Technological Basics
Bitcoin, the first application built on blockchain technology, is a decentralized payment system in which all participating computers (“nodes”) store a copy – or, more precisely, a replica, since there is no distinguished master – of the associated ledger. A ledger is commonly defined as a collection of accounts, stating one’s current rights of ownership of a particular asset – in the case of Bitcoin, units of the eponymous cryptocurrency. The underlying technology, blockchain, provides a means to store information chronologically and redundantly on a decentralized database, and an agreement process through which the nodes synchronize and modify their global state (“operate transactions”) (Crosby et al. 2016). It is, therefore, not exclusively suitable for use with cryptocurrencies, but can be applied to many processes in which the involvement of an intermediary such as a bank, a notary, or any (digital) platform owner is not desirable.
Blockchains, in general, achieve this synchronization by linking transactions to form batches (“blocks”) and adding these, sequentially, to the existing linear data structure (“chain”). Utilizing Merkle trees and hash-pointers, this data structure is highly tamper-sensitive, making retrospective manipulations easy to detect. Agreement about which new blocks to append is reached using a so-called consensus mechanism. Anyone can run a node for the common cryptocurrencies and participate in the consensus mechanism of their underlying blockchains using public key cryptography and hence without any form of registration. Consequently, blockchains underlying such open systems, which allow for unrestricted access and participation, are termed permissionless. Since, on a permissionless blockchain, the inclusion of a distinct entity to provide accounts and passwords is not viable, authentication based on a public key infrastructure is highly suitable. For such blockchains, a simple voting-based agreement process based on “one man – one vote” is not secure, since a potential attacker could simply create multiple accounts to gain a majority and take control of the system; this is called a Sybil attack (Douceur 2002).
Bitcoin’s key innovation was to provide a suitable consensus mechanism for the use in this scenario. Specifically, Bitcoin combined several well-known concepts from cryptography to form the so-called PoW. This refers to the right to create a new block from a subset of queued transactions when one finds a solution to a cryptographic, computationally intensive puzzle. The process of searching for a solution is called “mining”. This results in coupling the voting weight to a scarce resource – computing power and thus energy – and hence prevents Sybil attacks. The mining process is economically incentivized in that participants are rewarded for every valid block that is found and disseminated. The reward typically consists of a certain amount of the associated cryptocurrency and the fees for the associated transactions. The value of the former is proportional to the cryptocurrency’s market price, so the success of cryptocurrencies on financial markets in the last years has provided a very strong incentive to participate in mining. In turn, this has led to an enormous energy consumption associated with the underlying PoW blockchains.
It is essential to note that the high energy consumption of PoW blockchains is neither the result of inefficient algorithms nor of outdated hardware. Strikingly, such blockchains are “energy-intensive by design”. It is their high energy consumption that protects PoW blockchains from attacks: Depending on the scenario, an attacker must bear at least 25 to 50% of the total computing power that participating miners use for mining – and, thus, the same proportion of the total energy consumption (under the assumption of equal hardware) – to be able to successfully manipulate or control the system (Eyal and Sirer 2014). Consequently, the more valuable a PoW cryptocurrency is, the better it is protected against attacks, confirming that PoW is, indeed, a thoughtful design.
General Estimates
Starting with the work of O’Dwyer and Malone (2014), researchers have analyzed the energy consumption caused by Bitcoin in numerous scientific publications over recent years (Stoll et al. 2019). However, results regarding the energy consumption of PoW cryptocurrencies and blockchain technology in general are rare. Determining the exact value for the energy consumption of a multitude of open, distributed networks is a hard task because the precise number of participants, the properties of their hardware, and the effort which they put into mining are unknown. Fortunately, however, one can obtain good estimates for a lower and an upper bound of the energy consumption of any PoW blockchain by following Vranken (2017) and Krause and Tolaymat (2018): Since both the difficulty of the cryptographic puzzles and the frequency at which solutions are found are easily observable, one can calculate the expected value of the minimum frequency of calculations (“hash-rate”) needed to solve the puzzles as often as observed. This gives a lower bound of the energy consumption of an arbitrary PoW blockchain:
$$\begin{aligned} \text{total power consumption} \ge \text{total hash rate} \times \text{min energy per hash}. \end{aligned}$$
(1)
This estimate indicates the lower bound, reflecting the likelihood that more solutions are found than disseminated, that further computations – in addition to mining – are being carried out, and that not every miner has the most energy-efficient hardware.
Both the current hash rate of a public blockchain and the energy efficiency of the most efficient mining hardware can easily be retrieved from online material. However, one must be aware that mining hardware is in general blockchain-dependent because the algorithms used for hashing can differ. For example, Bitcoin uses SHA256, for which very efficient application-specific integrated circuits (ASICS) exist, i.e., chips that are highly optimized for computing hash values and, thus, for solving the puzzles. On the other hand, Ethereum was designed to prevent the use of highly specific mining hardware, so general-purpose GPUs can be used for mining. Note that (1) does not depend on any other parameters and, therefore, gives a very reliable lower bound. Entering the current numbers – retrieved from Coinmarketcap (2020) and Coinswitch (2019) on 2020-02-05 – into (1) yields a lower bound for power consumption of 6.8 GW, which equates to an annual energy requirement of at least 60 TWh. Alternatively, one could, of course, also integrate the time-dependent lower bound over the period under consideration.
