Re: SF: Back to theory

jstevh_at_msn.com
Date: 02/26/05 

Date: 26 Feb 2005 05:55:21 -0800

Tim Peters wrote:
> [Nora Baron, to JSH]

<deleted>

Oh, one note, I don't read "Nora Baron" posts carefully, as I see the
poster as a serial liar.

But I guess others do, which may be a good thing in at least this case.

>
> > What's the point?
> >
> > The point is, I have modified and greatly simplified your
> > central idea - and at the same time, greatly generalized it -
> > and on these two simple little examples - the only ones
> > I have tried - it works. It might work on lots of other
> > examples. If it doesn't, I can try changing the function
> > that defines X. I can add parameters, like your A, y, and z.
> > Your central theme, surrogate factoring of the number
> > T = M - j, is still there, and it might even explain why
> > it works (if it does).
>
> Not to mention that Baron-Harris probably always finds a factor, and
> seemingly needs fewer gcds than poke-and-hope.

If true that would be of interest.

> > After all, the factors of M ought to be related somehow to the
factors
> > of T.
>
> There doesn't currently seem to be a good reason to believe that's
the case,
> right? For example, if you could deduce the factors of M from those
of M-j
> or M+j efficiently, you could pick up a pile of RSA challenge checks
> tomorrow. Here's a start: if you know all the primes dividing N-1
or N+1,
> you don't have to bother checking whether they divide N <wink -- but
all the
> results I've read about this are as trivial and unexploitable as that
one>.
>
> > In the case of RSA numbers, in general you expect T to be easier
> > to factor than M.
>
> Yup. The other half is that if M _could_ be factored from a
factorization
> of T efficiently, it's more than a little puzzling that nobody yet
has found
> a way to do that. Well, maybe tomorrow's Baron-Harris-Decker-Filho
method
> will finally crack that nut.

Yes, and that goes back to the concept.

Someone picks two primes that are very large, if that's better for
those upset with my saying special primes, and someone else just comes
along, and gets another number, which though large has more than two
prime factors, though not much more than two, as the combinations can
run out of control, and they factor it anyway.

It's a simple idea that if it can be made workable puts a wrench into
the RSA machinery, totally blocking them from escaping it, as what can
they do?

They can just pick bigger and bigger primes, which can be broken up
into big numbers with smaller primes!!!

Now if mathematicians were honest, good folk, who are sensible, as some
of you seem to think they are, then there'd be talk about this beyond
Usenet in terms of checking to see if it's a real threat, and informing
people who are making decisions, like investment decisions based on old
knowledge.

But I don't think they will.

I think that mathematicians as a group are fairly stupid, and they will
wait, and hope, as if by *wishing* they can keep a technique from being
valid.

Why?

They don't like me. So they don't want me to get credit for having
good mathematical ideas.

Oh, and I think a lot of that is just not liking amateur
mathematicians.

Don't believe me.

Just sit back, and watch.

If surrogate factoring gets quietly developed, and NO ONE pays real
attention until the Internet is just overran, till it's so obvious that
security is compromised that top mathematicians being consulted who
continue to claim that everything is ok are no longer believed, when
hackers start buying Rolls Royces with money that can't be proven to
not be theirs, and banks quietly empty from "valid" transactions which
the account holders heatedly claim are invalid, then you'll know.

I think that's what's going to happen too.

James Harris

Relevant Pages

  • Re: SF: Back to theory
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