20 years of ECM
Résumé
The Elliptic Curve Method for integer factorization (ECM) was invented by H. W. Lenstra, Jr., in 1985 . In the past 20 years, many improvements of ECM were proposed on the mathematical, algorithmic, and implementation sides. This paper summarizes the current state-of-the-art, as implemented in the GMP-ECM software.