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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.
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. 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. Therefore, all estimates must be interpreted with caution. Nonetheless, bitcoin mining is a highly mobile industry, allowing it to migrate quickly to areas with cheap electricity. These key assumptions have been criticised to overestimate electricity consumption; indeed, BECI estimates represent the high range of published estimates to date.
They also conduct sensitivity analyses around key uncertainties, including electricity costs and capital depreciation schedules. Other researchers have calculated lower-bound estimates using a bottom-up approach e. The Bitmain Antminer S9 series 0. With the recent run up in price and hashrate, energy consumption is expected to be much higher in Crucially, the use of country average and in some cases, world average emissions factors inflates the GHG estimates, since bitcoin mines are typically concentrated in renewables-rich states and provinces.
It is important to recognise that bitcoin is just one cryptocurrency, which is one application of blockchain, which is itself one example of distributed ledger technology DLT. Over the coming years, other applications of blockchain — including those within the energy sector — are likely to garner more attention. As the scope and scale of blockchain applications increases, these trends combined are likely to materially reduce the future energy footprint of its technology.
That said, this is a very dynamic area that certainly requires careful monitoring and rigorous analysis — particularly, a careful monitoring of local hotspots. The energy use of bitcoin and blockchain is just part of the blockchain and energy story.
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