Maybe I was not clear enough.
By "cracking hashes" or "destroying Bitcoin from the inside" I mean... guessing all or as many as possible Bitcoin private keys out there. (And therefore unlocking all addresses out there, including, for example, hacking into Satoshi addresses)
I don't understand exactly how mining works but I assume it generates something different than private keys?
You cannot use a miner to crack Private Keys, because to crack private keys you have to have an input string that changes over iterations, but mining ASICs are not designed in this way... right?
So based on this, my question is, what if someone designs an ASIC specifically to crack Bitcoin Private Keys? Is this even possible?
We have a new trend rising, of quantum computing, if someone is able to combine quantum computing in an ASIC way, this may generate much much more than 1 TH/s... like 1 Million TH/s or even more.
But if you are telling that people can use miners to crack Bitcoin Private Keys, then my question is different: How long until everything falls apart?
If this were possible somebody would have already done it and Bitcoin would be dead. So you probably want to know why it's not possible. And by not possible I mean extremely extremely unlikely.
Mining (sha256 hash operation) has nothing to do with private/public keys calculations (an ECDSA operation). So 1THs miners cannot try 1 trillion private keys each second. But even if they could it would take him literally from the beginning of time until now (since the Big Bang) to crack one single Bitcoin address.
http://bitcoin.stackexchange.com/questions/2847/how-long-would-it-take-a-large-computer-to-crack-a-private-keySo even if you had a million of these machine (that by the way do not exist yet) it would still take you a dozen or so million years.