On 5/22/12 9:41 PM, Faramir wrote:
> [F]actoring your public key to obtain a working copy of your secret
> key is certainly something that may be done before the end of time,
> and won't require dyson spheres to power the machine.

I'm not so optimistic.  Factoring is a hard problem.  We may never
develop the technology to factor extremely large composites.  Doing so
would require either (a) the development of extremely large-scale
quantum computing, (b) a mathematical proof of P=NP, or (c) classical
computers that run close to the thermodynamic limits of the universe.
There are no guarantees we will ever develop any of those three
technologies.

That said, no one has ever proven that the only way to break RSA is to
factor large composites.  That's wholly conjecture, and there's some
evidence that it's not true.


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