Re: Critiquing surrogate factoring

jstevh_at_msn.com
Date: 03/31/05 

Date: 30 Mar 2005 18:22:29 -0800

Pubkeybreaker wrote:
> I have, by and large, stayed out of all of these discussions.
> However, I must
> point out that the idea of "surrogate factoring" is a valid
technique.
> However,
> it is not new, and for James to claim it as his own is disingenuous.
> All he has done is
> to supply the label "surrogate factoring".
>
> The continued fraction algorithm, QS, and NFS all work via
> "surrogate factoring".
> Instead of factoring N directly, we factor (or attempt to factor)
> MANY smaller
> numbers that are algebraically related to N. Most of these numbers
are
> not successfully factored. These get thrown away. We then take
those
> that ARE successfully factored and combine them using large scale
> linear algebra to then factor
> N.
>

Ok, I went and checked to finally see how they work, and I can see what
you mean about using other factorizations.

But look over the theorem I presented to open this thread, as there is
no guessing, no sieving, no throwing away, but instead a direct link
between the factorization of one number and the rational factor of your
target number.

No guessing. No sieving. No throwing away.

Now that theorem is a good starting point, and at least one
poster--probably trolling but hey I'm still going with it--claimed it's
not a theorem.

That might be a good place to start, as I feel I can answer issues
brought up against the surrogate factoring theorem's status as a
theorem.

And then move on from there with the critique.

James Harris