Two Existential Threats to Bitcoin and a Protocol to Avert Them
By Daniel Aronoff, Massachusetts Institute of Technology
Bitcoin faces two, diametrically opposed and temporally divergent, existential risks. Today, the massive energy consumed by Bitcoin mining is a focus of a political backlash aimed at de-legitimizing Bitcoin and restricting its use as a payments system.[1] In the future, as the minting of new UTXO’s (the indicator of Bitcoin value, or BTC, held by an owner [2]) to reward miners decreases toward zero, the revenue from mining will likely shrink, causing miners to exit and energy consumption to contract. Since an attacker with more than 50% of the hashrate (which correspond to 50% of energy consumption) can gain control of the Bitcoin blockchain, the security of the network will be undermined by the low cost of an attack. In effect, Bitcoin’s energy consumption will be too low. Targeted Nakamoto (“Targeted”)is a modification to the Bitcoin protocol that is designed to avert these twin potential disasters.
Two Existential Risks to Bitcoin
Today — too much hashrate: The trend increase in energy consumed by Bitcoin miners — estimated to be on a par with consumption in mid-sized countries — increases energy prices and contributes to global warming.[3] The driving force is the increase in mining revenue that is due to the trend increase in the USD/BTC exchange rate.
Fig 1: Bitcoin Growth in Energy Consumption and USD Block Rewards
The Future — too little hashrate: Mining revenue comes from two sources; voluntary fees offered to miners as compensation for placing a transaction on a block and the minting of new UTXO’s — called the “coinbase” — that is algorithmically genrated by the protocol and paid to miners at each block. The volume of coinbase halves approximately every 4 years and eventually reaches zero, when 21 million UTXO’s have been minted. The implies that transaction fees will become the primary source of block rewards — eventually the only source — no matter how much more the USD value of BTC increases. Figure 2 shows, e.g. that in 2032 miners will receive 25% of the coinbase they were paid in 2024. To maintain the dollar value of coinbase, the USD value of Bitcoin will have to quadruple from its 2024 value.
Fig 2: Coinbase Halving Schedule
Historically, transaction fees per block have been fairly stable in terms of USD value. They have comprised less than 10 % of total block rewards on average and there is no assurance that transaction fees will increase in the future if the USD value of the coinbase declines. If the USD value of transaction fees do not increase to cover any shortfall in the 4 year doubling of USD Bitcoin value, miners will reduce hashrate, which will lower the cost of an attack on the network. Figure 3 shows the historical pattern whereby transaction fee share of the block reward mechanically spikes when the Coinbase is halved, and then declines as the USD/BTC exchange rate increases.
Fig 3: Transaction Fees as a % of Block Rewards
The Tradeoff — An increase in hashrate reduces network vulnerability to attack (a reduction in security cost) while increasing carbon emissions and electricity cost (an increase in externalities cost). This implies a tradeoff in total cost at different levels of hashrate and the existence of a hashrate interval where total cost is minimized. “Today” hashrate is too high, implying an excess of energy consumption above what is necessary to maintain network security. “Tomorrow” hashrate will likely be too low, implying that the cost of acquiring the hashrate to successfully attack the Bitcoin network will be inexpensive, thereby undermining network security. Figure 4 displays the tradeoff.
Fig 4: Tradeoff Between Network Security and Energy Externalities
A Solution
I recently published a paper Targeted Nakamoto: A Bitcoin Protocol to Balance Network Security and Energy Consumption https://arxiv.org/abs/2405.15089 in which I propose a modification to the Bitcoin protocol that addresses the two existential threats by incentivizing miners to home in on a hashrate target. It works like this; when hashrate is above target a ceiling is placed on the block reward a miner can receive. When hashrate is below target a floor is placed underneath the miner’s block reward.
