It appears that they are finding the private keys for transactions that already occurred. Reusing an address is not part of Bitcoin's design and it was never intended for people to do that. By not reusing addresses (not reusing private keys) I think one would be immune to this attack. The article doesn't seem to have much detail; anyone have more detail on this? Edit: The details are in the URL posted by alphydan; it…
To receive anything, you must have an address (the public key). All coins (UTXO) are associated with addresses which must have private keys. It's impossible to only have a public/private keypair for the instant a transaction is being made because the UXTOs must be owned spendable by some public/private keypair while a transaction containing them is not immediately happening. You clearly don't understand what you're t…
edit: Though unrelated to this article, here is a case where address reuse (and software bugs) led to vulnerable wallets: http://www.nilsschneider.net/2013/01/28/recovering-bitcoin-p...