The price of a 51% attack : Bitcoin

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The price of a 51% attack : Bitcoin

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TL;DR The core design of the mining network means the cost to destroy Bitcoin is always roughly equivalent to the total transaction fees paid by users. This cost is likely to be relatively cheap for any sufficiently motivated government or corporation who feels threatened by Bitcoin.

The 51% (or more accurately, >50%) attack is generally accepted as a method an attacker could use to prevent confirmations for all Bitcoin transactions, as well as a few other benefits. Obviously, the inability to confirm transactions would be pretty detrimental to the network, so preventing such an attack is a big deal.

The standard wisdom (which originated in Satoshi's original paper) is that anyone able to gain 51% of the network's computing power would make more money using it to mine legitimately than blocking transactions or double spending their own, so such an attack is unlikely. However, national governments and competing payment processors are likely to care more about protecting themselves than the amount of money they could make mining, so it needs to be sufficiently expensive in order to prevent them from doing so.

Assuming the mining market as a whole will not operate at a loss (or at least, not very much of a loss), it stands to reason that the amount of money miners will spend mining will be roughly equal to or less than the amount of money they get out of it. The total amount of money they get out of it is exactly equal to the block reward + transaction fees. Since the block reward is phased out over time, the reward will eventually be only the transaction fees. Thus, the total amount of money spent on mining will be roughly equivalent to the total amount of money generated by transaction fees.

Since a 51% attack requires half of the mining power, you would need to match the current network hashing power plus a little more. From above, we know the cost to do this is roughly equivalent to the transaction fees paid by all Bitcoin users.

Currently that cost is ~40 BTC/day (see: http://blockchain.info/charts/transaction-fees), or ~$750/day at current exchange rates. Naturally, this is rounding error for any national government or multi-billion dollar corporation, so hopefully it grows much larger before the block reward goes away.

But how much larger can it really get? In the best case scenario, Bitcoin could replace all monetary transactions in the world, which would generate some pretty substantial transaction fees. But how substantial? Visa makes only $2B/year and they are one the world's largest payment processors. Let's say Bitcoin, instead of the promises of low transaction fees, ended up generating the same rate as Visa (~2-3%ish) but on a scale 10 times larger, so $20B/year. $20B was less than 1% of the US Government's budget for 2012.

Realistically, it won't take anywhere near that. You can currently own the Bitcoin network, block rewards and all, for $8 million worth of GPUs. Only $600k worth of ASICs. That's not very comforting math for a network that has a market cap of $200 Million. We can keep hoping that it grows faster than its enemies attention, but the highest imaginable ceiling (~$20B/year equiv) is still pennies for its largest enemies.

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