GSoC update - Week III

The past week, I optimized the current stage II, and tried out a new version of stage II ECM. The main way by which we can optimize stage II is by reducing the number of points we compute. My mentor pointed out a very nice way to do so. Unfortunately,…

ECM Stage II

I spend the larger half of last week studying elliptic curves and understanding possible stage II extensions, rather than coding. I got stuck at a lot of places and had to read a lot to understand. Implementing stage II was certainly harder than stage I. More on that a bit…

Implementing the ECM Stage I in FLINT

This week I tried implementing the Elliptic Curve Method of Factorization. I spent most of the time trying to understand how the algorithm works, and going through existing implementations (GMP-ECM and pyECM). After spending quite some time, I decided to stick to the Montgomery elliptic curve coordinates for the stage…

GSoC coding period begins

The official coding period for GSoC begins tomorrow, and I plan to start off with ECM, before beginning with the MPQS implementation. I think it would be better to have both the auxiliary factoring algorithms in hand before I proceed with the MPQS. I spent most of the community bonding…