If I understood the paper correctly (I skimmed it very quickly), this is a timing attack that requires the attacker send a bunch of things to be signed
with the same ECDSA private key.
The good news is it they also give a patch to OpenSSL to fix it. The other good news is bitcoin only signs things with private keys when you send coins, and if you have the ability to ask bitcoin to send coins then we don't really care if you can get the private key.
We do have a patch in the "pull queue" that adds a RPC command to let bitcoin sign stuff ( https://github.com/bitcoin/bitcoin/pull/183
), but, again assuming I read the paper correctly, even that doesn't worry me, since if you have the ability to run that RPC command you could either go through all the trouble of the timing attack to figure out the private key... or you could just issue a "send" command to steal all the bitcoins out of the wallet.