Re: SF: Incorrect equations

jstevh_at_msn.com
Date: 04/01/05 

Date: 31 Mar 2005 15:24:45 -0800

stush@rocketmail.com wrote:
> jstevh@msn.com wrote:
> > My take on it is that I have some deep fear that the work is too
> > dangerous and am sabotaging myself
>
> This is maybe a good quote to base my point from.
>
> You're obviously implying that SF is an extremely fast factornig
> method, so fast, in fact, that it might be used to crack encryption
> techniques in use today that bank on the fact that factoring large
> integers is very difficult.
>

I don't know. There are so many questions unanswered about it, which
is part of the reason for fear.

> True or not, there is one thing missing from your work to date on SF,
> and claims such as this (i.e. dangerous) would require, and that is a
> mathematical treatment of its efficiency to factor numbers.
>

I've done a lot of research on Usenet in a brainstorming process where
I toss out ideas basically as I get them, and come back later to
critique, when the ideas are mature.

I declared surrogate factoring mature just recently.

Previous discussions don't give credit to what's here now, as I have a
complete theorem that does possibly indicate how efficiently it should
work.

> That you have presented a factoring method is not at debate, but I
have
> not yet seen a treatment pertaining to the quickness that it can
arrive
> at factors. A new factoring algorithm that is slower (both
practically
> and asymptotically) than existing algorithms in all cases is perhaps
> acedemically interesting, but by no means a breakthrough in any
sense.
>

I'm focusing on theoretical issues now, which is why I'm spending more
time on the surrogate factoring theorem, which I just presented, than
on practical issues, at this time.

> But a new factoring algorithm that is faster (practically or
> asymptotically) than existing algorithms in all or special cases
would
> be at least publish-worthy, if not a breakthrough. However you cannot
> simply claim it is such--similar as to how you cannot present a
theorem
> and simply claim it is true. What is missing from your work on SF is
a
> treatment (e.g. a proof) of the expected and/or theoretical run-time
of
> the algorithm.

The surrogate factoring theorem directly links a rational factor of M^2
to factors of Tj^2, where T = M^2 - j^2, and j is some integer you
select.

It relates a rational factor, so you'd focus on the numerator of that
factor to see if it gives a non-trivial factorization of M^2.

If the implication from the theorem is correct, and you get a rational
factor at random, then it should factor, without regard to the size of
M, approximately 50% of the time for any particular set of factors of
Tj^2.

If that is true, then, for instance, using 4 such pairs would make the
probability of a non-trivial factorization about 92%.

Now there may be some deep mathematical reason not yet seen for why
algorithms that follow closely to the theorem would not factor with
that high of a percent, but I haven't figured any out yet, and I've yet
to test directly, preferring for now, to think about it theoretically.

To my knowledge there is no other known mathematical technique known
that directly links the factors of one number to the factors of
another, though admittedly there are techniques that rely on factoring
numbers different from your target.

So, at this point, even from a "pure math" standpoint, surrogate
factoring is now of interest.

If it has practical application, as in, if it does give factors at
random as I described, then it has already rendered RSA obsolete,
without regard to whether or not that has been accepted.

That is, RSA may be broken at this point, but it's just not known, or
is not widely known, and I don't know it's broken, as I still haven't
tested out the algorithms that follow from the theorem.

I think I'm afraid to test.

James Harris

Relevant Pages

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    ... I see a lot of negative postings about my ideas, ... factoring is getting a lot of bashing, but hey, it's just an idea. ... Basically with the latest surrogate factoring I've been analyzing the ... algorithms, which I'll get to later, require that both j and T be ...
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  • Re: SF: Back to theory
    ... > factoring is getting a lot of bashing, but hey, it's just an idea. ... > Basically with the latest surrogate factoring I've been analyzing the ... > algorithms, which I'll get to later, require that both j and T be ... > One thing that is clear is that the denominator of y for rational y's ...
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