Wednesday, January 09, 2008
JSH: Not obvious? Simple math test.
It has finally occurred to me that some of you may not understand what I thought was a basic math point, so this post is to check, with a simple math test:
Given a composite T, and z^2 = y^2 + T, if you have a prime p nad z mod p, for a non-trivial factorization of T, where p>sqrt(T), can you then directly factor T?
My guess is that some of you do not realize that the answer is: yes.
Because if the answer is yes, I have equations that GIVE you z mod p.
Of course, some of you may realize that and just assume that finding z mod p is difficult if the composite T is large, but if you look at the equations, it's not.
So if you assume that still, or rely on it, then you are just going with belief, and the mathematics trumps your belief.
If you know all those things already, and STILL are sitting back, then you are relying on politics and supposing that somehow, someway powerful people out there will protect against this new knowledge, and you are willing to try and forget it…
Given a composite T, and z^2 = y^2 + T, if you have a prime p nad z mod p, for a non-trivial factorization of T, where p>sqrt(T), can you then directly factor T?
My guess is that some of you do not realize that the answer is: yes.
Because if the answer is yes, I have equations that GIVE you z mod p.
Of course, some of you may realize that and just assume that finding z mod p is difficult if the composite T is large, but if you look at the equations, it's not.
So if you assume that still, or rely on it, then you are just going with belief, and the mathematics trumps your belief.
If you know all those things already, and STILL are sitting back, then you are relying on politics and supposing that somehow, someway powerful people out there will protect against this new knowledge, and you are willing to try and forget it…
# posted by James Harris @ 11:38 
