Which paper are you referring to?
The paper I linked to earlier in this thread,
paper and
discussion thread.
Double spending can be seen like this. How much money is your attacker willing to spend on hashing? How much hashing can they buy for that money?
If we come to the point that we're thinking in terms of the cost per gigahash then we already lost because the amount that can be at stake would be only linear in the number of confirmations, and double spending will be trivial.
Our only hope is if the attacker cannot obtain more than a certain total hashrate, and if that is low enough (as a portion of the network total), his probability of success will be low (exponentially decreasing in the number of confirmations). That will place a
real cost on double spending.
Also, if the attacker successfully double-spends, he
also gets the normal block reward (coinbase + tx fees) for the blocks he found in the process. Assuming the cost per gigahash is predictable, it should also be about equal to what you would get on average in rewards. In this case there is
no cost to double spending (if success is guaranteed). So again there is real hope only if the probability of success is low, and some small hope if the attacker can only secure the needed hardware at above the "normal" cost.