[MiWDesktopHack]

In practice you would need far more than 50% of the mining power to take complete control of the blockchain.

The greater the hashrate of your miners, the greater probability that your miners will find a valid nonce that satisfies the difficulty equation; it doesn't magically give you the ability to find a valid nonce before any other party. As long as there is one other party mining, there is a non-zero chance that their block will be accepted before yours.

What ratio of malicious/non-useful blocks vs valid, legitimate BTC transaction containing blocks would be required before the economy fails, that is an open question.

[mrb]

I think what you mean to say is that you need to match the performance of the current network. But this would put you at 50% of the global mining speed. For example the current network mines at 20 Thash/s, so you need to bring another 20 Thash/s for a majority attack, in which, an attacker can do the following: https://en.bitcoin.it/wiki/Weaknesses#Attacker_has_a_lot_of_...

Anyway, Titan is not powerful enough to perform a majority attack. First of all, there is no Bitcoin miner optimized for the latest GK104/GK110 Tesla and GeForce GPUs. With current miners, people report speeds of barely 110 Mhash/s on the GeForce GTX 680, which should translate to ~140 Mhash/s on the Tesla K20X (which is only 30% faster in terms of 32-bit integer ops per second.) Titan has 18688 K20X, so that's only 2.6 Thash/s total. Far from the 20 Thash/s required. It would still bring 400 coins/day, or $5600/day :)

I theorize here [1] that based on the number of ALUs and clock frequency, that a properly optimized miner should be in theory 4x-6x faster than this on GK104/GK110, bringing Titan to 10-16 Thash/s. (Nobody bothered optimizing Nvidia because everybody is mining on more efficient Radeon GPUs or FPGAs.) Still not enough to match 20 Thash/s. Disclaimer: I have only programmed AMD GPUs, never Nvidia. Maybe there is a reason this 4x-6x theoretical perf gain has never been realized, such as the inability to execute 1 32-bit integer instruction per ALU per clock due to instruction latencies greater than 1 clock, or throughput being less than 1 instruction per clock... I don't know. Theoretical FLOPS numbers published by Nvidia indicate that floating point instructions, as opposed to integer instns, can run at 1 instruction per ALU per clock. Which makes it even weirder that there would be such a huge perf gap between int and fp.

[1] https://bitcointalk.org/index.php?topic=129292.msg1381510#ms...

[0x0]

That's for one attempt, right? How often are the nonces found?

[MiWDesktopHack]

The bitcoin algorithm adjusts the difficulty so 2016 blocks are generated in 2 weeks, so a nonce is found every 10 minutes or so.