energy. However, while large, the rate of change in energy price is several orders of magnitude smaller than the rate of change in the number of hashes. Figure 3. The lower bound of the total energy costs of Bitcoin mining is estimated as the minimum energy cost of each hash multiplied by the total number of hashes computed over a given period of time a day in our case.
Note that this is the lower bound estimate and the actual cost is presumably much larger. The growth in mining costs is affected by both the changes in energy cost see Figure 3 and by the increase in the hashing rate in the Bitcoin network see Figure 2. We note that the variations in energy cost oscillates in a much narrow band with respect to the changes in the daily number of hashes and therefore, the minimum Bitcoin mining costs Figure 4 mostly mirrors the growth in the total number of hashes.
Figure 4. During the last 10 years the Bitcoin network activity has also increased with increasingly larger amount of money transferred daily through the network. Figure 5 reports the total transferred value per day in the Bitcoin network specified in USD. One can see that the total daily volume of transactions has grown from about one thousand USD in to nearly one billion USD in for an increase by six orders of magnitude. Figure 6 reports the ratio between the daily mining cost C t and daily transaction volume V t.
The largest variations occurred in the first few years then, after , the ratio value has stabilized into a plateau with then a jump to a higher plateau at the end of presumably due to the large decrease in Bitcoin price from over 19, USD in December to just a little over 3, USD in December Despite the change in this relation between mining costs and transaction volume in —18 and the change in Bitcoin prices in the same period, we note that in general this ratio is not correlated with the price of Bitcoin.
There is actually a small negative correlation between the two for the daily variations. Using regional electricity prices to calculate the mining costs shows a similar pattern over time, though on a slightly higher level after with the mean ratio being 0. Note that this band of oscillation is within one order of magnitude whereas the underlying quantities C t and V t vary of six orders of magnitude during the same period.
If we limit our analysis to the last period after the end of , we obtain a mean ratio of 0. Figure 6. The band is the region between the first and tenth decile and the center line is the mean value, which is 0. The proof of work allows a network of anonymous and untrustful parties to operate together without central authority control. It is a powerful instrument to keep a distributed system secure from malicious attacks.
However, it has a high cost. We estimate that presently at least a billion USD per year is burned by the Bitcoin network for the proof of work. This amount corresponds to a one million times increase with respect to the costs in Using data from to , this paper quantifies the lower bound for the energy costs of Bitcoin mining and examines the relationship between this bound to the total value of transactions over time. We reveal that the ratio between mining cost and total transaction volume has not increased nor decreased over the last 10 years despite Bitcoin mining activity having increased by ten billion times during the same period.
Such an overall constant ratio is consistent with an argument, introduced by Aste , suggesting that such a ratio must be a sizable fraction of the transaction volume and it corresponds to the minimum fraction that an attacker must double spend to make a profit the quantity p in Equation 2. This being a lower bound estimate that realistically could be an order of magnitude larger if all extra costs, beside the oil equivalent cost of mining energy, are included.
We could therefore conclude that in the Bitcoin network the cost of proof of work is not at all too high. On the contrary it is actually too low to protect against double spending attacks. However, the proof of work is not the sole mechanism that provides protection of the Bitcoin network. The system also depends upon the high entry barriers in terms of mining hardware and facilities costs. Further, Bitcoin value is built upon community trust so once a majority attack has been detected, the Bitcoin value is likely to collapse together with the potential attacker gains.
Finally, an attack involving a large fraction of the Bitcoin volume would be most likely detected by the network before its completion. Distributed systems and Blockchains can be secured through several other mechanisms that do not require computationally intensive proof of work. Indeed the proof of work is a mechanism introduced to produce qualified voters in a system of anonymous untrustful parties. Any mechanism that can verify identity of the voters' or that can in any other way avoid uncontrolled duplications of the voters can reduce or eliminate completely the cost and even the need of a proof of work.
However, these other mechanisms must relax also some other properties, such as anonymity, openness, or equalitarian distributed verification. The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation. TA proposed the research, supervised and contributed to the data collection, performed the data analytics, and co-drafted the paper. Y-DS collected, processed and analyzed the data, and co-drafted the paper. Both authors gave final approval for publication and agree to be held accountable for the content of the work.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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This article has been released as a pre-print to arXiv as Song and Aste Akcora, C. Andoni, M. Blockchain technology in the energy sector: a systematic review of challenges and opportunities. Energy Rev. Aste, T. Blockchain technologies: the foreseeable impact on society and industry. Computer 50, 18— Market Capitalization. Google Scholar. Chan, W. Holding bitcoin longer: the dynamic hedging abilities of bitcoin. Finance 71, — Derks, J. From chaining blocks to breaking even: a study on the profitability of bitcoin mining from to Markets 28, — Gervais, A.
Is bitcoin a decentralized currency?
IEEE Secur. Grobys, K. Cryptocurrencies and momentum. Kristoufek, L. Bitcoin and its mining on the equilibrium path. Energy Econ. Bitcoin mining: a global review of energy and power demand.
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