Re: Basically a sieve method, relation to quantum

jstevh_at_msn.com
Date: 01/22/05 

Date: 22 Jan 2005 08:35:31 -0800

Jesse F. Hughes wrote:
> jstevh@msn.com writes:
>
> > The original algorithm in my program, will, my current analysis
shows,
> > factor about 50% of the time, which is astounding.
> >
> > I get a sense that some of you don't get it, so let's say you take
some
> > RSA challenge number, and calculate j and T, and factor them, and
then
> > run them through the algorithm.
> >
> > My research indicates you have a 50% chance of factoring the
number.
>
> Funny. A few minutes later, you said, "So, if it fails to find
> factors 50% of the time, when it recurses with large numbers, it will
> rapidly do worse."
>
> But here you seem to say that the 50% rate holds for RSA-size
numbers.
>
> Does the success rate decrease as the size of the factors increases?
> Does it decrease dramatically?
>

You're not paying attention or you're not very bright.

The algorithm depends on factoring T, the surrogate.

I need a factorization of a number that can be fairly large in and of
itself.

In fact, T is about the size of M^2.

My program gets T by calling itself.

It is HEAVILY recursive.

It calls itself to factor T, so if it factors approximately 50% of the
time, you do the math.

Actually, I think now the algorithm factors at a much higher rate,
which is how the program is as successful as it is!

I know, for some of you the idea of recursion is too subtle, and you
can't quite understand how a factoring program that needs a
factorization to work, can actually work by calling itself!!!

In any event, you can do it a different way, by using some other means
to factor T, and my research indicates that it will factor at least 50%
of the time if you do that, while my heavily recursive program will
fall off in effective factoring at very dinky numbers.
Understand now?

James Harris

Relevant Pages

  • beta version of Victor Shoups book, "A Computational Introduction to Number Theory and Algebra&
    ... Computing with Large Integers ... The Basic Euclidean Algorithm ... Factoring and Computing Euler's phi-Function are Equivalent ... The Existence of Finite Fields ...
    (sci.crypt)
  • Re: Ultimate check, new way to factor or not?
    ... It's commonly known as a the "factoring sieve" and Fermat showed that ... It is listed as "algorithm ... "factoring with sieves" on pp.389. ... > when it defies the mathematics. ...
    (sci.crypt)
  • Re: I was right, surrogate factoring proof
    ... primes divide n -- at most I'll have to look through sqrt/ ... But don't forget that's included in the cost of the algorithm! ... if surrogate factoring ever becomes ... two values are congruent modulo p, and hopefully not congruent modulo n/p. ...
    (sci.math)
  • Re: I was right, surrogate factoring proof
    ... primes divide n -- at most I'll have to look through sqrt/ ... But don't forget that's included in the cost of the algorithm! ... if surrogate factoring ever becomes ... two values are congruent modulo p, and hopefully not congruent modulo n/p. ...
    (sci.crypt)
  • Re: More math stuff, truth and social reality
    ... > out that I use brainstorming, where you generate lots of ideas during ... fast as other efficient factoring algorithms. ... I don't see evidence of lying, ... algorithm) is in fact the truth. ...
    (sci.math)
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