Where and how is secp256k1 used within Bitcoin?

Bitcoin is unique that is uses secp256k1 to secure it’s transactions; and any cryptographic attack against this algorithm is probably going to be percieved as an attack against the bitcoin network.

Where is this algorithm used and in what manner is it used?

Does a low profit margin on mining reduce the integrity of the blocks stored in the transaction history?

As the mining Bitcoin payout decreases from 50 to zero, what incentive is there for miners to continue operating?

Is there a need for miners to continue to operate when the payout decreases to zero?

I thought part of the purpose of mining is to validate the Public key with the General Ledger that is replicated in P2P fashion between nodes. If the miners go away, will GL validation stop?

How do you import Block Chain from bitcoincharts?

I went to http://eu1.bitcoincharts.com/blockchain/ and downloaded the most recent build. Then I extracted it and was left with BLK0001.dat and BLK0002.dat. What is the next step? I tried replacing the current BLK files with those and performed a -rescan but that gave me a BLKINDEX error.

My wallet data was backed up by the way. Then I moved my BLKINDEX somewhere safe so it would have to create a new one but this process didn’t work because it’s building BLK0002.dat still. It was super fast until it reached about 70,000 blocks left and then majorly slowed down. What is the proper way to import it? Is there a special command-line parameter that I should use to fix this?

BTW: The whole reason I had to download it separately was because Bitcoin Wallet was taking forever to download the block chain and was stuck around 97% for an eternity!

EDIT: Why does this guy even provide this website (noted above) if Blkindex needs to be created anyways?

EDIT: I gave up and decided just to use multibit and blockchain.info my wallet. I found a way to store my blockchain address on multibit so I could view it there offline.

What is going to happen when it is totally infeasible to download the entire bitcoin transaction history?

As far as I know, the bitcoin system currently relies on the principle that all transactions are made by someone with access to the entire history of previous transactions. Since bitcoin’s public debut 2.5ish years ago, these records have stayed small enough that it’s still easy for one person to download and update it.

Once it gets large enough, though, it’s going to be hard to do that. When I ask most people about this problem they just tell me that eventually we will start trusting our money to some bank-organization-type-thing (e.g. Coinbase) and we won’t have to worry about the integrity of our records.

Imagine that in the distant future, the bitcoin system becomes widespread enough that the rate at which transactions history grows exceeds the rate of change in disk space technology. (far cry, I know, but let’s just assume a worst-case scenario.) How would bitcoin account for this problem?

Is a better, more widely agreed on solution?