Quote from: tromp on November 14, 2014, 05:28:54 PM

Quote from: gatra on November 14, 2014, 04:37:13 PM

All 400^k possibilities are very very likely to have less cumulative difficulty than the main chain, because 75% < 100%

You're not appreciating how the statistics work out here.

75% being less than 100% just means that the delay distribution is shifted to the right.
But sampling from a huge number like 400^k means you'll get much further into the left-tail
of this shifted distribution, so you can easily beat the unshifted average.

Ok, this is a different attack vector. The math is tricky and it's probably not worth it: we agreed that if you have that stake you can attack without hashrate!

still, for the sake of argument (http://xkcd.com/1432/):

ok, but each block is independent, you are in disadvantage on every block, and you want more cummulative difficulty after k blocks. On every block that you select any account of yours that is not the one with lowest delay, you get farther away from your goal expecting to offset that with "good luck" in following blocks. With a large sample you can expect to get lucky, but on each block that you don't use the optimal (minimal delay) account you need even more luck to catch up.
I still think that beating the unshifted average is not that easy and it could happen that in all your branches you end up with less cummulative difficulty. In NXT the target gets larger as time since last block passes by, so doing a simulation would be much easier than calculating. Still, my point is: if you have that stake you can attack without hashrate!

Regarding the other attack that someone posted a link to: they mention bruteforcing the private key in order to get a public key that will forge in the future. You can forge 1440 blocks after setting the public key, and you can't reorg more than 720 so it doesn't work. If you remove that limitation, yes, it's an attack that requires big amounts of hashrate.

So, I concede there are attacks that utilize lots of hashrate. However, I'll say it again: if you have that stake you can attack without hashrate!