Searching (who am I kidding, crack) private keys using FPGA and mining chips
It is amazing, that Satoshi thought about it:
Back in 2010, someone is asking ...
Although extremely unlikely, what would happen if two Bitcoin clients generated the same Bitcoin address? Would payments be delivered to whichever client encountered the payment first? If there is a mechanism in place to prevent such collisions, please explain it.
And Satoshi is answering ...
...
If you were to intentionally try to make a collision, it would currently take 2^126 times longer to generate a colliding bitcoin address than to generate a block. You could have got a lot more money by generating blocks.
...
Satoshi is not saying that it will remain impossible.
Thus, mining abandoned addresses is more profitable than mining new coins. Over time, the situation will change in this direction IMHO.
WBR, Ossy.