Article

The Fair Cost of Bitcoin Proof of Work

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Abstract

In this short note I provide a very simple estimation of the fair cost for the proof of work in Bitcoin mining. I conclude that the current cost, although large, is of a justified order of magnitude for an anonymous systems operating between untrustful parties.

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... 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. ...
... 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 In the previous unpublished note by Aste (2016) the following formula is reported: ...
... 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. ...
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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%.
... 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. ...
... 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: ...
... 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. ...
Article
Full-text available
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%.
... Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the mining cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that the proof of work must cost a sizable fraction of the value that can be transferred through the network in order to keep the Blockchain system secure from double spending attacks [1,2]. We estimate that in the Bitcoin network this fraction is of the order of 1%. ...
... One question arises: is this cost fair or could it be lowered? In [1] 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. ...
... The attacker will make profits if this cost is inferior to the gain made from duplicated spending. In the previous unpublished note by [1] the following formula is reported: ...
Preprint
The Bitcoin network is burning a large amount of energy for mining. In this paper we estimate the lower bound for the global energy cost for a period of ten years from 2010 to 2020, taking into account changing oil costs, improvements in hashing technologies and hashing activity. Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the mining cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that the proof of work must cost a sizable fraction of the value that can be transferred through the network in order to keep the Blockchain system secure from double spending attacks. We estimate that in the Bitcoin network this fraction is of the order of 1%.
... Bitcoin mining can be done with a CPU or GPU, but specialized hardware or FPGAs can outperform general purpose processors by many orders of magnitude [52]. ...
... The validity of a blockchain is maintained through proof-of-work, which is inherently inefficient. Maintaining the Bitcoin blockchain is estimated to cost $50,000 per hour [52]. ...
... Bitcoin's scarcity and novelty have given it a high monetary value compared to the mining (blockchain verification) cost [52]. Miners are currently awarded with 25 bitcoins for mining a block (technically miners award themselves bitcoins, the award is verified by other miners signing subsequent blocks). ...
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... Currently in Bitcoin a successful hash is generated in average after 2 10 21 (two billion trillions) hash attempts which correspond to an average electricity consumption per block of about 1,000 GW at an estimated cost of an order of magnitude around $10,000. This is a massive quantity of energy, however, it was pointed out in [34] that the cost of PoW must be equivalent to the amount one could potentially profit from an attach that attempt to alter transaction history. Given that a block contains around $1M in transactions and that an attacker should control a chain of around 10 blocks to falsify transaction history for long enough to collect the profits, a fair cost for the PoW should be indeed around $10,000. ...
... A worrying note must be added at this point. Bitcoin PoW was previously [34] estimated 'fair' by assuming current block values at about $1M and it is reasonable to expect that the system itself will dynamically adapt the PoW cost to the transferred value. However, if coloured coins introduce transactions associated with other external assets that are not represented in value as Bitcoin transfer, then the system becomes biased with blocks containing larger real value than the nominal content. ...
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... Aiming at the ethical point of reference of human rights-more specifically, the right to life, the right to health, work-related rights, and the right to an adequate standard of living, including the right to housing, food, and water [66]-the enormous energy consumption of the proof of work consensus method [67] is ethically problematic [68]. In the case of Bitcoin, for example, in order to reach the validity of a proof of work, a billion watts is estimated to be necessary [69]. In other words, "currently, global power demand from cryptocurrency mining hovers at about 22 terawatt hours (TWh), but increasing demand means consumption could surge in 2018 to 125-140TWh-a full 0.6% of world consumption. ...
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... A June 2016 estimate of the cost of the Bitcoin proof of work found that it consumed around US$50,000 of energy an hour, and concluded that the resources devoted to mining were "large, wasteful, but necessary". 29 Miners recoup this cost with a reward for finding valid blocks. This is likewise the case with diplomatic ritual, which can come across as wasteful, obscure and effete; but provides an essential role in the creation of trust between adversaries and the validation of diplomatic communication. ...
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