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Topic: SF: Finally, surrogate factoring
Replies: 86   Last Post: Jun 10, 2006 11:51 PM

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 jshsucks@yahoo.com Posts: 471 Registered: 3/26/05
Re: SF: Finally, surrogate factoring
Posted: Jun 5, 2006 9:38 PM

jstevh@msn.com wrote:
> Rick Decker wrote:
> > jstevh@msn.com wrote:
> > > Solving the Factoring Problem
> > >
> > >
> > > Consider a relation between two integer factorizations:
> > >
> > > f_1 f_2 = k + g_1 g_2
> > >
> > > and a solution with four unknowns w, x, y and z, as they are determined
> > > by four linear equations:
> > >
> > > L_1(w,x,y,z) = f_1
> > > L_2(w,x,y,z) = f_2
> > > L_3(w,x,y,z) = g_1
> > > L_4(w,x,y,z) = g_2
> > >
> > > What I have found is that remarkably you can use only two linear
> > > equations and k itself to find
> > > g_1 and g_2, through a process I call surrogate factorization.

> >
> > Indeed you can (subject to the corrections below), but as a
> > factoring algorithm it sucks big time. Remember, to be of
> > any worth whatsoever, a factoring algorithm must not only work,
> > but it must be efficient. Yours is worse than trial division.

> > >
> > > More specifically I use the system of equations
> > >
> > >
> > > (w + x - 2z)(w + 3x + 2y + 2z) = k + (w + x + y + z)(3w + x - y - 3z)
> > >
> > > where
> > >
> > >
> > > k = 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz
> > >
> > > as then I can use
> > >
> > >
> > > w + x - 2z = f_1
> > >
> > > w + 3x + 2y + 2z = f_2
> > >
> > >
> > > to find
> > >
> > > x = (f_2 - f_1 - 2y - 4z)/2, w = (3f_1 - f_2 + 2y + 8z)/2
> > >
> > > and with
> > >
> > > f_1 f_2 = T+k
> > >
> > > where T = (w + x + y + z)(3w + x - y - 3z)
> > >
> > > I have that
> > >
> > > 9(2y + 10z + 5f_1 - f_2)^2 = (18z + 6f_1 - 2f_2)^2 - 18T - 54k +
> > > 45f_2^2 - 99f_1^2
> > >
> > > (But it's a tedious calculation where it's easy to make a mistake.
> > > Note that k, x and w above have been carefully verified and I tried my
> > > best with the calc, but may have gotten it wrong.

> >
> > You did get it wrong. However, the identity
> >
> > (2y + 10z + 5f_1 - f_2)^2 = (4z +3f_1 - f_2)^2 + 4T
> >
> > is correct (not that this is of any use).
> >

>
> So, if I do the calculation carefully, and don't screw up the algebra,
> I just get a dependency on the factoring of T?
>
> That would make sense and would make this idea as useless as the
> previous surrogate factoring ones.
>
> The surrogate factoring idea may just not be feasible at all.
>
> I trust that you were careful as the consequences if you were not,
> well, you usually are.
>
> Thanks! That's a relief.
>
>
> James Harris

Real big shock. You are wrong again James. Do you not see the pattern?

Date Subject Author
6/4/06 JAMES HARRIS
6/5/06 Doug Schwarz
6/5/06 Tim Peters
6/5/06 Doug Schwarz
6/5/06 Christopher J. Henrich
6/5/06 Gib Bogle
6/5/06 Proginoskes
6/5/06 William L. Bahn
6/5/06 JAMES HARRIS
6/5/06 Abstract Dissonance
6/5/06 Abstract Dissonance
6/5/06 Salami Man
6/5/06 William L. Bahn
6/6/06 Brian Quincy Hutchings
6/5/06 guenther.vonKnakspott@gmx.de
6/6/06 Matthijs Hebly
6/6/06 Salami Man
6/5/06 Abstract Dissonance
6/5/06 Gordon Burditt
6/5/06 Sebastian Gottschalk
6/5/06 dkguru
6/5/06 Ed Weir \(ComCast\)
6/5/06 Abstract Dissonance
6/5/06 Andrew Swallow
6/5/06 gjedwards@gmail.com
6/5/06 Salami Man
6/5/06 Gib Bogle
6/6/06 TC
6/6/06 Salami Man
6/5/06 Sebastian Gottschalk
6/5/06 JAMES HARRIS
6/5/06 marc.t.davies@gmail.com
6/5/06 gjedwards@gmail.com
6/5/06 LarryLard
6/5/06 William L. Bahn
6/5/06 Richard Henry
6/5/06 Salami Man
6/5/06 Bob Marlow
6/5/06 Bob Marlow
6/5/06 none
6/5/06 rossum
6/5/06 Rick Decker
6/5/06 JAMES HARRIS
6/5/06 jshsucks@yahoo.com
6/5/06 Salami Man
6/5/06 Tim Peters
6/5/06 JAMES HARRIS
6/5/06 Tim Peters
6/6/06 Rick Decker
6/6/06 Rick Decker
6/6/06 Tim Peters
6/6/06 Rick Decker
6/7/06 David C. Ullrich
6/7/06 Rick Decker
6/7/06 Jesse F. Hughes
6/7/06 Rick Decker
6/8/06 David C. Ullrich
6/7/06 Bertie Reed
6/6/06 JAMES HARRIS
6/6/06 JAMES HARRIS
6/7/06 Rick Decker
6/7/06 Tim Peters
6/7/06 Rick Decker
6/8/06 JAMES HARRIS
6/8/06 Jose Carlos Santos
6/8/06 Rick Decker
6/8/06 LarryLard
6/8/06 David Bernier
6/8/06 Rick Decker
6/9/06 Tim Peters
6/9/06 david250@gmail.com
6/9/06 marcus_b
6/8/06 Richard Henry
6/8/06 jshsucks@yahoo.com
6/8/06 Paul Sperry
6/8/06 LarryLard
6/8/06 Denis Feldmann
6/8/06 David Bernier
6/8/06 David C. Ullrich
6/8/06 David Moran
6/8/06 David Bernier
6/8/06 Tim Peters
6/8/06 Proginoskes
6/10/06 Tim Peters
6/10/06 Tim Peters
6/6/06 gjedwards@gmail.com
6/6/06 Proginoskes