1. This is silly, but I don't really understand what a singular curve is. Is it where the determinant is zero? If the p-1 method and trial division are included in factorization with singular curves, why do we need to learn specifically about it? It seems like it's not any more efficient than just trying to factor n by itself.
2. I'm amazed that elliptic curves can be used for factorization. It's interesting all of the ways that we can try to factor n, but a lot of them include and even end in the same step, such as finding an inverse mod p using the Euclidean algorithm. If there's not an inverse, then we've found a factor.
No comments:
Post a Comment