We've spent some time developing a way to measure the cost to 51% attack the Bitcoin network under an equilibrium model in real time. It's a bit heavy on economic theory, but we believe it is the most accurate way to measure the costs involved (and the only way to do it in real time). Please let me know if you have any questions.
You can check it out at:
https://www.resallex.com/bitcoin/brixIntroductionEquilibrium 51% Attack Cost: This is a metric attempting to calculate the total present value cost required to attack the Bitcoin network through majority hashing power (51% attack). The metric is meant to be viewed as a snapshot in time as if an attacker decided to invest in attacking the network under the current conditions.
BRIX Score: "Bitcoin Robustness Index" - The relative rank of Bitcoin's 51% attack cost compared to annual military expenditures among all nations.
MethodThis metric is, in essence, equal to 51% of the present value ("PV") of all future revenues derived from bitcoin mining using current Mt. Gox prices. Revenues include both block rewards and transaction fees. The purpose behind using PV as a measuring tool is to approximate the incentives to miners to build upon the Bitcoin network. The measure can be viewed as an aggregate of all the cost-benefit analyses done by individual miners. We believe this is superior to other methods of calculating the attack cost, including variables such as current hash rates and current capital costs, because the model is independent of technology advancements. Under the equilibrium model, miners will continue to invest in equipment until they reach the point where marginal cost equals marginal revenue (the point of profit maximization). Under perfect competition (of which bitcoin mining is effectively), this point will also be where aggregate cost equals aggregate revenue. If we assume the variables that can affect mining revenue are held constant ($/btc & transaction fees), then it is easy to calculate aggregate revenue and therefore also aggregate cost. Since we know aggregate revenue equals aggregate cost, by calculating 51% of aggregate revenue we effectively calculate 51% of the aggregate cost to miners.
We calculated this metric by discounting each block reward (210,000 blocks) as if it were an annuity and then discounting it further to its present value. Then, we added estimated transaction fees based off historical records.
AssumptionsThis metric is meant to represent a model at equilibrium. Therefore it represents a snapshot of 51% of the incentive to miners at the current price and current transaction fee levels. The idea is that miners are willing to invest in the network as long as it is profitable to continue doing so. We assume the following:
Rational Actors: We assume all mining participants are rational actors and strictly pursue profit maximization. We ignore all other motivations, including political, emotional, and reputational. All other heuristics and biases are ignored.
Static Variables: We assume that the variables in the model are static, and therefore represent a 'snapshot in time'. There are no growth forecasts for either price or transaction fees.
Perfect Competition: We assume that all miners and potential attackers have access to the same technology, resources and information. There is no technological advantage for any party that would exclusively decrease mining costs or otherwise acquire mining equipment faster.
Discount Rate: 8% Our model discounts future cash flows by 8%.