ISSC 2014 / CIICT 2014, Limerick, June 26–27
`
`Bitcoin Mining and its Energy Footprint
`
`Karl J. O’Dwyer† and David Malone∗
`
`Hamilton Institute
`National University of Ireland Maynooth
`
`E-mail: †karl.a.odwyer@nuim.ie
`
`∗david.malone@nuim.ie
`
`Abstract — Bitcoin is a digital cryptocurrency that has generated considerable public
`interest, including both booms in value and busts of exchanges dealing in Bitcoins.
`One of the fundamental concepts of Bitcoin is that work, called mining, must be done
`in checking all monetary transactions, which in turn creates Bitcoins as a reward. In
`this paper we look at the energy consumption of Bitcoin mining. We consider if and
`when Bitcoin mining has been profitable compared to the energy cost of performing
`the mining, and conclude that specialist hardware is usually required to make Bitcoin
`mining profitable. We also show that the power currently used for Bitcoin mining is
`comparable to Ireland’s electricity consumption.
`
`Keywords — Bitcoin
`
`I
`
`Introduction
`
`Bitcoin is a peer-to-peer cryptocurrency mainly
`used for monetary transactions on the Internet [1]
`and is designed to be similar to fiat money and
`commodities. Bitcoins are intrinsically valueless,
`their worth is decided by those trading in them.
`At the time of writing, 1 Bitcoin (B) is worth ap-
`proximately 378.7 Euro(e). Bitcoin has generated
`a huge amount of interest in the media lately and
`has sparked a wave of copy-cat-currencies (Lite-
`coin, Gaelcoin, etc.) and even a fully working par-
`ody currency (dogecoin). It has also generated in-
`terest in academic circles due to issues it creates
`in user privacy e.g. [2], as well as attempts to gain
`insights into is behind transactions e.g. [3] and at-
`tempts to better understand its implications as a
`payment system e.g. [4].
`Bitcoin is based on a peer-to-peer network
`within the Internet. The members of the peer-to-
`peer network effectively maintain a ledger of Bit-
`coin transactions which have been accepted by the
`network. In this ledger, Bitcoins are owned by Bit-
`coin addresses, which are public keys from a key-
`pair. In order to assign Bitcoins, or some fraction
`thereof, to a new owner, the current owner must
`sign the transaction with the private key of the
`keypair using an ECDSA scheme. Before a trans-
`action is accepted by the network, the transaction
`
`is checked for validity, including the presence of
`these signatures.
`Bitcoins are not issued or governed by a cen-
`tral authority but, instead are created in a process
`called mining. Mining is one of the key concepts
`behind the Bitcoin protocol, in which valid trans-
`actions are collected into blocks and are added to
`the ledger by linking it to the previously accepted
`blocks. The network forms a common view, called
`the blockchain, of which transactions have taken
`place, preventing users from reusing Bitcoins and
`attempting to spend them more than once.
`To add a block to the blockchain, a signature
`must be found linking the transactions in the block
`to the previous blocks. This requires finding a
`nonce value which satisfies a particular equation
`involving the SHA256 cryptographic hash func-
`tion. This is a computationally expensive task;
`however, a member of the peer-to-peer network
`who finds a suitable value is rewarded by being
`able to assign newly mined Bitcoins to an address
`of their choosing.
`In this paper we consider the energy cost of Bit-
`coin mining. Solving of the computational prob-
`lem requires energy. We consider how this energy
`can be calculated and the impact of using different
`types of hardware for this computation. Using his-
`torical information from the Bitcoin network and
`
`CRUSOE 1025
`
`1
`
`