Hashrate Control is the Key
The pathway from Bitcoin mining to energy consumption and cost runs through hashrate, which is the number of puzzle guesses (“hashes”) per unit of time that miners generate. The USD value of the block reward provides the miner’s incentive to assemble transactions into blocks and compete for the block reward by guessing puzzle solutions posed by the Bitcoin source code.[4] The higher block reward the higher will be hashrate. This implies that it would be possible to control hashrate by controlling the block reward paid to the miner.
To maintain Bitcoin as a decentralized protocol that only relies on information that can be read from the blockchain, two things must obtain to acheive this goal. One is that it must be possible to estimate hashrate from on-chain data. The other is that it must be possible to adjust the block reward in response to hashrate.
Hashrate can be inferred from the ratio of puzzle difficulty to blockchain growth rate. Let D denote puzzle difficulty (the probability of solving the puzzle for each guess), T denote the average time it takes for the first miner to solve the puzzle and N denote hashrate. Then D/T is a consistent estimate of hashrate. In the Bitcoin protocol, puzzle difficulty is increased when the block propagation rate over an epoch (2016 blocks) is a shorter time than 1 block every 10 minutes, which occurs when hashrate increases, and puzzle difficulty is decreased when the block propagation rate is a longer time than 1 block every 10 minutes, which occurs when hashrate decreases. Thus, D/T moves up and down with hashrate (see Targeted Nakamoto for details).
(1) N = eP/(c + k)
Equation (1) represents the equilibrium hashrate of the mining sector, where P is the total block reward in BTC, e is the USD/BTC exchange rate, c is the USD cost of running an ASIC for the average time between blocks and k is a competition parameter, which implies that Equation (1) is agnostic to the struture of the mining industry (0 under perfect competition and > 0 under imperfect competition). Replacing N with D/T on the left side of Equation (1) displays how the ratio of puzzle difficulty to block propagation time is related to the variables that determine hashrate (see Targeted Nakamoto for details).
The Hashrate Adjustment Protocol
Equation (1) shows that a movement of the block reward P up or down has the marginal effect of moving hashrate in the same direction, The Targeted protocol uses the ratio of puzzle difficulty to block propogation time, D/T, (estimated hashrate) as a signal to adjust the block reward to home in on a target hashrate interval.
The adjustment protocol is pictured in Figure 5. The endpoints of the target interval are denoted NUB andNLB, which correspond to signals D/T(NUB), D/T(NLB). They bound the puzzle difficulty target interval. An adjustment to the miner’s block reward above or below the total block reward is made after the end of each epoch when puzzle difficulty is adjusted. Epochs are numbered sequentially in temporal order, starting from 1. Epoch 1 includes blocks numbered 1 (Genesis) to m. Epoch 2 includes blocks numbered m+1 to 2m, and so forth. A ceiling is placed on the miner’s block reward when D/T is above the target interval. After a ceiling has been put in place, it is lowered at each subsequent adjustment block until D/T drops below D/T(NUB). Similarly, a floor is placed on the miner’s block reward when D/T is below D/T(NUB). When a floor has been put in place, it is raised at each subsequent adjustment block until D/T moves inside the target interval. When D/T is inside the target interval, if a ceiling is in place from the prior adjustment block, the ceiling is raised, and so forth until it is removed altogether. If a floor is in place from the previous adjustment block, the floor is lowered at the current adjustment block, and so forth until it is removed altogether. In the figure, hashrate is inside the target interval at the first adjustment block B1, so there is no floor or ceiling imposed. At block B2 hashrate is above target and a ceiling is placed on the block reward paid to the miner. At block B3 hashrate is still above target and the ceiling is pushed down. At block B4 hashrate has returned to the interval and the ceiling is raised. At block B5 hashrate is below the target interval and a floor is placed underneath the block reward. (see Targeted Nakamoto for the algorithm).
