It's interesting to understand how SHA-256 and other similar functions work. Creating ambiguity through XOR functions means you get the same answer reducing the private key but in reverse you don't know where to look because the information has been lost. One grain of sand from all the sand on all the beaches.

What I don't know anything of is what quantum computers do that's different beyond fuzzy logic. I can't immediately see a way that the answer would magically appear even then. I'm also not sure why the military recommends a move to SHA-3 - and I've yet to find an ABC description of that function but it would be interesting to see the difference.


Edit: ignore this above.. keys are more about ECDSA