OK, I'm sorry for the touchy response. But I still don't understand your point.
Breaking a hash is a prototypical NP problem (ok maybe FNP). SAT is the prototypical NP-hard problem.
I was just trying to explain that using SAT to attack hashes is therefore unsurprising, and does not in any way imply that breaking hashes is NP-complete, the way that it would if the reduction went in the other direction.
Surely the same logic would make sense for another class M, if you had a problem "M-HASH" that's clearly in M, and an M-hard problem "M-SAT" to reduce it to? There might be other problems that you could also reduce to M-SAT, but mentioning that it solves all of M is what's relevant if M-HASH is in M.
Breaking a hash is a prototypical NP problem (ok maybe FNP). SAT is the prototypical NP-hard problem.
I was just trying to explain that using SAT to attack hashes is therefore unsurprising, and does not in any way imply that breaking hashes is NP-complete, the way that it would if the reduction went in the other direction.
Surely the same logic would make sense for another class M, if you had a problem "M-HASH" that's clearly in M, and an M-hard problem "M-SAT" to reduce it to? There might be other problems that you could also reduce to M-SAT, but mentioning that it solves all of M is what's relevant if M-HASH is in M.