### Wednesday, May 04, 2005

## JSH: SFT is not easy

Well actually verifying the SFT equations myself was very useful in multiple ways.

For one thing, it revealed the role of experimentation, and convinced me that the theorem itself is just a step along the path to a practical factoring method.

That is good and it probably means that it's not trivial to figure out all the in's and out's to getting it to work, but there are simple reasons why it must be possible to find a way to get it to work.

In trying to explain before I ran into a flurry of hostile and disparaging postings from people who were making it their business to try and distract from the actual issues.

Now that I realize that it takes some time to figure out how to get from the SFT to a practical factoring algorithm, I realize just how dangerous those people are.

It is quite reasonable that there has been a delay up until now, and it's possible that there will be an indefinite delay while the mechanics of using the SFT are figured out.

So, why do I know it must work?

Well, given

ab = M

where 'a' and 'b' are rationals, and M is an integer with, say, two prime factors, the number of factors that will give a non-trivial factorization is infinite, as is the number of factors that will give a trivial factorization.

For some odd reason, posters have gotten away with arguing a relative size difference between these twin infinities, to push the argument that as M gets larger and its prime factors get larger, you have a lower probability of getting 'a' and 'b' such that M is non-trivially factored.

That makes no sense though, as in even a small range, like from 1/2 to 1 in rationals, you have an infinity of solutions to 'a' that would non-trivially factor M, without regard to the size of M.

That's important. So, say, if M is the largest public key known, there are an *infinite* number of rationals in the range from 1/2 to 1 that will factor M non-trivially.

There are an infinite number that will trivially factor it as well.

The reality is that the SFT allows you to do what has never been possible before, which is, if you wished, check in the range from 1/2 to 1, to get one of your factors of the surrogate, and see what happens.

You can experiment.

That means that the people who check may figure out what the people who do not, can't.

And someone might just get lucky and stumble across something.

It's already clear that using integer factors of the surrogate doesn't work well--so easiest is out--and I'll probably research that area as I'm curious.

But who knows when I'll move on to fractions.

I kind of like you people. You're so...calm...and as you're calm, things can progress slowly, which I think may just save us all.

Eventually, yeah, I think that RSA is toast, but it might take a few months, as the research progresses.

It's about time and mental effort, and luck, at this point.

And everybody has a chance.

For one thing, it revealed the role of experimentation, and convinced me that the theorem itself is just a step along the path to a practical factoring method.

That is good and it probably means that it's not trivial to figure out all the in's and out's to getting it to work, but there are simple reasons why it must be possible to find a way to get it to work.

In trying to explain before I ran into a flurry of hostile and disparaging postings from people who were making it their business to try and distract from the actual issues.

Now that I realize that it takes some time to figure out how to get from the SFT to a practical factoring algorithm, I realize just how dangerous those people are.

It is quite reasonable that there has been a delay up until now, and it's possible that there will be an indefinite delay while the mechanics of using the SFT are figured out.

So, why do I know it must work?

Well, given

ab = M

where 'a' and 'b' are rationals, and M is an integer with, say, two prime factors, the number of factors that will give a non-trivial factorization is infinite, as is the number of factors that will give a trivial factorization.

For some odd reason, posters have gotten away with arguing a relative size difference between these twin infinities, to push the argument that as M gets larger and its prime factors get larger, you have a lower probability of getting 'a' and 'b' such that M is non-trivially factored.

That makes no sense though, as in even a small range, like from 1/2 to 1 in rationals, you have an infinity of solutions to 'a' that would non-trivially factor M, without regard to the size of M.

That's important. So, say, if M is the largest public key known, there are an *infinite* number of rationals in the range from 1/2 to 1 that will factor M non-trivially.

There are an infinite number that will trivially factor it as well.

The reality is that the SFT allows you to do what has never been possible before, which is, if you wished, check in the range from 1/2 to 1, to get one of your factors of the surrogate, and see what happens.

You can experiment.

That means that the people who check may figure out what the people who do not, can't.

And someone might just get lucky and stumble across something.

It's already clear that using integer factors of the surrogate doesn't work well--so easiest is out--and I'll probably research that area as I'm curious.

But who knows when I'll move on to fractions.

I kind of like you people. You're so...calm...and as you're calm, things can progress slowly, which I think may just save us all.

Eventually, yeah, I think that RSA is toast, but it might take a few months, as the research progresses.

It's about time and mental effort, and luck, at this point.

And everybody has a chance.