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The Cost of Bitcoin Mining Has Never Really Increased

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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 2010 to 2020, 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 10-billion-fold increase in hashing activity and a 10-million-fold increase in total energy consumption, we find the cost relative to the volume of transactions has not increased nor decreased since 2010. 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. We estimate that in the Bitcoin network this fraction is of the order of 1%.
ORIGINAL RESEARCH
published: 22 October 2020
doi: 10.3389/fbloc.2020.565497
Frontiers in Blockchain | www.frontiersin.org 1October 2020 | Volume 3 | Article 565497
Edited by:
Joerg Osterrieder,
Zurich University of Applied Sciences,
Switzerland
Reviewed by:
Daniel Traian Pele,
Bucharest Academy of Economic
Studies, Romania
Luca Di Persio,
University of Verona, Italy
Dagmar Linnertova,
Masaryk University, Czechia
Eftim Zdravevski,
Saints Cyril and Methodius University
of Skopje, North Macedonia
Dave Remue,
KPMG, Belgium
*Correspondence:
Tomaso Aste
t.aste@ucl.ac.uk
Specialty section:
This article was submitted to
Financial Blockchain,
a section of the journal
Frontiers in Blockchain
Received: 25 May 2020
Accepted: 31 August 2020
Published: 22 October 2020
Citation:
Song Y-D and Aste T (2020) The Cost
of Bitcoin Mining Has Never
Really Increased.
Front. Blockchain 3:565497.
doi: 10.3389/fbloc.2020.565497
The Cost of Bitcoin Mining Has Never
Really Increased
Yo-Der Song 1, 2 and Tomaso Aste 1,2
*
1Department of Computer Science, University College London, London, United Kingdom, 2UCL Centre for Blockchain
Technologies, University College London, London, United Kingdom
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
2010 to 2020, 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 10-billion-fold increase in
hashing activity and a 10-million-fold increase in total energy consumption, we find the
cost relative to the volume of transactions has not increased nor decreased since 2010.
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. We estimate that in the Bitcoin network this
fraction is of the order of 1%.
Keywords: bitcoin, proof of work, cryptocurrency, blockchain, mining cost
1. INTRODUCTION
Bitcoin is a digital currency launched in 2009 by an anonymous inventor or group of inventors
under the alias of Satoshi Nakamoto (Nakamoto, 2019). It is the largest cryptocurrency in
market capitalization with over 100 billion dollars (Chan et al., 2019; Grobys and Sapkota, 2019;
Blockchain.com, 2020). 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, 2017). Instead, Bitcoin relies on a highly replicated
public ledger, secured by means of a hash chain and validated through community consensus
(Akcora et al., 2018). 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-256 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. Therefore the community
performs a large number of hashing by modifying a random component of the block content until,
Song and Aste Bitcoin Mining Cost
by chance, someone finds a “valid” hash that is smaller
than the threshold. 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. In the words of Satoshi Nakamoto, “one
CPU one vote” (Nakamoto, 2019). Bitcoin mining hardware has
moved from CPU first to GPU (McNally et al., 2018) and later
FPGA and ASIC but the principle behind the proof of work
remains the same.
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 6.25 Bitcoins or around USD 60,000 at the
current exchange rate (see Table 1). For this reason, the hashing
process is called “mining” and miners often join to form large
mining pools to have a more stable source of income (Gervais
et al., 2014).
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. Normally a block is considered
finally valid after six blocks are attached to its chain, which
takes 1 h.
The Bitcoin proof of work is very costly economically (Thum,
2018) and environmentally (Stoll et al., 2019). Technological
improvements over the years have made hashing a very
efficient operation, consuming at little as 0.03 joules per
billion hashes (with specifically-designed Application-Specific
Integrated Circuit, ASIC, machines. 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 2020) computing nearly 1025 hashes
per day, up over 10 orders of magnitude from the 2010 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 2020. 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
TABLE 1 | Bitcoin reward per block mined.
