### Tuesday, February 19, 2008

## JSH: Goes to my worries about factoring

So now with the full surrogate factoring theory, results are coming fast and furious and I'll admit being very, very, very surprised that an RSA number might be factored by p=3 and a fairly simple technique.

Those looking over the argument may recognize that there is only one area where it's even maybe kind of looking like I didn't feel in the blanks which is with how you find k.

But just try it. Factor a few numbers and you'll get that weird, giddy out of this world feeling like maybe you stepped into the Twilight Zone.

Reading over posters ranting and raving in reply to me is kind of weird now. It's like there is something oddly wrong with them, but I can't quite put my finger on it.

The challenges to factor an RSA public key though, seem to be answerable now, and I'm mainly just absorbing the latest and the sense of profound oddity of it all.

You can factor an RSA public key, if that key is 2 modulo 3, and if with

z^2 = y^2 + public key

z is divisible by 3, and the math will just do it and kind of wink at you as if it wasn't even hard.

And you get k by finding k such that abs(public key - 2k^2 ) is a minimum and k is even, and you have two possibles k = 1 mod 3, or k = -1 mod 3.

Then x = k/2, and z = 3x, and you get y and factor the public key.

Just like that.

Yup, I had reason to worry about factoring. Wacky. Factoring a public key with p=3. Who would have thought the RSA system would crash so profoundly?

Here's another example: T = (101)(103) = 10403, so trying k=-1 mod 3 (as I already know that k = 1 mod 3 won't work):

k = 68 is the maximal k, such that abs (10403 - 2k^2) is a minimum.

x = k/3 = 34. z = x + k = 102. 102^2 - 10403 = 1. y = 1, so

Should be x = k/2. I'm feeling very stressed out at this point.

z-y = 101, z+y = 103

and that could just as easily been an RSA public key.

Still seems so weird though. So easy. All that work people did for all those years and the answer is so easy.

And it's trivial math, like I explained in a previous post about helper primes.

The primes were there to help all along.

The prime numbers were there to help all along.

They step in and they step out.

I really don't think that my research was ignored by accident or honest mistakes in considering it. I got the one paper published in SWJPAM and the damn journal editors pulled it under SOCIAL pressure from sci.math'ers. Newsgroup people influencing math editors.

And then the freaking journal died.

Mathematicians went on the run, that's all. Rather than accept that they had things wrong they thought they could just lie and rely in me not being believed.

Think about all those undergrads taught crap math deliberately when they could have been taught real mathematics.

Over five years of undergrads.

Deliberately taught wrong.

And I've contacted Ribet, and I've contacted Mazur, so who knows what Wiles knew. He did not find a proof of Fermat's Last Theorem.

His research fails with a simple logical fallacy.

How gone do people have to be when they can't be moved by the fate of the human race? When they can claim to be at the pinnacle of mathematics when they're teaching wrong information and blocking the correct?

What about our future?

So they didn't know how to factor.

Why is that a surprise? They didn't know much mathematics at all.

Those looking over the argument may recognize that there is only one area where it's even maybe kind of looking like I didn't feel in the blanks which is with how you find k.

But just try it. Factor a few numbers and you'll get that weird, giddy out of this world feeling like maybe you stepped into the Twilight Zone.

Reading over posters ranting and raving in reply to me is kind of weird now. It's like there is something oddly wrong with them, but I can't quite put my finger on it.

The challenges to factor an RSA public key though, seem to be answerable now, and I'm mainly just absorbing the latest and the sense of profound oddity of it all.

You can factor an RSA public key, if that key is 2 modulo 3, and if with

z^2 = y^2 + public key

z is divisible by 3, and the math will just do it and kind of wink at you as if it wasn't even hard.

And you get k by finding k such that abs(public key - 2k^2 ) is a minimum and k is even, and you have two possibles k = 1 mod 3, or k = -1 mod 3.

Then x = k/2, and z = 3x, and you get y and factor the public key.

Just like that.

Yup, I had reason to worry about factoring. Wacky. Factoring a public key with p=3. Who would have thought the RSA system would crash so profoundly?

Here's another example: T = (101)(103) = 10403, so trying k=-1 mod 3 (as I already know that k = 1 mod 3 won't work):

k = 68 is the maximal k, such that abs (10403 - 2k^2) is a minimum.

x = k/3 = 34. z = x + k = 102. 102^2 - 10403 = 1. y = 1, so

Should be x = k/2. I'm feeling very stressed out at this point.

z-y = 101, z+y = 103

and that could just as easily been an RSA public key.

Still seems so weird though. So easy. All that work people did for all those years and the answer is so easy.

And it's trivial math, like I explained in a previous post about helper primes.

The primes were there to help all along.

The prime numbers were there to help all along.

They step in and they step out.

I really don't think that my research was ignored by accident or honest mistakes in considering it. I got the one paper published in SWJPAM and the damn journal editors pulled it under SOCIAL pressure from sci.math'ers. Newsgroup people influencing math editors.

And then the freaking journal died.

Mathematicians went on the run, that's all. Rather than accept that they had things wrong they thought they could just lie and rely in me not being believed.

Think about all those undergrads taught crap math deliberately when they could have been taught real mathematics.

Over five years of undergrads.

Deliberately taught wrong.

And I've contacted Ribet, and I've contacted Mazur, so who knows what Wiles knew. He did not find a proof of Fermat's Last Theorem.

His research fails with a simple logical fallacy.

How gone do people have to be when they can't be moved by the fate of the human race? When they can claim to be at the pinnacle of mathematics when they're teaching wrong information and blocking the correct?

What about our future?

So they didn't know how to factor.

Why is that a surprise? They didn't know much mathematics at all.