Re: Surrogate factoring, update

From: James Harris (jstevh_at_msn.com)
Date: 07/11/04 

Date: 11 Jul 2004 13:25:42 -0700

Matthijs Hebly <heeb@iname.com> wrote in message news:<9B8Ic.114654$3N6.81661@amsnews05.chello.com>...
> James Harris wrote:
> > Matthijs Hebly <heeb@iname.com> wrote in message news:<hXUHc.98963$3N6.21454@amsnews05.chello.com>...
> >>James Harris wrote:
> >>>It's been a while since I mentioned surrogate factoring, and I'll
> >><znib>
> >>Maybe you should put your method to the test? Let your PC make a huge
> <znib>
> > Theoretical work can be VERY trying to many people. They want to see
> > THE RESULT and have most of the details nailed down and have
> > CERTAINTY.
>
> It can be trying to mathematicians too. Was it just a waste of time when
> Naom Elkies found out that:
> 2682440^4 + 15365639^4 + 18796760^4 = 20615673^4 ?
> No, because then people could stop looking for a proof that
> x^4+y^4+z^4=t^4 doesn't have solutions for positive integers x,y,z,t,
> because this idea obviously turned out to be false.

I don't disagree.
 
> Then there's the fact that you're posting in sci.crypt, and not only in
> sci.math. In sci.crypt, people are very much interested in *practical*
> as well as theoretical work. Questions like "How much faster is your
> method", "Can you give us some practical examples", etc., are as
> important here as the theory. It's nice to know a certain new method to
> accomplish something takes a time a factor 10^200 less than an old
> method, but if this new method still takes 10^(10^38374646)) years given
> today's hardware, then it's nice to know but of no practical value to
> cryptography. So I repeat: if there's anything in your method (assuming
> you have one, which I cannot tell), then (at least in sci.crypt) give us
> an example of you factoring a huge composite using your method.
>

I don't know if its practical.

But if it is practical or can be made practical then it probably
affects public key encryption.

It's scary because *theoretically* you can just factor some really big
number like T^2 - 1 and use its factors to then factor T.

> > However, no matter how certain so much knowledge that is tossed about
> > today is today, way back there were people at the beginning who were
> > lost and looking, trying to figure out what was going on.
> They were amazed that e.g. 3^2 + 4^2 = 5^2. People have been playing
> with numbers always. So why don't you want to do this with your method?
> Come on James, give us an example!
>

No matter how many of you are certain that sci.crypt is just about
practical issues as if theory doesn't matter, I think there are others
who think that cryptology cares about theoretical approaches as well
as ones proven by demonstration.

My aim here is to discuss an idea that *might* have huge implications,
and it might just be interesting, or it might not lead to much at all.

> > From small beginnings come human civilization itself.
> Then give us a small beginning of an example. Break RSA a *little*.
> Slightly factor a composite that's just a *little* huge. After that the
> rest of us will tell you whether you'll have reached human cilization or
> not.
>
> > Here and now though, there's this idea I'm tossing around, and it's at
> > the beginnings. Will it be a super idea, a potent idea? I'm not certain,
> > though I definitely think it's worth discussing.
> Break RSA. Then you'll have your discussion I'm sure.
>

If I knew I could definitely break RSA then I wouldn't be discussing
this idea here.

> > Now I know for some of you that's not the answer you want. You want
> > certainty. You want things nailed down and a fully fleshed out
> > product or theory.
> Isn't that why mathematicians are looking for proofs? They e.g. wanted
> certainty too that x^n + y^n = z^n wouldn't have solutions for positive
> integers x,y,z,n with n>2.
>
> > Most ideas don't pass all the tests.
> I guess here in sci.crypt people are interested in practical tests,
> because cryptography has practical as well as theoretical aspects.
>
> Matthijs Hebly.

You may guess all you wish, but you can't speak for everyone.

The practical people can just wait and see or dismiss, while those who
can get pulled in by theory can get involved.

I KNOW that for many of you it can be frustrating to hear about an
idea when you want a product.

But that's basic research. It's why some people can do it, and most
can't.

They can't handle the frustration and uncertainty.

James Harris

Relevant Pages

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