## JSH: Surrogate factoring already achieved perfection

The success rate for what I call surrogate factoring already achieved perfection as in 100% factoring months ago, back in March. What happened then is that posters claimed it was too slow to be useful.

And I wandered off from the subject as I ended up mostly facing taunts that I should factor a very large number which I won't do.

Instead now in looking back over the research I'm focusing on solving quadratic residues mod N, which involves using a result which follows from the other research where instead of using surrogate factoring to find the target T, you use factoring T to solve for what I call k, which gives you a quadratic residue solution as

k^2 = (T/2) mod p

in the original surrogate factoring equations, and I've generalized to k^2 = (T/2) mod N, which they allow.

The underlying mathematics is complex enough, while mostly simple algebra that I simply stay away from it in giving the latest methods, and I've just stayed very far away from talking about surrogate factoring itself, until this post.

It is my most controversial baby. My most conflicted research in terms of how I view it.

And possibly the most misunderstood of my findings.

A completely new way to factor that is too controversial for me to get much traction with it.