Start date Bitcoin reward
3 Jan 2009 50.00
28 Nov 2012 25.00
9 Jul 2016 12.50
11 May 2020 6.25
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.
One question arises: is this cost fair or could it be lowered?
In Aste (2016) 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. The attacker will try to double spend the largest amount
of Bitcoin possible, but this is limited to the amount normally
exchanged within a block (which, we estimate in this paper, is
currently around $10 million). 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
TABLE 2 | Mining hardware with optimal energy efficiency and their dates of
release.
Type Hardware name Date J/Th
CPU ARM Cortex A9 3 Oct 2007 877,193
GPU ATI 5870M 23 Sep 2009 264,550
FPGA X6500 FPGA Miner 29 Aug 2011 43,000
ASIC Canaan AvalonMiner Batch 1 1 Jan 2013 9,351
ASIC KnCMiner Jupiter 5 Oct 2013 1,484
ASIC Antminer U1 1 Dec 2013 1,250
ASIC Bitfury BF864C55 3 Mar 2014 500
ASIC RockerBox 22 Jul 2014 316
ASIC ASICMiner BE300 16 Sep 2014 187
ASIC BM1385 19 Aug 2015 181
ASIC PickAxe 23 Sep 2015 140
ASIC Antminer S9-11.5 1 Jun 2016 98
ASIC Antminer R4 1 Feb 2017 97
ASIC Ebang Ebit 10 15 Feb 2018 92
ASIC 8 Nano Compact 1 May 2018 51
ASIC Antminer S17 9 Apr 2019 36
ASIC Antminer S19 Pro 23 Mar 2020 30
Frontiers in Blockchain | www.frontiersin.org 2October 2020 | Volume 3 | Article 565497
Song and Aste Bitcoin Mining Cost
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 (2016) the following formula
is reported:
Equilibrium fair cost of proof of work per block
=Duplicated fraction of the value of a block
Number of blocks required for settlement . (1)
We can re-write this formula to formally express the cost of proof
of work per day, Ct, as
Ct=pVt
N(2)
where:
pis the duplicated proportion of block transaction volume;
Vtis the average transaction volume on day t;
Nis the number of blocks required for settlement.
In Equation (2) Nis roughly equal to 6 and the current average
volume of transaction is about Vt1 billion USD a day but it
was only a few thousands dollars a day in 2010. 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. Finally,
we should take into account that the attacker must have control
over more than 50% of the hashing power. 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. Therefore, we
expect the parameter pto be of the order of 1% or less.
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, 2016;
Aste et al., 2017). 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 (2016).
2. METHODOLOGY
2.1. Estimation of the Lower Bound for the
Cost of Bitcoin Mining
The cost of Bitcoin mining is composed of three key elements:
1. The energy cost of mining
2. The overheads for the maintenance of the mining farm, such
as infrastructure costs and cooling facilities
3. 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.
Frontiers in Blockchain | www.frontiersin.org 3October 2020 | Volume 3 | Article 565497
Song and Aste Bitcoin Mining Cost
2.2. Data
Historic data on Bitcoin prices, the average hash rate, and
the number of daily blocks per day can be found on https://
charts.bitcoin.com/btc and the estimated total value of all
transactions on the Bitcoin network on https://www.blockchain.
com/charts/. Hash efficiency and other information regarding
Bitcoin mining hardware were aggregated from manufacturer
data and previous studies (Küfeo˘
glu and Özkuran, 2019) and
independently verified.
Most prior works have priced energy usage according to
global average electricity prices (see for instance Vranken, 2017;
Derks et al., 2018; Küfeo˘
glu and Özkuran, 2019). 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. Historical
Brent Crude oil spot prices were collected from the EIA1with
the conversion rate between joules and barrels of oil equivalent
set at 1 barrel = 5.54543 gigajoules based on the figures released
by the BEIS2. 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. Based on the figures released
by the CCAF at https://cbeci.org/mining_map, China, USA and
Russia are responsible for over 80% of global hash rates. 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, Et,
to be calculated as
Ey=X
i
wipi(3)
where:
iis the set of regions in Table 3;
wiis the share of global hash rate accounted for by region i;
piis the industrial electricity price in region i, converted to
USD/kWh based on the average exchange rate.