One can also determine an upper bound for the energy requirement of the mining process for a PoW blockchain, assuming honest and rational miners whose utility from mining is solely financial profit: Participation in the mining process is only profitable as long as the expected revenue from mining is higher than the associated costs:
$$\begin{aligned} \text{mining rewards} + \text{transaction fees}&= \text{tot. mining revenue} \\&\ge \text{tot. mining costs} \\&\ge \text{tot. energy consumption}\times \text{min.electricity price.} \end{aligned}$$
A few easy manipulations yield the desired upper bound:
$$\begin{aligned} \text{total power consumption}\le \frac{\text{block reward} \times \text{coin price} +\text{transaction fees}}{\text{avg. blocktime}\times \text{min. electricity price}}. \end{aligned}$$
(2)
As hardware costs represent a substantial part of the costs side, and electricity prices vary significantly around the globe, we cannot assume that the upper bound is very tight. The block reward, i.e., the number of cryptocurrency coins one receives for solving a puzzle, the price of a coin, and current transaction fees are, again, publicly observable for every PoW cryptocurrency, meaning that only sensitive number which has to be estimated is the minimum electricity price. De Vries (2018), for example, argues that \(0.05\,\tfrac{{{\text{USD}}}}{{{\text{kWh}}}}\) is a reasonable lower bound for electricity prices. This gives an upper bound of approximately 125 TWh per year for the energy consumption of Bitcoin, using data from Coinmarketcap (2020) for 2020-02-05.
We repeated the calculation of the lower bound (1) and the upper bound (2) for the remaining 4 PoW cryptocurrencies with market capitalization of at least 1 billion USD. Figure 1 displays the resultant ranges for their respective energy consumption:
We see that the lower and upper bounds are, in general, quite close and, therefore, represent a meaningful estimate of the actual energy consumption for each of the 5 major PoW cryptocurrencies. A manifestation of this fact could be observed when in the course of a general drop in financial markets due to the Corona pandemic, market prices for Bitcoin dropped by up to 40% in March 2020. This implies a drop of the upper bound (2) in our model by the same rate, and, indeed, the total hash rate was observed to drop by approximately 30% shortly after: Seemingly, mining was no longer profitable for some miners at this point (Beincrypto 2020). This incident also illustrates that the upper bound is highly sensitive on the economic circumstances: Assuming that electricity prices dropped by the same rate as the prices for cryptocurrencies – which is in fact conceivable in an economic crisis – the upper bound (2) would remain unchanged. On the other hand, if electricity prices generally dropped by 50%, e.g., due to decreased demand or increased feed-in of renewables, or a rush for cryptocurrencies led to an increase of their prices by 100% and, therefore, to a level that we have already observed by the beginning of 2018, our upper bound would double in each of the scenarios, and even quadruple if both happened to occur at the same time. Consequently, we learn that we cannot take for granted that the given upper bound holds forever; it merely represents a snapshot for the current economic situation.
We also observe that the expected energy consumption of the 5 investigated cryptocurrencies strongly correlates with their market capitalization, which makes sense since parameters, such as block reward per time, are comparable among the cryptocurrencies and total transaction fees are generally low compared to block rewards. Moreover, the total market capitalization for all other PoW cryptocurrencies is significantly lower than that of Bitcoin itself. This indicates that the total energy consumption of all PoW cryptocurrencies other than Bitcoin will fall below our upper bound for the energy consumption of Bitcoin. A more precise estimate could be obtained by applying (2) to all remaining PoW cryptocurrencies. This would, however, be a tedious task, as one would have to collect specific parameters, such as block reward and average block time, for each PoW cryptocurrency, of which there are currently more than 1000.
In both estimates, we have, so far, only taken into account the energy consumption involved in mining, i.e., solving the cryptographic puzzles, and neglected the energy consumption of the other tasks which have to be performed on the participating nodes, mainly, validating new blocks and updating their local databases accordingly. This is, in fact, a reasonable approximation: for the lower bound, we only lose some tightness. To justify the validity of our upper bound, we argue that the energy consumption associated with maintaining the nodes, mining excluded, is, in fact, negligible compared to the energy consumption of mining for today’s major PoW blockchains: To validate a single block in today’s cryptocurrencies, every node must typically download up to a few Megabytes of data and perform as many as several thousand hash computations, as well as a comparable number of corresponding computations and database operations. For example, in a 1 MB block used in Bitcoin, there can only be a maximum of around 2000 transactions. These are the leaves of the Merkle tree and, therefore, give a total of 4000 hash value computations and a similar number of corresponding database manipulations and signature checks. By comparison, finding a single block currently involves around \(10^{23}\) hash computations to solve a puzzle in Bitcoin, around \(10^{20}\) hash computations for Bitcoin Cash and Bitcoin SV, and around \(10^{15}\) hash computations for Ethereum and Litecoin. Even for a million nodes – and taking into account differences in efficiency between common and specialized mining hardware, given that ASICS can be millions of times more efficient than CPUs at computing hashes – the energy consumption associated with mining is still orders of magnitude higher than the energy consumption required to maintain the nodes (De Vries 2018).