`

`Bitcoin exchanges, we compare the monetary cost
`of the energy to the reward for calculating a Bit-
`coin block. We also consider the likely power con-
`sumption of the whole Bitcoin mining operation,
`and show that it is comparable to Ireland’s average
`electricity consumption.
`
`II Bitcoin Mining
`
`As we mentioned, a Bitcoin miner is part of Bit-
`coin’s peer-to-peer network that collects recent
`transactions and aims to complete a proof of work
`scheme, based on the ideas of Hashcash[5]. In this
`scheme, there is a current target value T , which is
`periodically recalculated by the network (see Sec-
`tion II.a)). The miner’s aim is to find a nonce value
`so that
`
`H(B.N ) < T
`
`(1)
`
`where B is the string representing the recent trans-
`actions, N is the nonce value, ‘.’ is the concatena-
`tion operator and H is the Bitcoin hash function,
`in this case
`
`H(S) := SHA256(SHA256(S)).
`
`The proof of work can be achieved by choosing
`values for N randomly or systematically until eq.1
`is satisfied. When an N is found, the resulting
`block can be sent to the Bitcoin network and added
`to the Bitcoin blockchain. Finding a block results
`in a reward of extra Bitcoins for the block’s finder.
`Thus, the process of finding a suitable N value is
`referred to as Bitcoin mining.
`
`II.a) Difficulty
`
`The rate at which Bitcoins can be discovered can
`be controlled by the Bitcoin Network’s choice of
`the value of the target, T , in eq.1. However, the
`target depends on the current number and speed
`of miners in the Bitcoin network, and is normally
`quoted in terms of the difficulty, D. The relation-
`ship between the difficulty and the target T is
`
`D =
`
`Tmax
`T
`
`where the largest possible value of the target Tmax
`is (216 − 1)2208 ≈ 2224.
`The hash function H for Bitcoin has been chosen
`so that it behaves approximately as a uniformly
`random value between 0 and 2256−1. Thus, for any
`given nonce value, the probability of it satisfying
`eq.1 is
`
`Difficulty Over Time
`
`2014
`
`2013
`
`2012
`
`2011
`
`2010
`
`1010
`
`109
`
`108
`
`107
`
`106
`
`105
`
`104
`
`103
`
`102
`
`101
`
`100
`
`Difficulty
`
`Fig. 1: The change of the difficulty to generate a Bitcoin
`over time, based on aggregated statistics [6].
`
`block is successfully completed will be geometri-
`cally distributed, therefore the the expected num-
`ber of hashes to find a block is D232. If we have a
`system calculating hashes at a rate R, the expected
`time to find a block is
`
`(2)
`
`D232
`R
`
`.
`
`≈
`
`1 p
`
`E[t] =
`
`For example, if you can calculate a Bitcoin hash
`1 million times a second, and the difficulty is
`4, 250, 217, 9201, then E[t] ≈ 1.8 × 1013s.
`
`II.b) Change in Difficulty
`
`The difficulty, D, is recalculated every 2016 blocks,
`with the aim of keeping the average time to dis-
`cover a new block near 10 minutes. At this ideal
`speed, 2016 blocks will be discovered every two
`weeks. To calculate the new difficulty, the length
`of time that it took to calculate the the last 2016
`blocks is used to estimate the hash rate of the en-
`tire Bitcoin network. The new difficulty is selected
`so that if the same average hash rate is maintained,
`it will take two weeks to calculate the next 2016
`blocks. If the resulting difficulty is more than four
`times harder (or four times easier) than the cur-
`rent difficulty, then the result is capped to four
`times harder (or easier). Restrictions on the range
`of acceptable difficulties/targets are also applied.
`The historical values of difficulty to date are shown
`in Figure 1. The increasing trend in difficulty has
`been caused by an increase in the resources dedi-
`cated to calculating hashes in the Bitcoin network.
`
`II.c) Change in Reward
`
`There are two sources of reward for calculating a
`new block. First, the block is formed from Bit-
`coin transactions, and a transaction may choose
`to include a transaction fee, to be paid to who-
`ever finds a block containing this transaction. Sec-
`
`1Current as of mid March 2014.
`
`1
`D232
`
`.
`
`p =
`
`Tmax
`D2256
`
`≈
`
`T
`2256 =
`Each nonce value tested should behave like an in-
`dependent trial, so the number of trials until a
`
`2
`
`

