What is wrong with my math?

[RixiM]

Total BTC: 6,533,850 BTC
Market Cap: 124,139,230 USD
Network Hashrate: 6446.52 Gh/s
(Source: http://www.bitcoinwatch.com/)

Most cost effective GPU:
Radeon HD 5830
Hashrate: 244 Mh/s
price: $109.99   
(source: http://bitminer.info/)

from here we can do some hand-waving estimates:

Market Cap / cost of GPUs = worth of network in GPUs
$124139230.0 / $109.99 = 1128641.0582780254

so if you took the market cap of BTC and just bought one type of GPU with it you could buy 1,128,641 GPUs. Fair enough that’s more Radeon HDs than what’s available…
 …but that number is actually rather meaningless. How many GPUs would it take to have ~%50 of the network hashes?

network hashrate in Mh/s: 6446.52 * 1000 = 6446520.0
6446520.0 / 244 = 26420.163934426229

whoa.

So it would only take 26,421 GPUs to attempt the  > 50% attack?

In other words it would take an investment of $2,905,953.83 to destroy the BTC network which has a market cap of $124,139,230?

Let’s assume that the GPUs are half the total cost of operating a rouge BTC network for the duration of the attack. That means that for around $6 million dollars an institution could pretty much break the BTC network. Since the unit of this attack is GPUs isn’t the scaling of the hashing irrelevant? isn’t the cost of this attack based on the price of BTC at the time of the attack more than anything else?

Am I missing something?

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[Alex Beckenham]

In other words it would take an investment of $2,905,953.83 to destroy the BTC network which has a market cap of $124,139,230?

From my understanding it would not destroy it, but rather, temporarily disrupt it.

[dr_nix]

Interesting numbers. I think it can mean this attacker can do a few things:

They can generate way more than 50 BTC per block. But then the 'normal' clients will ignore the block chain generated by the attacker as the blocks don't follow the rules. This may be an annoying attack, but the 'normal' blockchain would still be generated in the background as normal.

The wiki https://en.bitcoin.it/wiki/Weaknesses lists some things that he can do while following the rules: (section "Attacker has a lot of computing power")

• Reverse transactions that he sends while he's in control
• Prevent some or all transactions from gaining any confirmations
• Prevent some or all other generators from getting any generations

Maybe someone else can elaborate on how much impact these things have, in the short and long term.

[riX]

• Reverse transactions that he sends while he's in control
• Prevent some or all transactions from gaining any confirmations
• Prevent some or all other generators from getting any generations

Maybe someone else can elaborate on how much impact these things have, in the short and long term.

The two last attacks only applies when the attacker have much more than 50%.
If he has 90%, he will of course get 90% of blocks as anyone not attacking the network although having 90% should.
Having 90% and not including other peoples transactions just means that they will have to wait 10 times longer for confirmations.

The only attack feasible is the first one, but it gets harder and harder for every confirmation.
If he has 50% of the network, he has 50% chance to reverse a transactions if he starts to reverse it immediately after it's sent. He can then continue on that fork, generating faster than all the others, making it the longest chain.
However, if he waits another confirmation before starting the attack, he has to generate two blocks in the time it takes for the rest of the network to generate one, so he'll need 67% at first, which gives him 50% chance to catch up with the real chain having two more blocks, and only after succeeding to create the two attack blocks he can sustain his chain with >50%.
For attacking three confirmations he'll need 75%, for four confirmations 80% etc.

For n confirmations he'll need n/(n+1) of the network (n times all the others).
Having x times the hashing power of the rest of the network gives him a x/(x+1) chance of succeeding.


EDIT:

As for generating more than 50 BTC/block, that would create a fork, no one else would include those blocks in their local blockchain.

[dinzy]

Is that the actual total hashrate?  Interesting.

Also I am not sure I buy that the 5830 is the most cost effective GPU.  Initially yes, but in terms of other resources and opportunity costs, it depends on the actual value of BTC and the amount of time over which they are mined.