Lenstra Elliptic-Curve Factorization Algorithm

The Lenstra elliptic-curve factorization method, named after Hendrik Lenstra, is a fast, sub exponential running time algorithm for integer factorization that employs elliptic curves. For general purpose factoring it ranks as the third fastest known method, after the general number field sieve and the multiple polynomial quadratic sieve, and it is considered a special purpose algorithm most suitable for finding small factors, remaining the best approach for divisors of roughly 50 to 60 digits since its running time depends on the size of the smallest prime factor rather than on the size of the number being factored as a whole.