Fig 5: Mining Puzzle Difficulty Signal Switch Points
Monetary Neutrality
The adjustments to the miner’s block reward caused by the hashrate adjustment algorithm changes aggregate UTXO’s. On its own, this causes UTXO value to deviate from the Bitcoin money supply rule. A miner’s block reward that is below the total block reward causes a reduction in aggregate UTXO value, from the effect of a ceiling placed on the share paid to the miner. A miner’s block reward that is above the total block reward implies minting of new UTXO’s, which adds to total money supply.
Targeted maintains the growth rate of Bitcoin money supply by adding a new feature that adjusts the “spending potential” of owners of Bitcoin. The speding potential of an address with UTXO value is the UTXO value plus or minus an adjustment factor. When it is a plus, miners are instructed to add UTXO value to a transaction output of the address. The miner obtains he extra UTXO’s from a pool of UTXO value that is accumulated from deductions to miner block rewards. When it is a minus, miners are instructed to burn UTXO value from the transaction input.
Targeted achieves monetary neutrality in two senses; (1) The growth of aggregate UTXO spending potential adheres to the scheduled increase in UTXO’s in the Bitcoin protocol and (2) an increase or decrease in UTXO spending potential that is required to offset a subtraction from or addition to the total block reward is distributed among addresses in proportion to their ownership of UTXO spending potential. The mechanics of how this is done is somewhat intricate. It should be noted that the subtraction of UTXO value requires a hard-fork from the current Bitcoin protocol. The interested reader is encouraged to consult Targeted for the details.
Limitations
Targeted is a necessary, but not a sufficient part of a solution that averts the two existential threats. Two other elements are required for Targeted to perform its function. One is that the target hashrate interval must be identified. I do not claim special insight into where it should be located. As a practical matter it probably requires a consensus that will not be tightly tied to an empirical cost/benefit analysis, though I am hopeful that Targeted will stimulate people to begin thinking about this. The other element involves periodic adjustments to the hashrate interval to offset changes cost and environmental impact, which will shift the curves in Figure 1. A reduction in per hash enery cost induced by improvements in ASIC efficiency and/or reduction in electricity cost will shift the network security curve to the right. A reduction in per hash carbon emissions from an increase in the use of clean energy will shift the hashrate/energy externalities cost curve to the right.
These matters can be quantified and estimated, but they imply that the target hashrate interval will shift over time and will require an oracle (i.e. inforamtion that is not on-chain) of some sort to signal the shifts.
Conclusion
Targeted is motivated by two observations about Bitcoin. One observation is that there are costs which increase with hashrate — electricity and carbon emissions — and costs which decrease with hashrate — network security. These imply there is an interval of hashrate in which total costs are minimized. The other observation is that hashrate is a function of the value of the block reward, which is unbounded. The Bitcoin protocol does not provide an incentive for miners to avoid hashrate dropping to a very low level or reaching a very high level. Targeted incentivizes miners to home in on a target hashrate interval. This is achieved by imposing a floor to the miner’s block reward when hashrate is below target and imposing a ceiling on the miner’s block reward when hashrate is above target. Targeted achieves aggregate and distributional monetary neutrality. Aggregate monetary neutrality means that Targeted does not alter the UTXO spending potential of the network at any block. Distributional monetary neutrality means that the UTXO spending potential of addresses are adjusted to offset increases and decreases in the block reward in proportion to their UTXO value.
[1] The other focus are the illicit transactions that use Bitcoin as a means of payment.
[2] UTXO stands for “unspent transaction outputs”. In Bitcoin there are no BTC tokens. Rather, UTXO’s are sent from one address to another. BTC denotes a value of UTXO’s.
[3] For an overview of Bitcoin’s environmental footprint see
https://www.jbs.cam.ac.uk/2022/a-deep-dive-into-bitcoins-environmental-impact/
[4] The cost of mining is denominated in official currencies. I use USD since a significant portion of mining takes place in the US and the exchange rate between USD and other official currencies is relatively stable.
Targeted Nakamoto: was originally published in Coinmonks on Medium, where people are continuing the conversation by highlighting and responding to this story.