Room 217

Factoring Integers With Elliptic Curves.

Sumit Giri.

IMSc

Under a reasonable conjecture concerning the density of smooth
numbers, the Elliptic Curve method determines with positive probability a
factor of a given composite integer $n$ in time $K(p)$. Where:
$p$ is the least prime factor of $n$ and K:$R^+ ----> R^+$ is given by
K(x)=exp[sqrt{2+o(1)}log(x)loglog(x)] for x----> infinity.