Maybe I am just being thick today but have tried to comprehend this and I just don't. Could you please explain this system to me in very simple terms?
So you want to learn about
Elliptic curve cryptography is very simple terms? I'm afraid my understanding of the subject lacks a bit to achieve that.
What I can try to explain is the high level process here;
We created a list of secrets that will be disclosed for the next two hundred something years, one per hour. With these secrets and a little EC magic we can create a new public key from your public key and from there calculate a bitcoin address. With a little more EC magic we can calculate the private key to that bitcoin address by using the same secrets and the private key for the public key you provided.
This means that without disclosing a future secret (we call these timepoint secrets) we can calculate a bitcoin address from a public key you provide, but you can't calculate the private key needed to redeem the funds. We are also not able to calculate the private key, so the funds there are 'locked'. No one can access them.
When the timepoint secret is revealed you can, using the lbaat static calculator or some 3rd party tool (Armory allows for this, for example), calculate the future address private key using said secret and the private key for the public key you provided initially.
It's late and I'm not sure I made much sense, but you can read all the details at
https://bitcointalk.org/index.php?topic=128581.0 including a pretty graph. If you have more questions don't hesitate to ask, we'll do our best to explain.
This particular thread gives away a bunch of addresses that were created using the above process, and also discloses the private key to be used calculating the addresses' keys. You should not, obviously, disclose yours to anyone unless you intend them to redeem the coins when the time comes.
