Re: I was right, surrogate factoring proof
jstevh_at_msn.com
Date: 02/14/05
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Date: 13 Feb 2005 18:25:50 -0800
Bruce Stephens wrote:
> jstevh@msn.com writes:
>
> [...]
>
> > It does matter. If M is odd, j *has* to be odd.
> >
> > And I did put in my instructions that information.
>
> You did, you even gave a specific choice of j.
>
> > You didn't follow the algorithm.
>
> True, but it's necessary to factorise T and j, so that puts practical
> constraints on j. Presumably it'll be possible to find a way to get
> an odd j, but I don't think it's clear that that will help.
>
> Anyway, I tried on two examples, one with M=47*101, j=2373, and that
> worked. M=1237*37463, j=23170865 didn't, but j=23170864 did.
>
> So that strongly suggests that the choice of j isn't as arbitrary as
> you're making out.
That could be true, but right now I don't see a mathematical reason for
it from the theory.
I think your finding an even j that worked is just random, as the
theory *does* indicate that M and j need to both be odd or both be
even.
> (I didn't carefully choose the counterexample: I just used the first
> prime after 1234, and the first prime after a number I got from
typing
> a few random digits. j is as your algorithm specified.)
Now I feel like I mapped out a mathematical proof, but if it doesn't
work, then either I screwed up, or implementations are screwed up, or
the algorithm I gave is flawed.
I prefer to concentrate on the mathematical proof as it is the
absolute, and is also easy to check.
>>From what I have so far, the argument is a proof, so it is perfect.
Problems must lie elsewhere, or I am wrong. If am wrong, then more
than experiment will prove me wrong, as the argument I gave must be
flawed.
> [...]
>
> > Well, if you'd followed my instructions, by now you might be
emailing
> > RSA.
> >
> > Unless you made some other mistake as well.
>
> You can see the PARI implementation, pari is freely downloadable,
> complete with tutorial, user guide, reference card. Why not compare
> the implementation with your idea of the algorithm, and see if they
> differ? It looks good to me, for what it's worth (I don't know pari,
> but I looked up what "fordiv" did, and that made everything clear).
I can program it in Java, easily.
Actually, I did try some of this a while back in Java, though I kind of
hacked at it.
I think of this approach where T and j have to be factored as
inelegant.
There's a more complete theory but it's *more* complicated.
No point in even considering it while the basic one from what I'm being
told doesn't work.
Maybe it is time for me to program it myself to be sure, but I'd prefer
to trust you guys, and find some flaw in my reasoning.
If I exhaust all possible areas for flaws, then I may look more closely
at experimenting again myself.
But, if the idea doesn't work, I'd prefer to figure that out
theoretically.
James Harris
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