Even if a bad guy does overpower the network, it's not like he's instantly rich. All he can accomplish is to take back money he himself spent, like bouncing a check. To exploit it, he would have to buy something from a merchant, wait till it ships, then overpower the network and try to take his money back. I don't think he could make as much money trying to pull a carding scheme like that as he could by generating bitcoins. With a zombie farm that big, he could generate more bitcoins than everyone else combined.

The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.

We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent.

A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.

If a merchant actually has a problem with theft, they can make the customer wait 2 minutes, or wait for something in e-mail, which many already do. If they really want to optimize, and it's a large download, they could cancel the download in the middle if the transaction comes back double-spent. If it's website access, typically it wouldn't be a big deal to let the customer have access for 5 minutes and then cut off access if it's rejected. Many such sites have a free trial anyway.

When a node receives a block, it checks the signatures of every transaction in it against previous transactions in blocks. Blocks can only contain transactions that depend on valid transactions in previous blocks or the same block. Transaction C could depend on transaction B in the same block and B depends on transaction A in an earlier block.

The Bitcoin network might actually reduce spam by diverting zombie farms to generating bitcoins instead.

To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back's Hashcash, rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.

I'm sure that in 20 years there will either be very large transaction volume or no volume.

Then you must also be against the common system of payment up front, where the customer loses. Payment up front: customer loses, and the thief gets the money. Simple escrow: customer loses, but the thief doesn't get the money either. Are you guys saying payment up front is better, because at least the thief gets the money, so at least someone gets it? Imagine someone stole something from you. You can't get it back, but if you could, if it had a kill switch that could be remote triggered, would you do it? Would it be a good thing for thieves to know that everything you own has a kill switch and if they steal it, it'll be useless to them, although you still lose it too? If they give it back, you can re-activate it. Imagine if gold turned to lead when stolen. If the thief gives it back, it turns to gold again. It still seems to me the problem may be one of presenting it the right way. For one thing, not being so blunt about "money burning" for the purposes of game theory discussion. The money is never truly burned. You have the option to release it at any time forever.