`

`BTC to USD Exchange Rate
` (Mt.Gox)
`
`Mar 2014
`
`Nov 2013
`
`013
`
`Jul 2
`
`Mar 2013
`
`Nov 2012
`
`012
`
`Jul 2
`
`Mar 2012
`
`Nov 2011
`
`011
`
`Jul 2
`
`Mar 2011
`
`Nov 2010
`
`1200
`
`1000
`
`800
`
`600
`
`USD
`
`400
`
`200
`
`0
`
`Average Transaction Cost
`
`1.6
`
`1.4
`
`1.2
`
`1.0
`
`0.8
`
`BTC
`
`0.6
`
`0.4
`
`0.2
`
`Mar 2014
`
`Feb 2014
`
`014
`
`n 2
`Ja
`
`Dec 2013
`
`Nov 2013
`
`Oct 2013
`
`Sep 2013
`
`Aug 2013
`
`013
`
`Jul 2
`
`013
`
`n 2
`Ju
`
`May 2013
`
`0.0
`
`Apr 2013
`
`Fig. 2: The average transaction fee per block per day.
`Data derived from http://blockchain.info/charts.
`
`Fig. 3: The exchange rate between Bitcoin and Dollars,
`based on aggregate statistics [6].
`
`ond, a standard reward is provided depending on
`how many blocks have been successfully calcu-
`lated. This reward started at B50 per block and
`is halved every 210,000 blocks. As of mid-March
`2014, the reward is B25. The reward will eventu-
`ally reach B0; after such time it is imagined that
`the network of miners will continue mining but will
`do so in order to gain processing fees. This means
`that there is a limit on the number of Bitcoins
`which will be mined, but each Bitcoin is divisible
`up to 8 decimal places.
`The mean value of the transaction fee over a
`day is plotted for a range of days in Figure 2. As
`we can see the current standard reward, B25, is
`considerably larger than the current or historical
`average transaction fees. This may change in the
`future, as the standard reward continues to halve.
`
`III Hardware Arms Race
`
`The major limiting factors in Bitcoin mining are
`the hash rate of hardware and the cost of running
`this hardware. The hash rate, R, is typically mea-
`sured in millions of hashes per second or Mega-
`hashes (Mhash/s). This is combined with the
`power usage, P , of the hardware to get the energy
`efficiency of the hardware E = R/P (Mhash/J)
`which serves as a helpful statistic to compare hard-
`ware. Statistics are shown for a selection of hard-
`ware in Table 1.
`Initially mining took place on normal2 comput-
`ers. As Bitcoin gained popularity, there was some-
`thing akin to an arms race as miners attempted
`to increase their hash rate. Graphics Process-
`ing Units (GPUs) which can perform many par-
`allel calculations are well-adapted to Bitcoin min-
`ing. Standard programming interfaces, such as
`OpenCL or CUDA, made GPUs popular among
`
`Bitcoin miners. Their higher hash rate compared
`with their lower energy footprint made them bet-
`ter suited to mining than normal CPUs.
`As the use of GPUs became more widespread,
`people were forced to look for alternatives to keep
`ahead of the crowd. Field Programmable Gate
`Arrays (FPGA) came into vogue for a brief pe-
`riod before Application Specific Integrated Cir-
`cuits (ASIC) came onto the scene. ASICS can per-
`form the Bitcoin hash at higher rates but with a
`much smaller energy requirement. The evolution
`of hardware for Bitcoin mining is described in de-
`tail in [7].
`
`IV Energy Cost/Reward Trade Off
`
`Bitcoin is similar to other currencies, in that the
`exchange rate between Bitcoin and other curren-
`cies fluctuates over time. This in turn impacts on
`the viability of Bitcoin mining:
`if the value of a
`Bitcoin is less than the cost of the energy required
`to generated it then there is a disincentive to con-
`tinue mining. The exchange rate to US dollars is
`shown in Figure 3.
`On the other hand, as the number of people min-
`ing Bitcoin increases and the difficulty of mining
`follows suit, so the likelihood of discovering a valid
`block decreases. To overcome this, more powerful
`hardware is required to achieve the same success
`rate. However, since the cost of energy is a limiting
`factor, newer hardware will have to have a higher
`hash rate and a lower energy footprint.
`Thus, there is a trade off between two time vary-
`ing factors: first, the energy cost of discovering a
`block,
`
`Ce = E[t]P U ≈
`
`D232P U
`R
`
`=
`
`D232U
`E
`
`2Where ‘normal’ is defined as a general purpose com-
`puter, such as an IBM PC type architecture with an x86
`CPU.
`
`where U is the unit cost for a Joule of energy; sec-
`ond is the cash reward for discovering the block,
`which is simply the reward for the block, in B,
`
`3
`
`

