Equilibrium 51% Attack Cost of Bitcoin Network

Rich Jones rich at openwatch.net
Sun Aug 25 15:25:37 PDT 2013


Nifty little tool showing the estimated cost of controlling the majority of
the Bitcoin network:

https://www.resallex.com/bitcoin/brix

Would love to see something similar for the Tor network - my guess is that
the cost there is probably at least an order-of-magnitude lower, but that's
just my intuition.

R

>From the site..

> Introduction
>
> *Equilibrium 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.
> Method This 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.
>  Assumptions
>
> This 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%.
>
>
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