What would happen if someone implemented a peer to peer currency exchange, as outlined here?: http://www.youtube.com/watch?v=mD4L7xDNCmA&feature=youtu.be&t=24m57s

edit: a text description: https://en.bitcoin.it/wiki/Ripple_currency_exchange

An attacker with 25% capacity might be able to notice a tie and then continually exploit it by causing subsequent ties. He could connect to every node so he's aware of exactly when someone else finds a block, and send out his own at that time (he has found one by now with p=0.5), to generate another tie. So, the probability of him generating n blocks in a row would be (1/2)^n; e.g. he'd have a 1/4 chance of controlling two blocks in a row.

How many blocks does an attacker need to generate in a row in order to cause trouble?

From Satoshi's paper (http://bitcoin.org/bitcoin.pdf):


In the event of a perfect tie, 50% of the honest nodes would be working on one branch, and 50% on the other. That means an attacker with only 25% of the power would have a 50% chance of choosing the next block. The false block would break the tie, and all the honest nodes would now work away at the new longest chain (the one with the false block). An attacker might even be able to detect ties, and thus know when to try to attack.

The frequency ties, and how evenly computational power is split during a tie, probably depend on the specifics of the gossip protocol. I don't know how often they happen in practice.

I'm a bitcoin newb, so this might not actually be a weakness -- if it's not, I'm interested in knowing what I don't understand!