3 ms·
It depends. If it turns out that every NP problem has an O(n^1000) solution, but no better, then P = NP but it won't matter much in practice. On the other hand,
by lacker 14y ago
It depends. If it turns out that every NP problem has an O(n^1000) solution, but no better, then P = NP but it won't matter much in practice. On the other hand, if every NP problem has an O(n) solution, then the entire field cryptography will be thrown into disarray. Not just Bitcoin but SSL and secure hashing will be in trouble.
If I were you, I wouldn't worry about the "P = NP" case. It is much more likely than an application-specific attack is found.