Lenstra elliptic curve factorization [SEP] named after
Lenstra elliptic-curve factorization
The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose factoring, ECM is the third-fastest known factoring method. The second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra.
Practically speaking, ECM is considered a special
number theory. Lenstra is well known for co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm in 1982 and for discovering the elliptic curve factorization method in 1987. In 1992, he computed all solutions to the inverse Fermat equation. The Cohen–Lenstra heuristics is a set of precise conjectures about the structure of class groups of quadratic fields that are partially named after him.
Three of his brothers, Arjen Lenstra, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is