I'll follow the people who have actually done work in cryptography. I'm neither under the impression that Wiles himself (or Fermat, if we could resuscitate him!) would have much to say about cryptography, nor do I believe that you have a "simple" proof of FLT.
But in any case you missed the substantial point of my comment: whether or not FLT is true (and no matter how short the proof is) is completely irrelevant to modern cryptography, which relies on entirely different problems (e.g. factoring or discrete logarithms).