ECM | Lenstra elliptic curve method

The elliptic curve factorization method, abbreviated ECM and sometimes also called the Lenstra elliptic curve method, is a factorization algorithm that computes a large multiple of a point on a random elliptic curve modulo the number to be factored N. It tends to be faster than the Pollard ρ factorization and Pollard p - 1 factorization methods. Zimmermann maintains a table of the largest factors found using the ECM. As of Jan. 2009, the largest prime factor found using the ECM had 67 decimal digits. This factor of 10^381 + 1 was found by B. Dodson on Aug. 24, 2006 (Zimmermann).

Atkin-Goldwasser-Kilian-Morain certificate | elliptic curve primality proving | elliptic pseudoprime | prime factorization | prime factorization algorithms