`

`Name
`
`Core i7 950
`Atom N450
`Sony Playstation 3
`ATI 4850
`ATI 5770
`Digilent Nexys 2 500K
`Monarch BPU 600 C
`Block Erupter Sapphire
`
`Type
`
`CPU
`CPU
`CELL
`GPU
`GPU
`FPGA
`ASIC
`ASIC
`
`Hash Rate Power Use Energy Efficiency
`R (Mhash/s)
`P (W)
`E (Mhash/J)
`18.9
`150
`0.126
`1.6
`6.5
`0.31
`21.0
`60
`0.35
`101.0
`110
`0.918
`214.5
`108
`1.95
`5.0
`5
`1
`600000.0
`350
`1714
`333.0
`2.55
`130
`
`Cost Reference
`($)
`350
`169
`296
`45
`80
`189
`2196
`34.99
`
`[8, 9]
`[10, 9]
`[11, 9]
`[12, 9]
`[13, 9]
`[14, 9]
`[15, 9]
`[16, 9]
`
`Table 1: Examples of Bitcoin-mining devices.
`
`Cost to Generate 1 BTC (in USD)
`
`ware could be profitable, though the gap is closing.
`
`V Network Power Usage
`
`As we know that the Bitcoin network aims for an
`aggregate block discovery rate of one every 10 min-
`utes, we can use eq.2 to estimate the hash rate of
`the entire network if we know the difficulty:
`
`Rnet ≈
`
`D232
`600s
`
`.
`
`Combining this with the efficiency E for different
`hardware, we can estimate the network’s power us-
`age as Pnet = Rnet/E. For commodity hardware
`(CPUs/GPUs), efficiency values above 2 Mhash/J
`are unlikely[9]. For FPGAs, values around ten
`times this are possible. For ASICs values of 100–
`1000 times are possible.
`Figure 5 shows conservative estimates for the to-
`tal power used for Bitcoin mining, assuming that
`it consists of either efficient commodity hardware
`(E = 2 Mhash/J) or efficient specialist hardware
`(E = 2000 Mhash/J). The actual network will be
`a mix of hardware of types at different levels of
`efficiency, so we expect that the actual efficiency
`will be between the two. This suggests that the
`total power used for Bitcoin mining is around 0.1–
`10GW. Average Irish electrical energy demand and
`production is estimated at around 3GW [18, 19],
`so it is plausible that the energy used by Bitcoin
`mining is comparable to Irish national energy con-
`sumption.
`
`VI Conclusion
`
`In this paper, we have described aspects of Bit-
`coin relevant to Bitcoin mining and its energy con-
`sumption. Even though the value of Bitcoin is de-
`cided by those who trade in them, it is also related
`in some way to the value of electricity. We have
`seen that the cost of Bitcoin mining on commod-
`ity hardware now exceeds the value of the rewards.
`Thus, the competition created in mining for Bit-
`coin has lead to a situation where in order to be
`financially viable the hardware has had to become
`faster and more energy efficient.
`
`106
`
`105
`
`104
`
`103
`
`102
`
`101
`
`100
`
`10-1
`
`10-2
`
`10-3
`
`10-4
`
`10-5
`
`10-6
`
`10-7
`
`10-8
`
`10-9
`
`USD
`
`Exchange Rate (USD)
`Core i7 950 (CPU)
`ATI 5770 (GPU)
`Digilent Nexys 2 500K (FPGA)
`Monarch BPU 600 C (ASIC)
`Sony Playstation 3 (CELL)
`
`2014
`
`2013
`
`2012
`
`2011
`
`2010
`
`Fig. 4: The Cost of Generating a Bitcoin and the value of
`the resulting reward.
`
`times the current exchange rate for a Bitcoin. Al-
`ternatively, we may normalise this per Bitcoin.
`Figure 4 shows the energy cost and the value for
`generating a Bitcoin for various hardware from Ta-
`ble 1. We use a dashed line for hardware before its
`release.
`To allow easy comparison with the Bitcoin ex-
`change rate, we use a cost of 0.10 US dollars per
`kWh. This is the lowest cost of electricity in Eu-
`rostat’s 2013 statistics[17]; for Industrial rates in
`Finland. As typical consumer prices are twice this
`or more, this should provide a lower bound for the
`energy cost of mining Bitcoins in Europe. When
`calculating the value of each block, we have used
`the standard reward and not included transaction
`fees, as we have seen that the transaction fees are
`uncertain and currently a small fraction of the to-
`tal reward.
`For the period for which exchange rate data is
`available, we see that it has never been profitable
`to use a generic Core i7 CPU, and it appears that it
`may only have been briefly been profitable to use a
`Playstation 3. Using FPGAs or GPUs appears to
`have been close to profitable until mid-2013, when
`the increase in difficulty outpaced the increase in
`Bitcoin value. The yet-to-be-available ASIC hard-
`
`4
`
`

`

`Network Power Usage
`
`Efficient Commidity Hardware (E=2)
`Efficient Specialist Hardware (E=2000)
`
`Hashcash-a de-
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`
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`Intel Core i7-950 3.06 GHz
`[8] Amazon.
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`pro-
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`[10] Amazon.
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`playstation
`Sony
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`
` 1e+12
`
` 1e+10
`
` 1e+08
`
` 1e+06
`
` 10000
`
` 100
`
` 1
`
` 0.01
`
`Power (W)
`
` 0.0001
`Jan
`2009
`
`Jul
`2009
`
`Jan
`2010
`
`Jul
`2010
`
`Jan
`2011
`
`Jul
`2011
`
`Jan
`2012
`
`Jul
`2012
`
`Jan
`2013
`
`Jul
`2013
`
`Jan
`2014
`
`Jul
`2014
`
`Fig. 5: Estimated Power Consumption of the Bitcoin
`Mining Network.
`
`In this paper we looked at the energy issues
`around Bitcoin mining and its profitability. We
`also estimated under reasonable, reasonable as-
`sumptions, that currently the entire Bitcoin min-
`ing network is on par with Ireland for electricity
`consumption.
`
`Acknowledgements
`
`This research was supported by HEA PRTLI Cycle
`5 TGI.
`
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