Re: unprovability of the security of computational cryptography
From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 10/12/03
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Date: 12 Oct 2003 23:05:25 +0300
Mack <macckone@a_nospamjunk123_ol.com> writes:
> On 11 Oct 2003 19:06:55 +0300, Phil Carmody
> <thefatphil_demunged@yahoo.co.uk> wrote:
>
> >Bryan Olson <fakeaddress@nowhere.org> writes:
> >> D. J. Bernstein wrote:
> >...
> >> > (i) Factoring 512-bit numbers will be infeasible for the next ten
> >> > years.
> >...
> >> The 'evidence' for the first is a curve of the size of numbers
> >> really smart people have figured out how to factor, plotted
> >> against time, and extrapolated. It's more than a little sketchy
> >> now, and if a P=NP bombshell drops, that extrapolation becomes a
> >> joke.
> >
> >Why?
> >
> >Phil
>
> Would not a proof that P=NP involve showing that at least one
> NP complete problem can be definitively solved in P?
>
> From what I remember an algorithm for solving one problem can
> be used to solve other problems. The conversion may not be
> simple but it would change the way we look at factoring.
Would it necessarily change the way we look at factoring
512 bit numbers? That was the problem in hand.
For example, let's say I had a Theta(digits^100)-time
Theta(digits^50)-space (with constants ~1) deterministic
factoring algorithm. What are you going to do with it. What
_concretely_ will have changed. Would you use my method or
would you stick to solutions like NFSNet, or Twinkle-alikes.
> Proving that a polynomial time factoring method exists would
> probably lead directly to such a method.
I think you're missing the point.
Phil
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