Reduction of Natural to Elliptic

Is there a proof stating that taking Discrete Logs on Elliptic Curves is at least as hard as on Natural Numbers GF(p)? If so, we can switch over from 1024-bit regular cryptosystems to 1024-bit ECC cryptosystems (almost definitely overkill) with little Fear, Uncertainty, or Doubt.

Yes, there is a performance penalty, but computers are getting faster all the time.