James Harris still at it

jshsucks_at_yahoo.com
Date: 05/16/05 

Date: 16 May 2005 12:00:50 -0700

The simplest way to think of the surrogate factoring theorem (SFT) is
as a generalized method for solving

x^2 = y^2 mod N

where N is the number to be factored.

So then, how can there be such quiet over my research?

Well, I think there are several factors, and I'll guess at them.

First off, if you actually try the SFT, it's quite natural to start by
using integer factors of the surrogate.

That's a natural thing to do, and I did it myself when I finally
decided to test out the equations, as I mentioned in a previous thread,
and I found that as the target to be factored got bigger, the
probability of factoring quickly dropped.

That can give the illusion of a comfort zone as it fits into what many
would like to believe which is that the SFT is not a viable path to a
practical factoring algorithm, despite being a general solution to a
difference of squares.

So I think that the natural human inclination to use integers, along
with the behavior of the SFT with integers, and the need to feel secure
about what otherwise might be a scary possibility, leads people who are
usually very intelligent about mathematics to leap to a desired
conclusion, which is that the method is just a curiosity.

However, my work on May 13th shows that it is not.

There I step through a simple argument which also indicates why
integers might not work well as you target bigger numbers as there I
introduce a number I call k, and using integers is like using k=1, when
I show that there is a range to be discovered by looking at the first
differential of a key function, set to 0.

So the naive approach of just picking certain
rationals--integers--seeing a drop in factoring percentage as the
target gets larger can lead to a false belief that the SFT is not worth
consideration.

I think the real surprise, given the ease with which I can prove that
the SFT is important, and given that the difference of squares has
NEVER been solved in this way before, is that mathematicians and
cryptographers have been so calm.

I know I haven't been contacted by anyone about my work, and my own
attempts at contact have for the most part failed, though a major math
journal did last week acknowledge receipt of a paper I wrote on the
surrogate factoring theorem, so maybe something may happen now.

But still, given the rapidity with which information travels in this
day and age, the importance of the factoring problem, and the various
proofs that show not only that it must cover the full domain of
solutions, but also the latest research pointing the way to focusing on
non-trivial solutions, the lack of much of a response from the
mathematics community at this time is a massive puzzle.

Today I saw the beginning of the movie "Superman" on television, and it
gives a clue to my current situation as in that beginning Jor'el tries
to convince a complacent counsel that the planet Krypton is about to
explode, and is forced down, and told not to talk about his research
results.

People need to feel safe and secure, and that need can cause people in
charge to say, "peace and security", whether it's there or not, and
against mathematical truth.

The reality is that mathematical proof is not enough for most
people--even mathematicians and cryptographers.

Being logical in that way is foreign to most human beings.

James Harris

Relevant Pages

  • SF: World politics and mathematicians
    ... So, I can explain that the SFT maps hyperbolas, so it's not ... which shows how you connect hyperbolas. ... In the social world, it's a factoring theorem. ... If you believe in mathematics, ...
    (sci.crypt)
  • Re: SF: World politics and mathematicians
    ... > factorization from the start the SFT gives you. ... which shows how you connect hyperbolas. ... it's a factoring theorem. ... then you don't believe in mathematics so you'll wait. ...
    (sci.crypt)
  • SF: Symmetry, practical matters, social realities
    ... The surrogate factoring theorem is mathematics at its most beautiful, ... Abstracted Surrogate Factoring Theorem: ... What the SFT is, is a connection betwee factorizations that covers the ... As we speak, if the idea has been exploited, and if Internet security ...
    (sci.crypt)
  • Factoring problem and the SFT
    ... with all non-zero integer, where x/y is determined by the rational ... That gives you what the SFT does in a nutshell. ... but emotion does not change mathematics. ... For the factoring problem A would be some number you wished to factor, ...
    (sci.crypt)
  • Re: JSH: Brainstorming over, for now
    ... Nora Baron wrote: ... I've finished brainstorming on the SFT and how to best present ... >> My fears about working on the factoring problem go back for YEARS ... >> There are other methods that rely on difference of squares, ...
    (sci.crypt)
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