At this point, it is important to emphasize that further increasing the energy efficiency of mining hardware would not reduce a PoW blockchain’s energy requirements in the long term: To keep the average time for solving a puzzle constant, and, hence, to ensure the security and constant functionality of the network, the difficulty of the cryptographic puzzles is periodically adapted to the total computing power of the network. Since energy costs outweigh hardware costs in the long run, participants with improved hardware can solve more puzzles at the same energy costs. Other participants have to follow suit with the competition. This, in turn, involves higher overall computing power, and means that the difficulty of the puzzle needs to be increased so that it is, on average, solved as frequently as before. Hence, it is only in the (short-term) conversion phase that positive effects are conceivable. In fact, competition in the mining hardware market, resulting from the hype around cryptocurrencies, has dramatically increased the energy efficiency of mining hardware in the last decade. In the long term, it is to be expected that even with groundbreaking innovation in the energy efficiency of mining hardware, Bitcoin’s and other PoW blockchains’ energy requirements will remain at the previous level unless the remaining economic quantities on the right-hand side of (2) change considerably.
Closing Notes on the Energy Consumption of PoW Blockchains
In summary, our lower and upper bounds represent different approaches and use different quantities that have to be estimated. Yet, these bounds are very consistent in the case of all of the cryptocurrencies we investigated. For example, we determined electricity consumption to be between 60 and 125 TWh per year for Bitcoin. This is in the range of the annual electricity consumption of countries such as Austria (75 GWh) and Norway (125 GWh). However, as cryptocurrencies currently process only few transactions per second, the theoretical limit is typically in the low two- or three-digit range, e.g., approx. 15 for Ethereum and Bitcoin and 100 for Bitcoin Cash. This is primarily determined by the parameters ’average block time’, ’minimum size of transactions’, and ’maximum block size’ (Georgiadis 2019). Accordingly, a single transaction currently requires enough electrical energy to meet the needs of the average size German household for weeks, or even months. By contrast, traditional payment systems process, on average, thousands of transactions per second, and as many as tens of thousands at peak times. In their publication in “Nature Climate Change”, Mora et al. (2018) extrapolate the energy consumption of a single Bitcoin transaction to the order of magnitude required for handling payments on a global scale. They claim that if Bitcoin were to handle the number of transactions required by a worldwide payment system, the associated emissions alone would lead to a global temperature increase of 2 °C in the coming decades. However – as has already been pointed out in a critical ’Matters Arising’ response by Dittmar and Praktiknjo (2019) – when increasing the blocksize and, therefore, the throughput, according to our previous arguments, the energy consumption associated with mining would remain constant, and the energy consumption associated with the remaining tasks would still be negligible. This means that, overall, there would be no noticeable increase in total energy consumption. This argument is, however, based on the assumption that the economic quantities from the estimate of the upper bound (2), namely, the prices for electricity and the respective cryptocurrency, remain constant.
In practice, however, the blocks cannot be enlarged at will. While in Bitcoin Cash, for example, the blocksize has been increased by a factor of 8 (compared to Bitcoin) without any problems, a significantly larger block size is currently not practicable. This is because, the larger a block is, the longer it takes for it to be propagated by the worldwide blockchain network. This can have a negative effect for latency (the time it takes to distribute a new block to all nodes) and, also, security: More solutions to the puzzles are likely to be found as a certain block propagates through the network, splitting the honest miners’ resources and, therefore, leaving the network more vulnerable to attack. Moreover, not every household can afford a high bandwidth and large hardware storage, so higher requirements can also lead to a lower degree of decentralization. This trade-off has already been discussed, e.g., in Bitcoin Magazine (2018). If, however, storage capacities (hard disks) and network speed continue to improve worldwide, a considerable increase in block sizes might be conceivable in the future. This would enable higher transaction rates without a noticeable increase in energy consumption.
Finally, for most PoW blockchains, the block reward is not constant, but periodically halved, typically, every few years. Since mining fees are currently negligible compared to block rewards, the upper bound (2) is proportional to the electricity price and block reward. Hence, if the prices for crypto-coins and electricity prices remain at the same level, one could even expect that in the long run, the energy consumption of PoW blockchains will also halve in each of these periods, until the rewards from mining are comparable to the total transaction fees.
We conclude that, although the energy consumption of PoW blockchains is arguably enormous in relation to their technical performance, it does not represent an essential threat to the climate, even if significantly more transactions are processed in the future. Moreover, since the area of application of most blockchains – and, in particular, the major cryptocurrencies – is often far beyond payments, plenty of opportunities for new ecosystems and business models arise. An evaluation should therefore not only compare performance metrics and energy consumption, but also take into account the unique opportunities offered by this technology.