my sense is that the literature already knows how to break RSA-1024 given enough compute
"given enough compute", we can break any crypto just with pure bruteforce, although in practice I believe there's a point at which the amount of power that would be required becomes physically impossible due to the limits of computation within the universe (i.e. Moore's Law will definitely end sometime). To me, that says using extremely large hash sizes can keep things quite secure - even attacks that reduce complexity by many orders of magnitude could be impossible in practice - e.g. a 2048-bit hash for which a 2^500 complexity attack is found won't be any less practically secure.
...unless we somehow discover that P = NP, in which case the world could become a very interesting place...
"given enough compute", we can break any crypto just with pure bruteforce, although in practice I believe there's a point at which the amount of power that would be required becomes physically impossible due to the limits of computation within the universe (i.e. Moore's Law will definitely end sometime). To me, that says using extremely large hash sizes can keep things quite secure - even attacks that reduce complexity by many orders of magnitude could be impossible in practice - e.g. a 2048-bit hash for which a 2^500 complexity attack is found won't be any less practically secure.
...unless we somehow discover that P = NP, in which case the world could become a very interesting place...