Saturday, October 28, 2006

 

JSH: Factoring relations must hold

So I showed some factoring relations:

x^2 - y^2 = 0 mod T

and

k^2 = 2xk mod T

so

(x+k)^2 = y^2 + 2k^2 + nT

and some may try to disagree with them, so I need to explain how the math sees T, so that you can tell when you're being lied to by corrupt people who have nothing left but to just hope they can fool you.

If you pick T some composite and then pick k and work out x and y, you'll find that if you check with

k^2 - 2xk and x^2 - y^2

you will see what the math has decided T is.

That may be the composite you picked, or it may be a factor of that composite, or it may be 1 or -1.

Those are the possibles.

So yes, the idea can fail in non-trivially factoring T, but only in specific ways, which means some unsavory individual lying to you because, well, cons don't have anything else when they're in too deep, could pick an example where the math picks the full composite or picks 1 or -1 as T, and claim the idea does not work.

I'd guess it factors somewhere around 50% of the time so an unsavory individual could try to find lots of examples to "prove" the idea doesn't work, but ask them to show k^2 - 2xk and x^2 - y^2 to see what T is.

And then consider that there are some truly evil people on this planet who will stop at nothing to get what THEY want, no matter who it hurts, and lying is nothing to them.





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