Why would you need to "catch up" in the 51% attack?

Question

There is a lot of information on the 51% attack where an attacker is able to branch the chain and "catch up" and build a new branch that is longer than the old branch. Other than requiring more than 50% of the network's computing power, the biggest thing that makes this attack infeasible is that the further behind an attacker is, the harder it is to catch up. Some places say that this means that a payment receiver can simply wait for a couple of blocks to go by and by that time is becomes infeasible for an attacker to catch up from that far behind.

But why would an attacker ever have to "catch up"? Couldn't an attacker with 51% of the network's power branch the chain as soon as a new block is released and work on that branch in secret? Then at any point the attacker could publish his branch, effectively reversing any transactions that occurred between the time he branched the chain and the time it is published to the network.

Answer 1

You're exactly right; there's no need to catch up if you don't start off behind.

As soon as I get 51% of the network's hashing power, I start building my fork in private, then buy something on the 'real' fork and allow the purchase to get as many confirmations as it needs. It will be a lot, because I'll be buying something really expensive. I take care not to include my transaction in the private fork.

Then, once the goods are shipped I publish my secret fork and get my coins back.

The Finney attack is only good for double spending when the recipient accepts unconfirmed transactions.

Answer 2

The "catching up" is more a product of the theoretical scenarios posed than the technicals of the 51% attack itself. The typical scenario posed for a 51% attack is that the attacker has already spent coins and would like to reverse that transaction. In this scenario it makes sense that the attacker must start at least at the block before his/her transaction, meaning they must catch up with the network, hence the necessity of controlling at least 51% of total hash power - any less and they'll never catch up.

If someone weren't trying to reverse a transaction but rather wanted to double spend coins that hadn't yet been spent at all, they wouldn't need 51% of the network to do so; a Finney attack would suffice, hence scenarios in which the coins have not yet been spent tend to be considered for this attack vector instead.