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 0.738 multiplier based on empirical data from 2013 to 2018
1https://www.eia.gov/dnav/pet/hist/rbrteD.htm
2https://assets.publishing.service.gov.uk/government/uploads/system/uploads/
TABLE 3 | Geographic distribution of the share of hash rate on the Bitcoin
network, 2019–2020.
Nation/Provinces % of global hash activity
China 71.70
- Xinjian 30.13
- Sichuan 18.58
- Inner Mongolia 7.71
- Yunnan 7.07
- Gansu 2.02
- Beijing 1.37
- Zhejiang 1.06
- Other provinces 3.76
Russia 6.08
USA 5.29
was applied on national Chinese electricity prices to calculate
EChina. 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., 2019), such as the use of associated gas that would
otherwise be flared (Loris, 2019) which could further lower the
energy cost of Bitcoin mining below the national averages. 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.
2.3. Estimation of the Energy Costs of
Bitcoin Mining
A mining hardware has an energy consumption that can be
measured in joules per terahash (J/Th), and has a hashing speed
that can be measured in terahashes per second (Th/s). 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, Ct, is:
Ct=etHt
bPt(4)
Frontiers in Blockchain | www.frontiersin.org 4October 2020 | Volume 3 | Article 565497
Song and Aste Bitcoin Mining Cost
where:
etis the energy efficiency of the most efficient mining hardware
available on day tin (J/Th);
Htis the daily number of hashing operations in (Th) on day t;
bis the joule of energy equivalent per barrels of oil 5.55 ×109
(J/barrel);
Ptis the Brent crude oil spot price (USD/barrel) on day t.
3. RESULTS
3.1. Hardware Efficiency Variations
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. The improvement in energy efficiency
for Bitcoin mining over time is reported in Figure 1 where each
symbol represents the most energy efficiency hardware at the
respective time and the red dotted line displays a best-fit with
an exponential curve: Energy Consumption cexp(λt). The
best fit parameter is λ=0.0025, which means that hardware
efficiency has been doubling every 10 months in average. In a
previous work a power-law model was proposed by Kristoufek
(2020). 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, 1998).
3.2. Hash Computations Variations
Figure 2 displays the total number of hashing operations per day.
We note that the number of daily hashes have increased from
1015 to 1025 in the period between September 2010 to May 2020
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,
2014). However, we can see from the figure that there are four,
very distinct, periods with different grow rates. Specifically: (i)
mid 2010 to mid 2011; (ii) mid 2011 to early 2013; (iii) early 2013
to early 2015; (iv) early 2015 to early 2020. The estimated best-fit
doubling times in these periods are respectively: (1) 33 days; (ii)
261 days; (iii) 38 days; (iv) 198 days.
FIGURE 1 | Estimate of the lower bound for the energy consumption of the
most efficient Bitcoin mining hardware, measured in J/Th.
3.3. Energy Price Variations
Figure 3 shows the variations of the energy price per gigajoule
in the period 2010–2020 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 2011 to mid
2014 and around 10 USD from late 2014 to early 2020. 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.
3.4. Lower Bound Mining Cost Estimate
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
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 2010 to mid 2011; (ii)
261 days, during mid 2011 to early 2013; (iii) 38 days during early 2013 to
early 2015; (iv) 198 days, during early 2015 to early 2020.
FIGURE 3 | Energy cost per gigajoule, measured in USD and converted from
Brent Crude spot prices.
Frontiers in Blockchain | www.frontiersin.org 5October 2020 | Volume 3 | Article 565497
Song and Aste Bitcoin Mining Cost
of time (a day in our case). Figure 4 reports the total mining
daily cost in USD estimated by using Equation (4), it varies from
around 3 USD a day in 2010 to over 4 million USD a day in early
2020. 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.
