But if we somehow invent quantum ASIC, we may hack addresses.
Inventing a quantum computer to steal bitcoins?
Without knowing the public key is near impossible.
Having the public key, knowing the range, having a few million TB RAM, will cost millions to find. Hence the importance of distributing your coins across several addresses and discarding an address after the first transaction, addresses should be treated as dynamic pin numbers for credit cards, they are only valid for 2 minutes.
When someone makes a transaction, public key is revealed too. So, one can easily get list of bitcoin addresses with a lot of coins that had spent some coins at past.
In the words of Satoshi:
Sigh... why delete a wallet instead of moving it aside and keeping the old copy just in case? You should never delete a wallet.
Thanks for including original URL in quote. I just discovered that once upon a time there was a person who had 20-30% of the network's CPU power.
But I don't agree with the opinion that it's good to keep all of your used wallets. The more info you collect and save about yourself, more information will be leaked in case something bad happens. Though, this situation is highly individual to my mind.