Notes on 51% attacks: Symmetric Cost Principle and 51% attacker’s equation

Symmetric Cost Principle

Offense and defense in a POW blockchain is symmetrical. The action required to keep a POW blockchain secure, is the same action required to attack it. That action is mining. Further more, any adversarial activity will be met with resistance. Using current hashrates to estimate the cost of a 51% attack (such as this site) ignores the important fact that additional hashrate could be brought online to resist a 51% attack.

By recognizing 51% attacks as a game fought between two opposing forces, we can make a general rule that applies to all POW blockchains regardless of the hash rate called the Symmetric Cost Principle. The Symmetric Cost Principle states that: The cost that a 51% attacker must incur to succeed has to be more than the cost that the defender will bare in order to prevent it.

For an attacker, the important question is what is the cost that the defender will bare? First, we need to understand that there are a variety of reasons a 51% attack might be performed. I will separate them into two broad categories: global and local.

Global 51% attacks affect most or all users of a POW blockchain. Objectives of a global attack could be to render the chain unusable forever. The cost of a global attack cannot be estimated by just the current total network hash rate because it does not take into account how many defenders there are and how much resources they are willing to expend in order to protect it. For an attacker, they can only guess who their potential adversaries are and how much they are willing to sacrifice to defend the chain.

Consider the case of Bitcoin, which currently has enriched its early holders with considerable wealth and has created an ideological and political foundation which is necessary for mass mobilization and organization. If an entity decided to 51% attack Bitcoin in order to completely destroy it, these people will not sit idly. People with older miners will bring them back online, massive amounts of commodity hardware could be mobilized, and additional ASIC’s could be manufactured to counter the 51% attack. In order to kill Bitcoin, the willpower and resources of the attacker must exceed that of the Bitcoin community.

Local 51% attacks affect a few, or a specific target user on a POW blockchain. The most common use of a local attack is to reverse a specific transaction and perform a double spend attack on a merchant. In a local attack, only a few individuals will be affected by it, and these individuals may not have the will power or resources to fight back against the attack. For this reason, the cost to perform a local attack is more likely to be dominated by a function of the current total network hash rate. Note that we are only saying that it’s “more likely” compared to a global 51% attack. The individual affected by the local attack could have significant resources to fight back against the attack depending on how rich or well connected the individual is.

In summary, the Symmetric Cost Principle gives us an intuitive and simple way to think about the likeliness of a 51% attack succeeding. Who does the attack affect, and what are the costs that the affected will bare in order to defend against the attack.

also see: Evan Voskuli’s Dedicated Cost Principle