Network size and the cost benefit of an attack

The formula can be rearranged to work out the maximum price of safecoin for a specific network size before an attack becomes viable. Yes - ensuring security means there is a maximum possible value for the price of safecoin (probably something of interest to those in the price and trading topic).

SP = (NS^2 * Q * VC) / (TC * VPS)

For example, assuming the same parameters as the original post ($1 lifetime cost per vault, 50 vaults per section) a network with 5M vaults could support a maximum safecoin price of $58.21 before it would be viable to attack the network.

This also works in reverse - if the network is very large it means a high safecoin price can safely be sustained, but if the network is small a high price can become dangerous.

If the price suddenly rose it would allow existing operators to increase the size of the network and hopefully prevent an attack becoming viable. Sort of a nice self-reinforcing mechanism there, albeit also sort of centralising.

If an attack were to happen and all the stolen coins suddenly sold it would reduce the price, possibly to the point an attack is no longer viable. But perhaps this is extending the concept a bit too far! Regardless, market depth is another important factor in the success of an attack since it decreases the benefit to the attacker during a large rapid sale.

The boundary between viability somewhat indicates a model for growth. If price goes up above the boundary into viable attack territory, network size should increase to bring the attack back to non-viability. If price goes up again above the boundary, the network should increase in size again.

Maybe price manipulation will have important consequences for the security of the network? Maybe the security model will end up naturally damping price manipulation (wouldn’t that be fascinating to take to the financial regulatory bodies)? Nobody can know exactly how the price and security will interact, especially during bear markets, but it will be very interesting to see since they are closely related.


Some more notes on the depths of complexity if this model were to be taken further

  • safecoin price is not a fixed value. Market depth would affect the price as coins are sold. There’s also a time risk, where attacker coins want to be sold quickly but the faster they sell the more they impact the market. Safecoin price is also not just exposed to market depth, there are also arbitrary market conditions such as bitfinex speed bumps or mtgox security flaws, not to mention AML / KYC hurdles to manage.

  • quorum is only formed by elders, not by all vaults in the section, so age distribution of attacking vaults vs other vaults must be accounted for in lifetime vault cost.

  • safecoin quantities are not evenly distributed by section. Section prefixes may differ in length which means sections will each be in charge of different numbers of safecoins. An attacker may get lucky and be part of a section with relatively more coins or be unlucky and in a section with relatively less coins. This adds uncertainty to the value for safecoins per section, which affects the benefit obtained from the attack.

  • age distribution is not even across sections. In some sections the attacker may only require very old vaults to obtain quorum but in others they may require relatively young vaults. This adds uncertainty to the lifetime vault cost.

  • vaults are not evenly distributed through every section, so the attacker may have many vaults in one section and none in others. This affects the total attacking vaults required to obtain quorum, usually resulting in a lower total number of attacking vaults (see the birthday paradox thread as posted by @drehb above).

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