3.5. Transaction Volume Variations
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
FIGURE 4 | Total daily mining cost Ct, reported in USD, estimated by using
Equation (4).
FIGURE 5 | Daily transaction volume Vtreported in USD.
about one thousand USD in 2010 to nearly one billion USD in
2020 for an increase by six orders of magnitude.
3.6. Ratio Between Mining Cost and
Transaction Volume
Figure 6 reports the ratio between the daily mining cost Ctand
daily transaction volume Vt. We observe that the ratio Ct/Vt
does not have any increasing or decreasing trend but rather is
oscillating within a certain band over most of the period from
2010 to 2020. The largest variations occurred in the first few years
then, after 2014, the ratio value has stabilized into a plateau with
then a jump to a higher plateau at the end of 2017 presumably
due to the large decrease in Bitcoin price from over 19, 000 USD
in December 2017 to just a little over 3, 000 USD in December
2018. Despite the change in this relation between mining costs
and transaction volume in 2017–18 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.
Over the entire period, the mean value of Ct/Vtis 0.15% with
the first decile being 0.02% and tenth decile being 0.4%. Using
regional electricity prices to calculate the mining costs shows
a similar pattern over time, though on a slightly higher level
after 2014 with the mean ratio being 0.21%. Note that this band
of oscillation is within one order of magnitude whereas the
underlying quantities Ctand Vtvary of six orders of magnitude
during the same period. If we limit our analysis to the last period
after the end of 2017, we obtain a mean ratio of 0.3% and D1, D10
deciles with values equal to 0.1 and 0.4%.
4. DISCUSSION AND CONCLUSIONS
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
FIGURE 6 | Ratio between the cost of mining and the total transaction volume
Ct/Vton daily basis. The band is the region between the first and tenth decile
and the center line is the mean value, which is 0.15% for oil and 0.21%.
Frontiers in Blockchain | www.frontiersin.org 6October 2020 | Volume 3 | Article 565497
Song and Aste Bitcoin Mining Cost
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 2010. However,
although large, this amount is <0.5% of the transaction volume
over the network during the same period.
Using data from 2009 to 2020, 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 (2016),
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
pin Equation 2). Assuming the default block depth of N=6
in Equation (2), and using the last 3 years mean value for the
fraction Ct/Vtat 0.3%, we obtain that Bitcoin proof of work
protects from a double spend attack at least a fraction around
p1.5% of the global transaction volume. This result indicates
that attacks that duplicate more than 1.5% of the transaction
volume could be profitable for the attacker because the cost of
energy spent for the attack will be lower than the gain from the
attack. 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. This means that to launch a majority attack
on Bitcoin, the attacker would thus not only need to invest
substantial amounts of energy resources to gain over 50% of
the hashing power, they would also have to accept that many
of the hardware costs incurred are unlikely to be recovered due
to the inability of specialized ASICs to be repurposed for uses
other than cryptocurrency mining and that even if the attack
was successful, the value of Bitcoin would collapse so rapidly that
there would be little economic gain. 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.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be
made available by the authors, without undue reservation.
AUTHOR CONTRIBUTIONS
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.
ACKNOWLEDGMENTS
TA acknowledges support from ESRC (ES/K002309/1), EPSRC
(EP/P031730/1), and EC (H2020-ICT-2018-2 825215).
This article has been released as a pre-print to arXiv as
Song and Aste (2020).
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Conflict of Interest: 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.
Copyright © 2020 Song and Aste. This is an open-access article distributed under the
terms of the Creative Commons Attribution License (CC BY). The use, distribution
or reproduction in other forums is permitted, provided the original author(s) and
the copyright owner(s) are credited and that the original publication in this journal
is cited, in accordance with accepted academic practice. No use, distribution or
reproduction is permitted which does not comply with these terms.
Frontiers in Blockchain | www.frontiersin.org 8October 2020 | Volume 3 | Article 565497
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