> And the implications for security would be huge because we would have to redefine what we mean by provable security, and then have to make some other arbitrar

> And the implications for security would be huge because we would have to redefine what we mean by provable security, and then have to make some other arbitrary distinction. Is n^100 secure, but n^99 not? That doesn't sound right. After all, there's already an arbitrarily smooth continuum between polynomial-time and exponential-time algorithms. See quasipolymomial or sub-exponential algorithms.